# Appraising healthcare ventilation design from combined infection control and energy perspectives.

This article considers an approach for assessing the balance
between energy use and infection control in hospital ward ventilation by
combining a stochastic disease outbreak model with a cost evaluation.
Disease dynamics are simulated using a
susceptible-exposed-injector-removed infection modeling approach, with
the contact rate due to airborne transmission incorporated through
coupling with the Wells-Riley model. Results presented for a
hypothetical ward scenario demonstrate that stochastic effects in a
small population, such as a hospital, are a controlling factor in the
risk of an outbreak and that conventional deterministic models may give
misleading results. Cost appraisals clearly show that the trade-off
between ventilation provision and infection risk depends on many
factors, including disease characteristics, the people concerned,
ventilation system design, and the rate and costs of both providing
ventilation and treating infections. Although limitations in the input
data currently reduce the robustness of the outputs, the approach is
shown to be a useful framework for a tool that can quantitatively assess
ventilation design from different perspectives for healthcare
environments. This article also highlights some of the knowledge
required from further research to enable better quantification of the
behavior of pathogens and the transmission processes for hospital
infections.

Introduction

The choice of ventilation system for hospital environments is influenced by many factors. High-risk environments, such as isolation rooms, operating theaters, and pharmaceutical areas, are generally dominated by infection concerns, with this driving the ventilation agenda. For example, airborne infection isolation rooms, and the provision of a high airflow rate to ensure dilution of pathogens within the room and an appropriate pressure regime to limit transfer of pathogens between the room and neighboring spaces that are delivered by a mechanical means, tend to be the ventilation system of choice (Booth et al. 2009). Depending on the application and level of risk, fine particle filtration or other air disinfection techniques may be employed on the supply and/or extract air (Department of Health 2007; Jensen et al. 2005). Ventilation is also driven by the infection control agenda in operating theater environments, with the complexity of the system increasing with risk. At the highest end, ultra-clean ventilation theaters for high-risk surgery, such as orthopedics, have downflow air movement of up to 0.6 m/s (1.97 ft/s) in the central zone (Friberg et al. 2002), with room airflow circulated through ceiling-mounted high-efficiency particulate (HEPA) filters to provide a constant velocity downflow region over the operating area (Chow and Yang 2004). While such factors as energy use and plant size will be considered during design, they are generally not the primary drivers in the specification of these specialized ventilation systems. In both of these cases, airflow rates, pressure differentials, and levels of air cleaning generally increase with the likely risk in the environment. Clearly, this will substantially increase costs but, on the whole, is easily justified by the better clinical outcomes for the patients. For example, the ventilation costs for an immune-compromised transplant patient who requires positive pressure isolation with a HEPA-filtered supply after surgery are likely to be minor compared to the clinical costs of carrying out a transplant.

However, in most patient environments, such as wards, waiting areas, outpatient clinics, and treatment rooms, the most appropriate ventilation design is not so clear cut. In this case, the thermal comfort of patients and the energy performance of the system are seen as equal, if not more important, concerns than the transmission of infection. Balancing these demands is typically tackled by a broad guidance approach, using generic ventilation rates and comfort temperatures set out in national documents (Department of Health 2007) and the choice of mechanical or natural ventilation determined by local conditions, other elements of the building design, and the expertise of those designing the system. The resulting ventilation, while probably adequate, will generally have no formal evaluation that considers the balance between infection control, comfort, and energy. As ventilation for infection control is associated with airborne transmission, this, on the whole, takes a back seat, as most infections in general patient environments are regarded as being contact borne. However, there is increasing evidence that the transport of pathogens through the air is linked to many common healthcare-acquired infections (HCAI's) that are not regarded as airborne infections.

In recent years, several studies have linked Methicillin-resistant Staphylococcus aureus (MRSA) with airborne transmission, both through the analysis of outbreaks (Farrington et al. 1990; Kumari et al. 1998) and through the sampling of air and surfaces in the environment (Noble 1962; Hathway et al. 2008). Many such studies indicate the role of general nursing activities, such as bed-making (Roberts et al. 2006; Hathway et al. 2008), on the dispersion of the bacteria in the environment, leading to environmental contamination and increased risk of subsequent infection through indirect contact transmission. Clostridium difficile has also been associated with environmental dissemination and anecdotal suggestions of an airborne route have recently been supported by the sampling and culturing of Clostridium difficile spores from the air and high surfaces in a ward (Roberts et al. 2008). Of particular concern for hospitals, and of relevance to this article, are those pathogens that are highly contagious and have a relatively short incubation period such that infected individuals are likely to spread the infection during the timescale that they are hospitalized. Several infections fall into this category, including norovirus and influenza, which have the potential to rapidly infect whole wards, including the healthcare staff, resulting in ward closures, canceled operations, and pressure on the hospital operation (Chadwick et al. 2000). The incubation period for influenza is typically one to three days, and patients may then be infectious for a period of four to six days (Hawker et al. 2001). Norovirus has a similar incubation period (one to two days), but the patient is usually only highly infectious for around two days (Farr et al. 2004).

With mounting pressure on those who design and manage healthcare estates to meet both stringent infection and C[O.sub.2] reduction targets, there is a need for a better understanding of the interrelationships between airflow, infection, energy, and comfort that can be applied to generic patient areas. This article considers an approach to formally evaluating the trade-off between infection risk and energy performance through linking epidemic models with cost data. A stochastic formulation of a susceptible-exposed-infector-removed (SEIR) model coupled with the Wells-Riley equation is applied to a hypothetical hospital ward to explore the influence of environmental and disease parameters on the progression of an outbreak. A cost comparison is then made by evaluating the cost of treating infections against the costs of ventilating an environment. The study examines the level of uncertainty in the model and the data required to attain a reliable output.

Airborne infection outbreak model

Disease dynamics

Models describing the dynamics of infectious diseases have been developed since the 1900s, when scientists started to recognize patterns in the transmission of diseases that could be described mathematically. Today, general models for disease transmission are widely used and are well documented. A disease outbreak in a general population is commonly described by the process illustrated in Figure 1.

[FIGURE 1 OMITTED]

Susceptible individuals (S) are exposed to infection at a particular rate ([beta]), depending on the disease, transmission characteristics, and prevalence within the population. Once exposed (E), individuals incubate the disease for a period of time ([alpha]) before becoming infectious themselves. As infectors (I), they potentially transmit the disease to others for a period of time ([gamma]) before they are removed (R) from the process. The term removed is commonly used as a "catch-all" state that could include those who recover, those who may be physically removed by, say isolation, and those who die from the disease. If appropriate, the process can be amended to separate these different states. The total population involved in the process (N) comprises the sum of the susceptible, exposed, infectors, and removed states at any point in the outbreak.

The basic process outlined in Figure 1 is known as an SEIR model and forms the underlying approach in this analysis. In its simplest deterministic form, it is a series of differential equations that describe the rate of transition of people between the four states (Noakes et al. 2006). This can be appropriate for evaluating overarching behavior and the role of different parameters as well as modeling disease transmission in large populations. However, as the focus on this study is in a hospital ward, where the population is small and potentially transient, it is essential to consider further the dynamics of transmission and the application of the SEIR model.

