Towards a simulation environment for modeling of local influenza outbreaks Toomas Timpkaa , Magnus Morinb, Johan Jenvaldb, Henrik Erikssona, Elin A. Gurskyc a
Department of Computer and Information Science, Linköping University, Linköping, Sweden b
VSL Research Labs, Linköping, Sweden c
ANSER, Arlington, VA, USA
Abstract Objective: To analyze the design of a simulation environment for dynamic prediction of influenza transmission in local communities. Methods: The technique trade-off method was used to identify and analyze basic design requirements on a simulation environment for modeling of influenza transmission. Data were collected through literature review and interviews with infectious disease experts. The identified requirements were matched to a set of design issues for the simulation environment, and a high-resolution prototype was implemented. Results: Basic reproductive numbers for influenza transmission in a set of Swedish municipalities were calculated. Tradeoffs were necessary in the design between a focus on reproductive numbers vs. case fatality proportions, algorithm validity vs. model adaptability, and specificity in population description vs. generalizability. Conclusion: Computer-based simulations can become important tools for local authorities preparing for influenza outbreaks. Balanced tradeoffs between model detail and public health effectiveness are important in simulation environment design.
Keywords: Epidemiological simulation, influenza pandemics, simulation environments, design analyses, system requirements.
Introduction Despite advances in medical treatment, influenza causes thousands of deaths annually in industrialized countries [1]. In the near future, the emergence of an influenza pandemic with an even more destructive virus subtype is anticipated, with a case fatality proportion (CFP) close to the most destructive epidemics experienced during the previous century (1918, 1957 and 1968) [2]. Moreover, the zoonotic aspects of
avian influenza, which until 1997 were considered to be of limited relevance in human medicine, are currently of central interest due to the potential of generating a reassortant virus resulting in human pandemics [3]. Understanding and representing the mechanisms and speed with which influenza may be transmitted across human populations is crucial to effective pandemic preparation. Influenza can be transmitted through multiple mechanisms; aerosolised droplets of respiratory secretions are the primary means of person-to-person influenza transmission, but spread can also occur through direct person-to-person contact or through fomites [4]. The transmission speed can be represented as a function of the reproductive number (R) and the serial interval, which is the average time between a primary and secondary case. The incubation period is 1-4 days with an average of 2 days [5]. Persons can be infectious starting the day before symptom presentation through approximately 5 days after illness onset; children can be infectious for a longer period. The basic reproductive number is often calculated as a basis for analysis of different intervention strategies. It is defined as the average number of secondary infections produced by a randomly selected infected person in a fully susceptible population [6]. For a heterogeneous population, it is the average of all the secondary cases that this randomly selected initial infective person would infect over all the social contexts of which he/she is a part. In most countries, the responsibility for responding to threats from infectious diseases is delegated to local health authorities, e.g. county councils and municipal boards. The magnitude of the effective reproductive number, R, can here be used to determine the intensity of measures required to halt transmission. However, estimates of R for pandemic influenza reported in the literature have varied widely, ranging from 1.7 to 20 [7,8]. One reason is that R depends on both the infectious agent and the host population; e.g. the age spectrum, the level of urbanization and population density, and antigenic immunity from previous exposure [9]. In the case of an influenza pandemic with a “destructive” virus, there is thus a need to rapidly calculate the updated reproductive number for particular community settings. However, to our knowledge,
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there are no tabulated estimates available of the range of R values that can be applied to specific local communities. The large number of variables involved and the limited availability of actual transmission data suggests that such estimates would need to be computed dynamically for each particular setting and refined through continually updated information inputs. The aim of this study is to analyze the design of a simulation environment for dynamic prediction of influenza transmission in local communities with different socio-economic composure. Data from Swedish municipalities (n =4/290) are used for initial prototype applications and preliminary evaluations. In the results section of this paper, the basic requirements with motivations are first presented, divided into demands on the simulation model and the simulation output, respectively. Thereafter the design of a prototype system is outlined. In the final part of the results section, trade-off argumentation about the central design decisions is displayed with a point of departure in the techniques included in the prototype.
Methods The technique trade-off method [10] was used for the analysis of the system design. Basic design requirements for the simulation environment were identified based on a literature review and interviews with national experts (n=6) on containment of infectious diseases. The review was based on a PubMed search (December 2004) using the search terms influenza, epidemiological simulation, disease modeling, and combinations of these expressions. Following reading of the article abstracts, a final set of 31 papers was identified for the requirements analyses. The identified requirements were matched to a set of design issues for the simulation environment, allocating a subset of design issues to each requirement. Based on knowledge about the characteristics of the user group, primarily community epidemiologists and public health professionals, the different needs were interpreted and translated into a set of system functions manifested in a first prototype. After an evaluation in a laboratory setting, modifications were made and a ‘high-resolution’ prototype was created [11]. The prototype simulator was developed in the C# programming language. The development and experiments were performed under the Windows® XP operating system. To be able to focus on the simulation and disease models, the first versions of the simulator were developed as a batch program on the .NET platform. In later versions, an interactive user interface has been added. Arguments regarding each design decision were recorded during the development process, and finally represented in terms of techniques and tradeoffs.