It is straightforward in an SEIR model to include the rates at which people enter or leave a population. In a population as a whole, this is most commonly the birth and death rates, while in the context of a hospital outbreak, this could be admission and discharge rates (Cooper et al. 1999). The model can also be extended to incorporate a range of other effects, including the impact of vaccination and immunity (Chen and Liao 2008) and interaction between different diseases, such as the impact of HIV/AIDS on tuberculosis dynamics (Massad et al. 1993). Dealing with different groups within a population is also possible, although it is more complex. Populations in hospital wards will comprise a range of people, including patients, visitors, nursing staff, clinicians, and ancillary staff; and the type of ward and management of the hospital will determine the time that each group spends in a ward and the frequency of visits. Cooper et al (1999) considered the dynamics of MRSA transmission in a ward and separated the population into separate staff and patient cohorts to incorporate the different interactions between them. Several researchers, including Fraser (2007), have developed models to simulate transmission within and between households to address the nonhomogeneous mixing seen in real populations; such an approach could also be applicable to mixing between groups in hospital wards.

In this case, the approach is simplified by considering that the population remains constant and not differentiating between groups of people. However, a stochastic formulation is considered to include "chance" effects that are inherent in small populations. This case follows the approach used in Noakes and Sleigh (2009) and considers the outbreak as a series of events over time. In a small time interval, dt, such that the probability of more than one event is negligible, one of four outcomes is possible.

1. A new susceptible becomes exposed with probability Pr(SE) (S - 1; E + 1; I and R remain the same).

2. An exposed person becomes infectious with probability Pr(EI) (E - 1; I + 1; S and R remain the same).

3. An infector is removed with probability Pr(IR) (I - 1 ; R + 1 ; S and E remain the same).

4. Nothing happens (S, E, I, and R remain the same).

In each case, the probability of the event happening is governed by the rate parameters in Figure 1 and the current values of S, E, I, and R to give

Pr(SE) = [beta]SI, Pr(EI) = E / [alpha], Pr(IR)= I / [gamma] (1)

Following Renshaw's (1991) approach as described in Noakes and Sleigh (2009), the model uses a computationally efficient method to consider the time to the next event. This is done by first calculating the total probability that an event (outcomes 1-3 above) may occur, which is given by

[summation] Pr = Pr(SE) + Pr(EI) + Pr(IR). (2)

Each event probability can then be normalized to give

Pr(se) = Pr(SE) / [summation] Pr, Pr(ei) = Pr(EI) / [summation] Pr, Pr(ir) = Pr(IR) / [summation] Pr. (3)

The inter-event time t can then be determined using

t = - ln(Y) / [summation] Pr, (4)

where Y is a uniformly distributed random number, 0 [less than or equal to] Y [less than or equal to] 1.

The numerical simulation of the outbreak then follows the process:

* calculation of Pr(se), Pr(ei), and Pr(ir) at the current time step;

* generation of a first random number 0 [less than or equal to] Y [less than or equal to] 1 to find the inter-event time;

* generation of a second random number 0 [less than or equal to] X [less than or equal to] 1 to select the infection event with:

Event 1 if 0 [less than or equal to] X [less than or equal to] Pr(se),

Event 2 if Pr(se) < X [less than or equal to] (Pr(se) + Pr(ei)),

Event 3 if Pr(se)+Pr(ei) < X [less than or equal to] (Pr(se)+ Pr(ei) + Pr(ir)), and

Event 4 if Pr(se) + Pr(ei) + Pr(ir) < X [less than or equal to] 1 ;

* change in the values of s, e, i, and R according to the infection event.

The infection simulations were conducted using Excel and VBA (Microsoft) with a Monte Carlo approach to enable each model to be run up to 500 times to establish the mean and variance in behavior. As the inter-event times are different in every simulation due to the random number in the event time definition, the results were mapped onto a regular time scale at the end of each run to be able to compare data across more than one simulation.

Airborne transmission model

The risk of airborne transmission is incorporated through the widely used Wells-Riley model (Riley et al. 1978), which relates infection risk to the pulmonary ventilation rate of susceptible individuals p (1/min [[ft.sup.3]/min]); the ventilation rate of a space Q (1/min [[ft.sup.3]/min]); and the rate of infectious material produced by each infector, known as the quanta generation rate, q (quanta/h). As shown in Noakes et al. (2006), the Wells-Riley model can be incorporated into the SEIR model through defining the transmission rate parameter [beta] as

[beta] = pq / Q. (5)

It is important to note that this model is not without its limitations, and while more detailed discussions are given elsewhere (Noakes and Sleigh 2009, Sze To and Chao 2010), there are two points that should be acknowledged here. First, the risk model assumes a completely mixed airflow, which is unlikely in the best ventilated rooms and even more unlikely across a whole hospital ward. Although not included here, this limitation can be relatively easily addressed by combining the model with multizone ventilation tools, such as CONTAM or computational fluid dynamics (CFD) models, to assess the role of airflow patterns on the spatial distribution of infectious quanta (Noakes and Sleigh 2009; Qian et al. 2009). The model results also depend upon the value of quanta generation, which is a difficult parameter to define as it essentially encompasses the concentration of infectious material, virulence of the pathogen, host susceptibility, and ability of the infector to produce an aerosolized pathogen. Values of quanta are generally derived from past outbreaks and rely on often incomplete knowledge of airflows and averaged infection rates to determine typical values. Values reported in the literature for a number of infections are given in Table 1 and indicate the variability even within a particular disease.

Outbreak model behavior

The behavior of the infection model was examined using a hypothetical case that is intended to be representative of a ward environment. The parameter ranges used in the model are given in Table 2. As the focus of the modeling here is on the level of control offered by ventilation, it is assumed that there is no physical isolation of infected cases, and therefore, people move from state I to state R in the SEIR model at a rate determined by the infectious period of the disease.

Outbreak dynamics

Figures 2 and 3 show typical simulation results, presenting average behavior over 500 simulations and outbreak dynamics from a single run, respectively. As expected, the mean results in Figure 2 show classic epidemic model behavior, which concur with previous deterministic approaches (Noakes and Sleigh 2006; Chen and Liao 2008) and suggest that an increase in ventilation rate may reduce both the total number of cases of an infection and the peak number of infectors. However, the stochastic model enables the variability of the transmission process to be modeled, and as can be seen in Figure 3, the same set of conditions can lead to very different results. In Figure 3a, the first infector (index case) only manages to infect one other before both are removed. The infection therefore fails to spread, and as such, there is no outbreak. However in Figure 3b, the infection has started to spread before cases are removed, and a full blown outbreak occurs. As both scenarios have the same set of physical and disease parameters, the difference between the two cases is due to the random nature of the stochastic model and the particular combination of parameters.

[FIGURE 2 OMITTED]

To further examine the variability in the model and the influence of disease and environmental parameters, Figure 4 presents the probability distributions for the total number of cases over 500 simulation runs for both air change rates. A probability of only 1 case indicates that the infection has not spread beyond the index case, while 30 cases indicate that every person has succumbed to the infection. The results clearly show that as the transmission rate ([beta]) increases, the distribution of the total size of the epidemic changes. As may be expected, a lower value of [beta] (lower quanta rate or higher ventilation rate) results in a distribution that is skewed to the left, with the epidemic tending to die out before significant numbers are infected. However, as [beta] increases, the results show a bimodal distribution, with the likely outbreak size clustered at either end of the graph. Although the average behavior of the model for such scenarios indicates that the number of cases will be in the middle of the range (Figure 2), the results in Figure 4 suggest that in most cases, the behavior is at the extremes; either the outbreak fails to get going with only a small number of cases or it progresses to a critical point whereby the majority of people are likely to be infected. This behavior has been identified in mathematical texts examining the total size of stochastic epidemics and is related to the reproductive rate of the infection. In classic epidemic modeling theory, the reproduction rate, Ro, of an outbreak is a measure of the average number of infections produced by a typical case and defined as

Ro = [beta] / [gamma] N. (6)

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The parameter gives an indication of the likelihood of an epidemic, and in a deterministic model, Ro < 1 indicates that the disease will die out, while Ro > 1 is indicative of a full outbreak. Similar behavior is seen in the probability distributions produced by stochastic models. Allen (2008) indicates that an outbreak with Ro less than or close to one will tend to die out early on, and the distribution for the number of cases will be skewed to the left. When Ro > 1, the distribution becomes bimodal and increasingly skewed to the fight as Ro increases. The values of Ro for the cases modeled in Figure 4 are given in Table 3 and can be seen to concur with the behavior indicated in Allen (2008).

Cost-benefit analysis

While the results suggest that, for some infections, improved ventilation, leading to greater dilution of airborne pathogens, could potentially reduce the size and severity of an outbreak, it is not immediately clear whether investing to improve ventilation is really a viable approach for a hospital to take. To provide a means for formally assessing this, a simple financial appraisal method is explored by considering a cost for each air change provided and a cost to treat each case of an infection. By running the infection risk model for a range of disease and environmental parameters to determine the average total number of cases, it is straightforward for a particular scenario to create a plot typical of Figure 5a, showing the costs versus air change rate for both treatment of infections and energy consumption. For a particular disease scenario, it is then possible to determine the optimum ventilation from the minimum total cost, as shown in Figure 5b.

In the case of Figure 5, it was assumed that, in a hospital with eight wards of 1000 [m.sup.3] (35,315 [ft.sup.3]), there was one outbreak of an infection in a year that followed the average behavior predicted by the infection-risk model. The infection had an incubation period of 1 day, an infectious period of 1 or 2 days, and a quanta generation rate per infector of 5 or 10 quanta/h. Each infection was assumed to cost the hospital 2000 [pounds sterling] ($2985); this could be in treatment, lost bed days, or staffing issues. The energy cost per air change rate for all eight wards was assumed to be 3000 [pounds sterling] ($4480) based on continuous operation of a mechanical system with a fan power of 2 W/l/s (56.6 W/[ft.sup.3]/s) and a cost of electricity of 7.7 p/kWh. The results clearly show that the trade-off between energy costs and infection will depend very strongly on the disease characteristics, with the optimum ventilation ranging from 3 AC/h for the lowest infectivity disease (case a), to 6 AC/h for cases b and d, and 9 AC/h for case c. As may be expected, a higher quanta generation rate or a longer infectious period increases the likely severity of an outbreak and, hence, the treatment cost for a hospital. In such cases, the case for the improved ventilation provision becomes stronger even to prevent only one outbreak per year.

[FIGURE 5 OMITTED]

Although in theory this approach is straightforward, there is a considerable challenge in practice in being able to incorporate both the variability in the risk of infection and to put realistic costs to both the treatment of the infection and the ventilation provision. The case considered in Figure 5 serves to demonstrate potential outcomes but will be very dependent on the specifics of the disease and the various costs. Here, the most appropriate level of ventilation appears to be between three and nine air changes per hour, but this will change significantly depending on the cost of the infection. In addition, the ventilation costs presented here only consider those that are associated with moving the air. While this would be reduced in a naturally ventilated hospital, regardless of the ventilation approach, there is almost certainly a cost associated with heating and/or cooling and conditioning the air, which will be highly dependent on local climate, design of system, and regulations. For example, in the United Kingdom, heating is a certainty for at least six months of the year, cooling/conditioning will depend on application, and location and recirculation of mechanically ventilated air is not permitted (Department of Health 2007), restricting energy saving to heat recovery devices that are, again, system dependent. In other climates, cooling and conditioning will be the primary concerns, with heating a negligible aspect. However, regardless of system design or location, the need to modify the condition of the air will add to the cost, in many cases substantially, and will rise with air change rate.

To evaluate this further, if it is assumed that that the hospital is in a region requiring heating but no cooling/conditioning and has a full fresh air system with 50% heat recovery the ventilation heat loss can be estimated through combining the ventilation conductance (CIBSE 2006) with the degree day approach using the equation

annual heat loss (Wh) = 0.5 1/3 NV24[D.sub.d]E. (6)

Here, N is the ventilation rate (AC/h), V is the volume of the space ([m.sup.3]), [D.sub.d] is the number of degree days, and E is the intermittancy factor. For the case in Figure 5 with 2100 degree days (typical for London region in the United Kingdom), E = 1, and an energy cost for heating of 4 p/kWh (assumed to be gas and, therefore, lower than the electricity costs), this would increase the cost per air change rate from 3000 [pounds sterling] ($4480) to 11,064 [pounds sterling] ($16,515). As a consequence, this would put the optimal ventilation rate at three air changes per hour or less, and any increases will only be cost effective for the highest risk infections. While this is a simple theoretical example, it is clear that the heating and/or cooling costs will almost certainly dominate in a real case, will vary substantially with system design and climate, and unless there is effective heat recovery in place, will substaintially change the result. However despite this variation, putting a cost to the ventilation in a real case, while specific to a particular building and climate, is likely to be the easiest of the values to determine with modern dynamic thermal modeling software tools and/or building energy management system data. Other than fluctuations in weather conditions and energy costs, the ventilation costs will remain broadly constant in a particular space, regardless of infection, clinical process, or operational procedures.

However, putting costs to an infection presents a much greater challenge. In this case, the costs will encompass both direct treatment costs, such as antibiotics, and the impact of the infection on the operation of the hospital. The latter may include the costs of additional patient stay, the costs associated with staff shortages, the costs associated with cancelation of operations and procedures, the costs of additional cleaning and disinfection, and even the need to accommodate patients in another ward or even another hospital. The actual costs here will depend on the actual infection concerned and the other pressures that the hospital is under at the time and, in reality, may even change over time, depending on the severity of an outbreak. For some infections, the social and economic costs that result from the spread of an infection may also be a significant factor, as seen particularly in the SARs outbreak and, to a lesser extent, with the 2009 H 1N1 influenza pandemic. In both cases, the high mortality rate and/or high level of transmissibility make reducing the risk of transmission to the wider community a priority that should also be considered in cost calculations. Indeed, in the United Kingdom, it has been estimated that the preparation and response to the influenza pandemic totalled 1.2 billion [pounds sterling] ($1.8 billion; Hine 2010) for the vaccine and antiviral drug manufacture, extra face-masks and respirators, and public health campaigns alone, without even including the cost of work absenteeism and other societal impacts. While in this case there is no evidence that higher levels of control in hospitals could have reduced the costs, it serves to emphasize the very high economic cost of major infectious disease outbreaks and the savings that can be made where containment is a viable option.

Even considering just the hospital aspects of an infectious disease outbreak, establishing costs will also depend on the method of calculation. In many cases, this is dominated by how a marginal bed-day is valued, which is in part linked to a country's healthcare system (Graves et al. 2010). Published data on costs is both limited and variable; however, a number of authors give evaluations that are useful for establishing very rough appropriate costs. Plowman et al. (2001) considered 4000 patients admitted to a district general hospital in 1994-5 and estimated the additional cost across all infections to be of the order of 3000 [pounds sterling] ($4480) per patient. In a disease-specific assessment, Ghantoji et al. (2010) reviewed published studies on C diff infections and, from the limited data available, indicated costs of $2871-$4846 (approximately 2000 [pounds sterling] 3300 [pounds sterling]) per primary case within the United States and $5243-$8570 (approximately 3500 [pounds sterling]-5800 [pounds sterling]) outside. Zingg et al. (2005) estimated the cost of a norovirus outbreak among 16 patients and 29 healthcare workers to be $40,675 (approximately 27,500 [pounds sterling]), which equates to a per-patient cost of approximately 1700 [pounds sterling] ($2610). Based on these very approximate estimates, Figure 6 indicates the effect that changing both the cost of infection and the cost of energy may have on the total cost and, hence, the optimum ventilation for case b in Figure 5. The results indicate that changing either cost has a dramatic effect on the overall outbreak cost and supports the need for good economic data if such a model is used for assessment.