Results Basic requirements – simulation model: • Forward prediction of number of cases at time t.
•
Backward estimation of number of cases at time t, given the reported number of cases at time tr. • Adaptation of the simulation from time ti with specific interventions in place. Motivation: Managing an influenza outbreak is a dynamic decision-making task [12]. In such a task, a series of interdependent decisions is required to reach the defined goal in an environment where the state of the decision-problem changes, both spontaneously and as a result of the decision-maker’s actions. As a consequence, dynamic decision-making must be treated as an ongoing, real-time process striving to control an emerging situation. Crucial in this process is the decisionmaker’s model of the task and of the effects of the actions available. For the task of managing an infectious disease, this model must capture the nature of the disease and its transmissibility mechanisms, the structure of the population affected, and the socio-economic composition of the community. Interventions such as vaccination, pharmacological prophylaxis, quarantine, and risk communication must be represented in the model with respect to those factors. Basic requirements – simulation output: • Number of new cases per time unit. • Total number of cases at any time t • Geographic and socio-economic distribution of cases. • Number of fatalities. • Tabulated results of what-if analyses. Motivation: Given presumably incomplete information about cases, decision-makers need to be able to make a best estimate of the projected disease situation. Among their many responsibilities they need to assess the current situation; forecast future morbidity given the particular structure and population of the local community; identify and implement effective interventions; and monitor the effectiveness of interventions that are put in place. Before the actual disease outbreak, policies and guidelines have to be developed specific to the social structure and population characteristics of the local community. Prediction of the number and distribution of cases in the local community under various intervention programs can here be proactively computed and stored. Similarly, the estimation of geographic and socio-economic distribution of cases in the local community can be computed and proactively displayed. Simulation environment design The main components of the simulation environment are the data interface, the population generator, the disease case generator, and the simulation engine. Local community data are imported by the data interface and made available to the population generator, which uses them to generate a population model that captures local conditions. The disease case generator stochastically generates cases on the basis of disease parameters. The simulation engine uses a discrete time model to step and update the population and disease models accordingly (Table 1). It also collects data for analysis.
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Table 1. Example simulation. Kfors municipality 20501 inhabitants 8831 households 41 neighborhoods 3 school districts (1 middle school, 4-5 elementary schools, and 7 day care centres each) Distribution of secondary cases from a single index case (30 simulations) 0 (n = 20) 1 (n = 3) 2 (n = 4) 3 (n = 1) 6 (n = 1) 20 (n = 1) Ro = 1,33
Design issue: Simulation model Technique: Based on previous studies, we developed a generic stochastic simulation model of influenza spread within structured populations [13]. The model simulates stochastic spread of influenza among persons interacting in known contact groups [14]. To calculate R0, we assumed a scenario in which a randomly chosen, unvaccinated infected person is seeded into each municipality population where everyone else’s ability to transmit is 0. We then count the number of secondary infections. By repeating this procedure, we generate the whole distribution of secondary cases due to a randomly selected infected person. The mean of this distribution is R0. To estimate the actual R in each population for a given period of time, the probability of becoming infected is calculated for each day and each susceptible person on the basis of that person’s antiviral or vaccination status, who is infectious in his contact groups and their antiviral or vaccination status, and the group-specific transmission probabilities. Influenza is introduced by randomly assigning 1-4 initial infective persons. As an example, a child attending elementary school is exposed to the number of child and adult infective persons in his household, Ihc and Iha; his school, Is; his neighborhood, In; and the population, Ic, with corresponding transmission probabilities for each contact of phcc (child to child), phac (adult to child), ps, pn, and pc, respectively. Trade-offs: Our analyses were initially focused on calculations of R. However, we found it difficult to obtain accurate data sets for these calculations. We also observed that it has been reported that the high CFP in young adults, rather than an unusually high R, was what distinguished the epidemic curve of the destructive pandemic 1918 from more recent outbreaks [15]. By fitting a deterministic SEIR (susceptibleexposed-infected-removed) model to the excess pneumonia and influenza death curves for 45 US cities, it has been found that R for 1918 pandemic influenza was approximately 2–3 [16]. The initial R estimate was not significantly correlated with factors that included latitude, longitude, population size, population density, age distribution or sex distribution. Nevertheless, extreme R estimates were weakly positively correlated with population density, but the association did not remain statistically significant after correction for multiple comparisons. These results suggest, first, that R for 1918 pandemic