[FIGURE 6 OMITTED]

A further consideration is the stochastic variance in the likely dynamics of an infection as demonstrated in Figure 4. Figure 7 takes this into account by plotting the total cost (energy + treatment cost) against the probability for four different air change rates. Here, the disease parameters are again q = 10 quanta/h and [gamma] = 2 days, and the energy and treatment costs are assumed to be 9000 [pounds sterling] ($13,440) per AC/h and 3000 [pounds sterling] ($4480) per case, respectively. At the lowest air change rate, the base cost associated with energy only is minimized; however, such low dilution is ineffective against airborne transmission, and results indicate that there is around a70% chance that the cost will be approximately five times greater. Increasing the ventilation rate to 3 AC/h increases the base energy cost but substantially reduces the risk of a high-cost outbreak to approximately 13%. A further increase to 6 AC/h shows that the ventilation is now effective at reducing the epidemic; however, increasing the air change rate to 12 AC/h is clearly not cost effective for this particular infection scenario, although it is the only case where the value of Ro is reduced below 1.

Comparing Figures 6 and 7 suggests that using the optimum ventilation rate derived from a mean infection rate is a reasonable approach for design. While it does not capture the variance that will be present in reality, a hospital could regard the mean as the trend that they are likely to see over a period of a number of years. Although increasing the ventilation rate will not guarantee a reduction in infections, it will reduce the probability of an outbreak occurring. However, it is likely that in some cases when an outbreak does occur, the severity will be the same regardless of the ventilation rate. As a result, the cost and operational impact of a single large outbreak may remain the same, despite changes to the ventilation, but the frequency with which a hospital is likely to experience a large outbreak could well be reduced.

[FIGURE 7 OMITTED]

Discussion

The models presented here offer some insights into the risk of airborne-related outbreaks in hospital environments. While the models as they stand could not be considered robust or validated, they do provide a greater understanding as to the factors that influence the transmission of infection and, therefore, the criteria for designing ventilation in hospital wards. Perhaps the most valuable insights are around the level of uncertainty that is involved in predicting disease outbreaks in small populations and the need for case-specific data to be able to validate and subsequently use such models. The cases presented here, although based on appropriate parameters for infectious diseases in hospitals, deliberately do not attempt to simulate an actual infection, as the level of uncertainty in the model parameters are such that there is a danger of the results being misinterpreted. Although limitations in the ventilation parameters are starting to be addressed (Noakes and Sleigh 2009; Qian et al. 2009), disease parameters present a greater difficulty. The infectious and incubation periods for most diseases are variable and, although the range can be estimated with reasonable certainty fixed rate constants, cannot deal with the change in infectiousness as a disease progresses or the increasing likelihood that a person will leave the state with time (Wearing et al. 2005). The value of quanta is perhaps the greatest unknown and, as discussed with Table 1, is both variable and difficult to establish for the majority of diseases. As infections relevant to hospital outbreaks are likely to be transmitted by a combination of airborne, droplet, and contact routes, determining the value of quanta is even more of a challenge. Researchers are looking to address some of these issues through developing disease transmission models based on a dose-response approach (Chen et al. 2009), and it is clear that further research in this area is essential to improve the robustness of risk models for hospital environments.

Dealing with the complexities of the population and the management of the hospital should also be considered for a real case. While the static population of 30 patients simulated here using a stochastic approach may be representative for certain hospital environments, in others it is too simplistic, and it will be necessary to consider the interaction between different groups and the impact that this may have on the risk of transmission (Fraser 2007; Cooper et al 1999). This is particularly of concern where transmission of infection may occur prior to symptoms appearing, which was shown by Fraser et al. (2004) to make control of an outbreak much more difficult. While using ventilation as a control strategy may offer greater protection in such cases compared to reliance on identification and isolation of infected cases alone, environments where there is movement of patients or staff between wards may still allow undetected transmission between spaces. The models presented here only consider the role of ventilation and are, in some senses, a worst-case scenario. In reality, combining ventilation or other airborne controls with good surveillance and prompt treatment or isolation may enable an outbreak to be brought under control more easily than the models presented here suggest.

It is also worth commenting on the challenge of validating such models by comparing to real outbreak data. In many cases, this is particularly difficult, as data records dates of cases rather than when individuals were actually infected, and there are often several cases in an outbreak before it is identified as such; therefore, the early cases are often missing (Fraser 2007). The issue is further compounded as changes in infection control procedure in response to the outbreak will probably change the dynamics of transmission and, therefore, alter modeling assumptions. Fraser (2007) described an approach for developing reproduction numbers at an individual level, which takes account of the fact that the contact rate parameter [beta] may change during the course of an outbreak and indicates that this offers a potential solution to dealing with incomplete infection data during a real outbreak.

Despite these difficulties, the models presented here set out an approach for evaluating the ventilation design parameters from a cost-benefit perspective and as such offer a potential framework for assessment. While there are challenges in appropriately simplifying the transmission scenario and determining suitable costs for both ventilation provision and the consequences of infection, the ability to consider the ventilation from a quantitative risk perspective at the design stage offers a rational for selecting appropriate ventilation that is beyond the comfort and energy requirements of a space. For example, the results presented here for short incubation period infections with a quanta generation rate under 20 quanta/h, support the case for good ventilation in the region of 3-8 AC/h, depending on the actual infection, local climate, and ventilation system but do not show significant further benefit beyond this range for any of the costs considered. Even this level of knowledge at the design stage, combined with a view on patient cohort and the likelihood of a ward to experience outbreaks, could help to ensure that ventilation is not over- or underspecified. In addition, the models have the potential to help understand the likely extent and financial impact of an outbreak in an existing ward, benefiting those planning mitigation strategies.

Acknowledgments

The authors would like to acknowledge the support of the Engineering and Physical Sciences Research Council, UK (EPSRC), for funding this study.

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Catherine J. Noakes, * P. Andrew Sleigh, and Amirul Khan

Pathogen Control Engineering Institute (PACE), School of Civil Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK

* Corresponding author e-mail: C.J.Noakes@leeds.ac.uk

Received March 2, 2011; accepted May 23, 2011

Catherine J. Noakes, PhD, CEng, is Reader and member IMechE. P. Andrew Sleigh, PhD, is Senior Lecturer. Amirul Khan, PhD, is Postdoctoral Researcher.

DOI: 10.1080/10789669.2011.592054

Introduction

The choice of ventilation system for hospital environments is influenced by many factors. High-risk environments, such as isolation rooms, operating theaters, and pharmaceutical areas, are generally dominated by infection concerns, with this driving the ventilation agenda. For example, airborne infection isolation rooms, and the provision of a high airflow rate to ensure dilution of pathogens within the room and an appropriate pressure regime to limit transfer of pathogens between the room and neighboring spaces that are delivered by a mechanical means, tend to be the ventilation system of choice (Booth et al. 2009). Depending on the application and level of risk, fine particle filtration or other air disinfection techniques may be employed on the supply and/or extract air (Department of Health 2007; Jensen et al. 2005). Ventilation is also driven by the infection control agenda in operating theater environments, with the complexity of the system increasing with risk. At the highest end, ultra-clean ventilation theaters for high-risk surgery, such as orthopedics, have downflow air movement of up to 0.6 m/s (1.97 ft/s) in the central zone (Friberg et al. 2002), with room airflow circulated through ceiling-mounted high-efficiency particulate (HEPA) filters to provide a constant velocity downflow region over the operating area (Chow and Yang 2004). While such factors as energy use and plant size will be considered during design, they are generally not the primary drivers in the specification of these specialized ventilation systems. In both of these cases, airflow rates, pressure differentials, and levels of air cleaning generally increase with the likely risk in the environment. Clearly, this will substantially increase costs but, on the whole, is easily justified by the better clinical outcomes for the patients. For example, the ventilation costs for an immune-compromised transplant patient who requires positive pressure isolation with a HEPA-filtered supply after surgery are likely to be minor compared to the clinical costs of carrying out a transplant.

However, in most patient environments, such as wards, waiting areas, outpatient clinics, and treatment rooms, the most appropriate ventilation design is not so clear cut. In this case, the thermal comfort of patients and the energy performance of the system are seen as equal, if not more important, concerns than the transmission of infection. Balancing these demands is typically tackled by a broad guidance approach, using generic ventilation rates and comfort temperatures set out in national documents (Department of Health 2007) and the choice of mechanical or natural ventilation determined by local conditions, other elements of the building design, and the expertise of those designing the system. The resulting ventilation, while probably adequate, will generally have no formal evaluation that considers the balance between infection control, comfort, and energy. As ventilation for infection control is associated with airborne transmission, this, on the whole, takes a back seat, as most infections in general patient environments are regarded as being contact borne. However, there is increasing evidence that the transport of pathogens through the air is linked to many common healthcare-acquired infections (HCAI's) that are not regarded as airborne infections.

In recent years, several studies have linked Methicillin-resistant Staphylococcus aureus (MRSA) with airborne transmission, both through the analysis of outbreaks (Farrington et al. 1990; Kumari et al. 1998) and through the sampling of air and surfaces in the environment (Noble 1962; Hathway et al. 2008). Many such studies indicate the role of general nursing activities, such as bed-making (Roberts et al. 2006; Hathway et al. 2008), on the dispersion of the bacteria in the environment, leading to environmental contamination and increased risk of subsequent infection through indirect contact transmission. Clostridium difficile has also been associated with environmental dissemination and anecdotal suggestions of an airborne route have recently been supported by the sampling and culturing of Clostridium difficile spores from the air and high surfaces in a ward (Roberts et al. 2008). Of particular concern for hospitals, and of relevance to this article, are those pathogens that are highly contagious and have a relatively short incubation period such that infected individuals are likely to spread the infection during the timescale that they are hospitalized. Several infections fall into this category, including norovirus and influenza, which have the potential to rapidly infect whole wards, including the healthcare staff, resulting in ward closures, canceled operations, and pressure on the hospital operation (Chadwick et al. 2000). The incubation period for influenza is typically one to three days, and patients may then be infectious for a period of four to six days (Hawker et al. 2001). Norovirus has a similar incubation period (one to two days), but the patient is usually only highly infectious for around two days (Farr et al. 2004).

With mounting pressure on those who design and manage healthcare estates to meet both stringent infection and C[O.sub.2] reduction targets, there is a need for a better understanding of the interrelationships between airflow, infection, energy, and comfort that can be applied to generic patient areas. This article considers an approach to formally evaluating the trade-off between infection risk and energy performance through linking epidemic models with cost data. A stochastic formulation of a susceptible-exposed-infector-removed (SEIR) model coupled with the Wells-Riley equation is applied to a hypothetical hospital ward to explore the influence of environmental and disease parameters on the progression of an outbreak. A cost comparison is then made by evaluating the cost of treating infections against the costs of ventilating an environment. The study examines the level of uncertainty in the model and the data required to attain a reliable output.

Airborne infection outbreak model

Disease dynamics

Models describing the dynamics of infectious diseases have been developed since the 1900s, when scientists started to recognize patterns in the transmission of diseases that could be described mathematically. Today, general models for disease transmission are widely used and are well documented. A disease outbreak in a general population is commonly described by the process illustrated in Figure 1.

[FIGURE 1 OMITTED]

Susceptible individuals (S) are exposed to infection at a particular rate ([beta]), depending on the disease, transmission characteristics, and prevalence within the population. Once exposed (E), individuals incubate the disease for a period of time ([alpha]) before becoming infectious themselves. As infectors (I), they potentially transmit the disease to others for a period of time ([gamma]) before they are removed (R) from the process. The term removed is commonly used as a "catch-all" state that could include those who recover, those who may be physically removed by, say isolation, and those who die from the disease. If appropriate, the process can be amended to separate these different states. The total population involved in the process (N) comprises the sum of the susceptible, exposed, infectors, and removed states at any point in the outbreak.

The basic process outlined in Figure 1 is known as an SEIR model and forms the underlying approach in this analysis. In its simplest deterministic form, it is a series of differential equations that describe the rate of transition of people between the four states (Noakes et al. 2006). This can be appropriate for evaluating overarching behavior and the role of different parameters as well as modeling disease transmission in large populations. However, as the focus on this study is in a hospital ward, where the population is small and potentially transient, it is essential to consider further the dynamics of transmission and the application of the SEIR model.

It is straightforward in an SEIR model to include the rates at which people enter or leave a population. In a population as a whole, this is most commonly the birth and death rates, while in the context of a hospital outbreak, this could be admission and discharge rates (Cooper et al. 1999). The model can also be extended to incorporate a range of other effects, including the impact of vaccination and immunity (Chen and Liao 2008) and interaction between different diseases, such as the impact of HIV/AIDS on tuberculosis dynamics (Massad et al. 1993). Dealing with different groups within a population is also possible, although it is more complex. Populations in hospital wards will comprise a range of people, including patients, visitors, nursing staff, clinicians, and ancillary staff; and the type of ward and management of the hospital will determine the time that each group spends in a ward and the frequency of visits. Cooper et al (1999) considered the dynamics of MRSA transmission in a ward and separated the population into separate staff and patient cohorts to incorporate the different interactions between them. Several researchers, including Fraser (2007), have developed models to simulate transmission within and between households to address the nonhomogeneous mixing seen in real populations; such an approach could also be applicable to mixing between groups in hospital wards.

In this case, the approach is simplified by considering that the population remains constant and not differentiating between groups of people. However, a stochastic formulation is considered to include "chance" effects that are inherent in small populations. This case follows the approach used in Noakes and Sleigh (2009) and considers the outbreak as a series of events over time. In a small time interval, dt, such that the probability of more than one event is negligible, one of four outcomes is possible.

1. A new susceptible becomes exposed with probability Pr(SE) (S - 1; E + 1; I and R remain the same).

2. An exposed person becomes infectious with probability Pr(EI) (E - 1; I + 1; S and R remain the same).

3. An infector is removed with probability Pr(IR) (I - 1 ; R + 1 ; S and E remain the same).

4. Nothing happens (S, E, I, and R remain the same).

In each case, the probability of the event happening is governed by the rate parameters in Figure 1 and the current values of S, E, I, and R to give

Pr(SE) = [beta]SI, Pr(EI) = E / [alpha], Pr(IR)= I / [gamma] (1)

Following Renshaw's (1991) approach as described in Noakes and Sleigh (2009), the model uses a computationally efficient method to consider the time to the next event. This is done by first calculating the total probability that an event (outcomes 1-3 above) may occur, which is given by

[summation] Pr = Pr(SE) + Pr(EI) + Pr(IR). (2)

Each event probability can then be normalized to give

Pr(se) = Pr(SE) / [summation] Pr, Pr(ei) = Pr(EI) / [summation] Pr, Pr(ir) = Pr(IR) / [summation] Pr. (3)

The inter-event time t can then be determined using

t = - ln(Y) / [summation] Pr, (4)

where Y is a uniformly distributed random number, 0 [less than or equal to] Y [less than or equal to] 1.

The numerical simulation of the outbreak then follows the process:

* calculation of Pr(se), Pr(ei), and Pr(ir) at the current time step;

* generation of a first random number 0 [less than or equal to] Y [less than or equal to] 1 to find the inter-event time;

* generation of a second random number 0 [less than or equal to] X [less than or equal to] 1 to select the infection event with:

Event 1 if 0 [less than or equal to] X [less than or equal to] Pr(se),

Event 2 if Pr(se) < X [less than or equal to] (Pr(se) + Pr(ei)),

Event 3 if Pr(se)+Pr(ei) < X [less than or equal to] (Pr(se)+ Pr(ei) + Pr(ir)), and

Event 4 if Pr(se) + Pr(ei) + Pr(ir) < X [less than or equal to] 1 ;

* change in the values of s, e, i, and R according to the infection event.

The infection simulations were conducted using Excel and VBA (Microsoft) with a Monte Carlo approach to enable each model to be run up to 500 times to establish the mean and variance in behavior. As the inter-event times are different in every simulation due to the random number in the event time definition, the results were mapped onto a regular time scale at the end of each run to be able to compare data across more than one simulation.

Airborne transmission model

The risk of airborne transmission is incorporated through the widely used Wells-Riley model (Riley et al. 1978), which relates infection risk to the pulmonary ventilation rate of susceptible individuals p (1/min [[ft.sup.3]/min]); the ventilation rate of a space Q (1/min [[ft.sup.3]/min]); and the rate of infectious material produced by each infector, known as the quanta generation rate, q (quanta/h). As shown in Noakes et al. (2006), the Wells-Riley model can be incorporated into the SEIR model through defining the transmission rate parameter [beta] as

[beta] = pq / Q. (5)

It is important to note that this model is not without its limitations, and while more detailed discussions are given elsewhere (Noakes and Sleigh 2009, Sze To and Chao 2010), there are two points that should be acknowledged here. First, the risk model assumes a completely mixed airflow, which is unlikely in the best ventilated rooms and even more unlikely across a whole hospital ward. Although not included here, this limitation can be relatively easily addressed by combining the model with multizone ventilation tools, such as CONTAM or computational fluid dynamics (CFD) models, to assess the role of airflow patterns on the spatial distribution of infectious quanta (Noakes and Sleigh 2009; Qian et al. 2009). The model results also depend upon the value of quanta generation, which is a difficult parameter to define as it essentially encompasses the concentration of infectious material, virulence of the pathogen, host susceptibility, and ability of the infector to produce an aerosolized pathogen. Values of quanta are generally derived from past outbreaks and rely on often incomplete knowledge of airflows and averaged infection rates to determine typical values. Values reported in the literature for a number of infections are given in Table 1 and indicate the variability even within a particular disease.

Outbreak model behavior

The behavior of the infection model was examined using a hypothetical case that is intended to be representative of a ward environment. The parameter ranges used in the model are given in Table 2. As the focus of the modeling here is on the level of control offered by ventilation, it is assumed that there is no physical isolation of infected cases, and therefore, people move from state I to state R in the SEIR model at a rate determined by the infectious period of the disease.

Outbreak dynamics

Figures 2 and 3 show typical simulation results, presenting average behavior over 500 simulations and outbreak dynamics from a single run, respectively. As expected, the mean results in Figure 2 show classic epidemic model behavior, which concur with previous deterministic approaches (Noakes and Sleigh 2006; Chen and Liao 2008) and suggest that an increase in ventilation rate may reduce both the total number of cases of an infection and the peak number of infectors. However, the stochastic model enables the variability of the transmission process to be modeled, and as can be seen in Figure 3, the same set of conditions can lead to very different results. In Figure 3a, the first infector (index case) only manages to infect one other before both are removed. The infection therefore fails to spread, and as such, there is no outbreak. However in Figure 3b, the infection has started to spread before cases are removed, and a full blown outbreak occurs. As both scenarios have the same set of physical and disease parameters, the difference between the two cases is due to the random nature of the stochastic model and the particular combination of parameters.

[FIGURE 2 OMITTED]

To further examine the variability in the model and the influence of disease and environmental parameters, Figure 4 presents the probability distributions for the total number of cases over 500 simulation runs for both air change rates. A probability of only 1 case indicates that the infection has not spread beyond the index case, while 30 cases indicate that every person has succumbed to the infection. The results clearly show that as the transmission rate ([beta]) increases, the distribution of the total size of the epidemic changes. As may be expected, a lower value of [beta] (lower quanta rate or higher ventilation rate) results in a distribution that is skewed to the left, with the epidemic tending to die out before significant numbers are infected. However, as [beta] increases, the results show a bimodal distribution, with the likely outbreak size clustered at either end of the graph. Although the average behavior of the model for such scenarios indicates that the number of cases will be in the middle of the range (Figure 2), the results in Figure 4 suggest that in most cases, the behavior is at the extremes; either the outbreak fails to get going with only a small number of cases or it progresses to a critical point whereby the majority of people are likely to be infected. This behavior has been identified in mathematical texts examining the total size of stochastic epidemics and is related to the reproductive rate of the infection. In classic epidemic modeling theory, the reproduction rate, Ro, of an outbreak is a measure of the average number of infections produced by a typical case and defined as

Ro = [beta] / [gamma] N. (6)

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The parameter gives an indication of the likelihood of an epidemic, and in a deterministic model, Ro < 1 indicates that the disease will die out, while Ro > 1 is indicative of a full outbreak. Similar behavior is seen in the probability distributions produced by stochastic models. Allen (2008) indicates that an outbreak with Ro less than or close to one will tend to die out early on, and the distribution for the number of cases will be skewed to the left. When Ro > 1, the distribution becomes bimodal and increasingly skewed to the fight as Ro increases. The values of Ro for the cases modeled in Figure 4 are given in Table 3 and can be seen to concur with the behavior indicated in Allen (2008).

Cost-benefit analysis

While the results suggest that, for some infections, improved ventilation, leading to greater dilution of airborne pathogens, could potentially reduce the size and severity of an outbreak, it is not immediately clear whether investing to improve ventilation is really a viable approach for a hospital to take. To provide a means for formally assessing this, a simple financial appraisal method is explored by considering a cost for each air change provided and a cost to treat each case of an infection. By running the infection risk model for a range of disease and environmental parameters to determine the average total number of cases, it is straightforward for a particular scenario to create a plot typical of Figure 5a, showing the costs versus air change rate for both treatment of infections and energy consumption. For a particular disease scenario, it is then possible to determine the optimum ventilation from the minimum total cost, as shown in Figure 5b.

In the case of Figure 5, it was assumed that, in a hospital with eight wards of 1000 [m.sup.3] (35,315 [ft.sup.3]), there was one outbreak of an infection in a year that followed the average behavior predicted by the infection-risk model. The infection had an incubation period of 1 day, an infectious period of 1 or 2 days, and a quanta generation rate per infector of 5 or 10 quanta/h. Each infection was assumed to cost the hospital 2000 [pounds sterling] ($2985); this could be in treatment, lost bed days, or staffing issues. The energy cost per air change rate for all eight wards was assumed to be 3000 [pounds sterling] ($4480) based on continuous operation of a mechanical system with a fan power of 2 W/l/s (56.6 W/[ft.sup.3]/s) and a cost of electricity of 7.7 p/kWh. The results clearly show that the trade-off between energy costs and infection will depend very strongly on the disease characteristics, with the optimum ventilation ranging from 3 AC/h for the lowest infectivity disease (case a), to 6 AC/h for cases b and d, and 9 AC/h for case c. As may be expected, a higher quanta generation rate or a longer infectious period increases the likely severity of an outbreak and, hence, the treatment cost for a hospital. In such cases, the case for the improved ventilation provision becomes stronger even to prevent only one outbreak per year.

[FIGURE 5 OMITTED]

Although in theory this approach is straightforward, there is a considerable challenge in practice in being able to incorporate both the variability in the risk of infection and to put realistic costs to both the treatment of the infection and the ventilation provision. The case considered in Figure 5 serves to demonstrate potential outcomes but will be very dependent on the specifics of the disease and the various costs. Here, the most appropriate level of ventilation appears to be between three and nine air changes per hour, but this will change significantly depending on the cost of the infection. In addition, the ventilation costs presented here only consider those that are associated with moving the air. While this would be reduced in a naturally ventilated hospital, regardless of the ventilation approach, there is almost certainly a cost associated with heating and/or cooling and conditioning the air, which will be highly dependent on local climate, design of system, and regulations. For example, in the United Kingdom, heating is a certainty for at least six months of the year, cooling/conditioning will depend on application, and location and recirculation of mechanically ventilated air is not permitted (Department of Health 2007), restricting energy saving to heat recovery devices that are, again, system dependent. In other climates, cooling and conditioning will be the primary concerns, with heating a negligible aspect. However, regardless of system design or location, the need to modify the condition of the air will add to the cost, in many cases substantially, and will rise with air change rate.

To evaluate this further, if it is assumed that that the hospital is in a region requiring heating but no cooling/conditioning and has a full fresh air system with 50% heat recovery the ventilation heat loss can be estimated through combining the ventilation conductance (CIBSE 2006) with the degree day approach using the equation

annual heat loss (Wh) = 0.5 1/3 NV24[D.sub.d]E. (6)

Here, N is the ventilation rate (AC/h), V is the volume of the space ([m.sup.3]), [D.sub.d] is the number of degree days, and E is the intermittancy factor. For the case in Figure 5 with 2100 degree days (typical for London region in the United Kingdom), E = 1, and an energy cost for heating of 4 p/kWh (assumed to be gas and, therefore, lower than the electricity costs), this would increase the cost per air change rate from 3000 [pounds sterling] ($4480) to 11,064 [pounds sterling] ($16,515). As a consequence, this would put the optimal ventilation rate at three air changes per hour or less, and any increases will only be cost effective for the highest risk infections. While this is a simple theoretical example, it is clear that the heating and/or cooling costs will almost certainly dominate in a real case, will vary substantially with system design and climate, and unless there is effective heat recovery in place, will substaintially change the result. However despite this variation, putting a cost to the ventilation in a real case, while specific to a particular building and climate, is likely to be the easiest of the values to determine with modern dynamic thermal modeling software tools and/or building energy management system data. Other than fluctuations in weather conditions and energy costs, the ventilation costs will remain broadly constant in a particular space, regardless of infection, clinical process, or operational procedures.

However, putting costs to an infection presents a much greater challenge. In this case, the costs will encompass both direct treatment costs, such as antibiotics, and the impact of the infection on the operation of the hospital. The latter may include the costs of additional patient stay, the costs associated with staff shortages, the costs associated with cancelation of operations and procedures, the costs of additional cleaning and disinfection, and even the need to accommodate patients in another ward or even another hospital. The actual costs here will depend on the actual infection concerned and the other pressures that the hospital is under at the time and, in reality, may even change over time, depending on the severity of an outbreak. For some infections, the social and economic costs that result from the spread of an infection may also be a significant factor, as seen particularly in the SARs outbreak and, to a lesser extent, with the 2009 H 1N1 influenza pandemic. In both cases, the high mortality rate and/or high level of transmissibility make reducing the risk of transmission to the wider community a priority that should also be considered in cost calculations. Indeed, in the United Kingdom, it has been estimated that the preparation and response to the influenza pandemic totalled 1.2 billion [pounds sterling] ($1.8 billion; Hine 2010) for the vaccine and antiviral drug manufacture, extra face-masks and respirators, and public health campaigns alone, without even including the cost of work absenteeism and other societal impacts. While in this case there is no evidence that higher levels of control in hospitals could have reduced the costs, it serves to emphasize the very high economic cost of major infectious disease outbreaks and the savings that can be made where containment is a viable option.

Even considering just the hospital aspects of an infectious disease outbreak, establishing costs will also depend on the method of calculation. In many cases, this is dominated by how a marginal bed-day is valued, which is in part linked to a country's healthcare system (Graves et al. 2010). Published data on costs is both limited and variable; however, a number of authors give evaluations that are useful for establishing very rough appropriate costs. Plowman et al. (2001) considered 4000 patients admitted to a district general hospital in 1994-5 and estimated the additional cost across all infections to be of the order of 3000 [pounds sterling] ($4480) per patient. In a disease-specific assessment, Ghantoji et al. (2010) reviewed published studies on C diff infections and, from the limited data available, indicated costs of $2871-$4846 (approximately 2000 [pounds sterling] 3300 [pounds sterling]) per primary case within the United States and $5243-$8570 (approximately 3500 [pounds sterling]-5800 [pounds sterling]) outside. Zingg et al. (2005) estimated the cost of a norovirus outbreak among 16 patients and 29 healthcare workers to be $40,675 (approximately 27,500 [pounds sterling]), which equates to a per-patient cost of approximately 1700 [pounds sterling] ($2610). Based on these very approximate estimates, Figure 6 indicates the effect that changing both the cost of infection and the cost of energy may have on the total cost and, hence, the optimum ventilation for case b in Figure 5. The results indicate that changing either cost has a dramatic effect on the overall outbreak cost and supports the need for good economic data if such a model is used for assessment.

[FIGURE 6 OMITTED]

A further consideration is the stochastic variance in the likely dynamics of an infection as demonstrated in Figure 4. Figure 7 takes this into account by plotting the total cost (energy + treatment cost) against the probability for four different air change rates. Here, the disease parameters are again q = 10 quanta/h and [gamma] = 2 days, and the energy and treatment costs are assumed to be 9000 [pounds sterling] ($13,440) per AC/h and 3000 [pounds sterling] ($4480) per case, respectively. At the lowest air change rate, the base cost associated with energy only is minimized; however, such low dilution is ineffective against airborne transmission, and results indicate that there is around a70% chance that the cost will be approximately five times greater. Increasing the ventilation rate to 3 AC/h increases the base energy cost but substantially reduces the risk of a high-cost outbreak to approximately 13%. A further increase to 6 AC/h shows that the ventilation is now effective at reducing the epidemic; however, increasing the air change rate to 12 AC/h is clearly not cost effective for this particular infection scenario, although it is the only case where the value of Ro is reduced below 1.

Comparing Figures 6 and 7 suggests that using the optimum ventilation rate derived from a mean infection rate is a reasonable approach for design. While it does not capture the variance that will be present in reality, a hospital could regard the mean as the trend that they are likely to see over a period of a number of years. Although increasing the ventilation rate will not guarantee a reduction in infections, it will reduce the probability of an outbreak occurring. However, it is likely that in some cases when an outbreak does occur, the severity will be the same regardless of the ventilation rate. As a result, the cost and operational impact of a single large outbreak may remain the same, despite changes to the ventilation, but the frequency with which a hospital is likely to experience a large outbreak could well be reduced.

[FIGURE 7 OMITTED]

Discussion

The models presented here offer some insights into the risk of airborne-related outbreaks in hospital environments. While the models as they stand could not be considered robust or validated, they do provide a greater understanding as to the factors that influence the transmission of infection and, therefore, the criteria for designing ventilation in hospital wards. Perhaps the most valuable insights are around the level of uncertainty that is involved in predicting disease outbreaks in small populations and the need for case-specific data to be able to validate and subsequently use such models. The cases presented here, although based on appropriate parameters for infectious diseases in hospitals, deliberately do not attempt to simulate an actual infection, as the level of uncertainty in the model parameters are such that there is a danger of the results being misinterpreted. Although limitations in the ventilation parameters are starting to be addressed (Noakes and Sleigh 2009; Qian et al. 2009), disease parameters present a greater difficulty. The infectious and incubation periods for most diseases are variable and, although the range can be estimated with reasonable certainty fixed rate constants, cannot deal with the change in infectiousness as a disease progresses or the increasing likelihood that a person will leave the state with time (Wearing et al. 2005). The value of quanta is perhaps the greatest unknown and, as discussed with Table 1, is both variable and difficult to establish for the majority of diseases. As infections relevant to hospital outbreaks are likely to be transmitted by a combination of airborne, droplet, and contact routes, determining the value of quanta is even more of a challenge. Researchers are looking to address some of these issues through developing disease transmission models based on a dose-response approach (Chen et al. 2009), and it is clear that further research in this area is essential to improve the robustness of risk models for hospital environments.

Dealing with the complexities of the population and the management of the hospital should also be considered for a real case. While the static population of 30 patients simulated here using a stochastic approach may be representative for certain hospital environments, in others it is too simplistic, and it will be necessary to consider the interaction between different groups and the impact that this may have on the risk of transmission (Fraser 2007; Cooper et al 1999). This is particularly of concern where transmission of infection may occur prior to symptoms appearing, which was shown by Fraser et al. (2004) to make control of an outbreak much more difficult. While using ventilation as a control strategy may offer greater protection in such cases compared to reliance on identification and isolation of infected cases alone, environments where there is movement of patients or staff between wards may still allow undetected transmission between spaces. The models presented here only consider the role of ventilation and are, in some senses, a worst-case scenario. In reality, combining ventilation or other airborne controls with good surveillance and prompt treatment or isolation may enable an outbreak to be brought under control more easily than the models presented here suggest.

It is also worth commenting on the challenge of validating such models by comparing to real outbreak data. In many cases, this is particularly difficult, as data records dates of cases rather than when individuals were actually infected, and there are often several cases in an outbreak before it is identified as such; therefore, the early cases are often missing (Fraser 2007). The issue is further compounded as changes in infection control procedure in response to the outbreak will probably change the dynamics of transmission and, therefore, alter modeling assumptions. Fraser (2007) described an approach for developing reproduction numbers at an individual level, which takes account of the fact that the contact rate parameter [beta] may change during the course of an outbreak and indicates that this offers a potential solution to dealing with incomplete infection data during a real outbreak.

Despite these difficulties, the models presented here set out an approach for evaluating the ventilation design parameters from a cost-benefit perspective and as such offer a potential framework for assessment. While there are challenges in appropriately simplifying the transmission scenario and determining suitable costs for both ventilation provision and the consequences of infection, the ability to consider the ventilation from a quantitative risk perspective at the design stage offers a rational for selecting appropriate ventilation that is beyond the comfort and energy requirements of a space. For example, the results presented here for short incubation period infections with a quanta generation rate under 20 quanta/h, support the case for good ventilation in the region of 3-8 AC/h, depending on the actual infection, local climate, and ventilation system but do not show significant further benefit beyond this range for any of the costs considered. Even this level of knowledge at the design stage, combined with a view on patient cohort and the likelihood of a ward to experience outbreaks, could help to ensure that ventilation is not over- or underspecified. In addition, the models have the potential to help understand the likely extent and financial impact of an outbreak in an existing ward, benefiting those planning mitigation strategies.

Acknowledgments

The authors would like to acknowledge the support of the Engineering and Physical Sciences Research Council, UK (EPSRC), for funding this study.

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Catherine J. Noakes, * P. Andrew Sleigh, and Amirul Khan

Pathogen Control Engineering Institute (PACE), School of Civil Engineering, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK

* Corresponding author e-mail: C.J.Noakes@leeds.ac.uk

Received March 2, 2011; accepted May 23, 2011

Catherine J. Noakes, PhD, CEng, is Reader and member IMechE. P. Andrew Sleigh, PhD, is Senior Lecturer. Amirul Khan, PhD, is Postdoctoral Researcher.

DOI: 10.1080/10789669.2011.592054

Table 1. Quanta production rate for a range of infectious diseases. Disease Case Tuberculosis Average patient Tuberculosis Outbreak in office building Tuberculosis Human to guinea pig transmission Multi-drug resistant Human to guinea pig tuberculosis transmission (highest infectors) Measles Outbreak in a school Influenza School cases in Taiwan Influenza Aircraft outbreak SARs Taipei Hospital outbreak Rhinovirus 16 Experimental data Disease Quanta/h Reported by Tuberculosis 1.25 Nardell et al. (1991) Tuberculosis 12.7 Nardell et al. (1991) Tuberculosis 0.3-44 Escombe et al. (2007) Multi-drug resistant 40, 52, 226 Escombe et al. (2008) tuberculosis Measles 570 Rudnick and Milton (2003) Influenza 66.91 (log normal) Liao et al. (2005) Influenza 79-128 Rudnick and Milton (2003) SARs 28.77 (log normal) Liao et al. (2005) Rhinovirus 16 1-10 Rudnick and Milton (2003) Table 2. Parameters used in the simulations. Ward volume, V 1000 [m.sup.3] (35,315 [ft.sup.3]) Ventilation rate 3-12 AC/h Initial number of 30 susceptibles, S Initial number of infectors, I 1 Initial number of exposed, E 0 Initial number of removed, R 0 Pulmonary ventilation 101/min (0.35 [ft.sup.3]/min) rate, p Quanta generation rate, q 5-20 quanta/h Disease incubation 1 day period, 1/[alpha] Disease infectious 1-2 days period, 1/[gamma] Duration of simulation 20 days Table 3. Reproduction rate (Ro) for conditions in Figure 4. Ventilation rate (AC/h) Quanta/h [beta] Ro 3 5 1 x [10.sup.-3] 1.49 10 2 x [10.sup.-3] 2.98 20 4 x [10.sup.-3] 5.96 6 5 5 x [10.sup.-4] 0.74 10 1 x [10.sup.-3] 1.49 20 2 x [10.sup.-3] 2.98

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Author: | Noakes, Catherine J.; Sleigh, P. Andrew; Khan, Amirul |
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Publication: | HVAC & R Research |

Geographic Code: | 4EUUK |

Date: | Aug 1, 2012 |

Words: | 7564 |

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