influenza was not particularly large relative to that for many other infectious diseases [9]. Second, they imply that consideration only of R is not sufficient for a simulation environment to be used in the response to pandemic influenza. Calculation of other indices for virus transmission have also to be supported, e.g. of the basic reproductive number, R0, for different local communities. Design issue: Disease model Techniques: People infected with influenza virus are expected to first pass through an incubation period when they are not infectious. The lengths of the incubation and infectious periods follow empirical probability distributions, with mean lengths of 1.9 and 4.1 days, respectively [14]. During the infectious period, the infected person may or may not develop influenza symptoms. In the model, persons with symptoms are assumed to withdraw with some probability to the home, exposing only the other members of their household. The baseline epidemic is assumed to have age-specific illness attack rates similar to those of the 1957–1958 influenza pandemic in the United States [17, 18]. The probability that a person will be symptomatic given that person has been infected is 0.67. An asymptomatic infection is assumed to be 50 percent as infectious as a symptomatic infection. Additionally, this model assumes persons to withdraw from all of their social contexts except the family unit if they become symptomatic. The CFR per 1,000 cases of influenza used were 0.3 in young children, 0.2 in older children, 3 in young adults, and 20 in older adults. These rates were derived using the mortality rates published by Thompson et al. [1] in combination with illness attack rate data, and adjusted with regard to numbers from the 1918 pandemic, with a CFP ten times higher than in other annual influenza outbreaks. Trade-offs: While on the one hand supporting a sufficient level of detail, a model to be used in the management of an influenza outbreak must also deal with the imperfections of the information available. In our model parameters are made explicit to allow manipulation and the model facilitates multiple executions with different parameter settings. For instance, the number of infectious persons circulating in a community at a particular point in time is typically not known. Hypothetically, this number could be estimated from the number of cases of influenza-like-infections (ILIs) treated at local health facilities or even from purchases at local pharmacies. Depending on the reporting procedures and the technical infrastructure employed, this information may suffer from varying degrees of incompleteness, uncertainty, and delay. Incomplete information forces the user of the model to specify parameter values based on assumptions and estimates. As more information becomes available, the model must therefore allow assumptions and estimates to be refined or removed. To explore the sensitivity of the model and to identify a range of possible outcomes, a user needs to run the model repeatedly with different parameters. Delayed information may here seriously undermine the results of simulations. There is thus a need to easily be able to reevaluate the situation taking into account the new information, even if it pertains to an earlier point in time.
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Design issue: Population model Techniques: Data describing the number of inhabitants and the number and types of schools in Swedish municipalities are retrieved from Statistics Sweden’s on-line database (http://www.scb.se). For each municipality populations are stochastically generated on the basis of that data. Family units are generated and assigned to neighbourhoods of approximately 500 people. A family unit is a group of up to seven persons living together, with one or two adults. Each person has an age, a disease status indicator, and a vaccination status indicator. Day-care centres, elementary schools, and middle schools are assigned to school districts, with one middle school and a number of elementary schools and day-care centers, on the basis of school data. Each neighbourhood belongs to a school district. Preschool-aged children are assigned to either neighbourhood playgroups (2-4 children) or day-care centers (20-40 children). School-aged children are assigned to an elementary school, middle school, or high school on the basis of their age. All neighbourhoods share the same set of high schools. Trade-offs: Acquiring data for the same population variables from different municipalities was found to be a major problem. Given the degree of freedom provided to municipal governments, municipalities vary with regard to what population data that is regularly collected. Therefore, by relaxing the level data stratification, simplifications were introduced in the population description. For instance, the age distribution of children was assumed to be uniform over the intervals 0–5 years and 6–18 years of age. Young adults (19–64 years) and older adults (>64 years) were also assumed to be uniformly distributed within their respective age groups.
Discussion The aim of this study was to analyze the design of a simulation environment for prediction of influenza transmission in local communities with different socio-economic composure. We found that making balanced tradeoffs between model detail and system effectiveness in a real-world public health setting is essential in the design of such environments, e.g. between a focus on algorithm validity vs. model adaptability, and specificity in population description vs. the possibility to generalize the results. In addition, we calculated the basic reproductive numbers for influenza transmission in a set of Swedish municipalities. These numbers can be used proactively to identify communities where influenza outbreaks may become rapidly destructive or where particular intervention methods are likely to fail. The study has important limitations that must be considered in light of the results. The simulation model is dependent on a reliable supply of surveillance data on influenza occurrence in the community. However, recent reviews indicate that clinical findings only identify patients with influenza-like symptoms but are not useful for confirming the disease [20]. The modeling environment is thus dependent upon an efficient microbiological laboratory system. Moreover, many epi-
demiological reporting systems are designed with regard to infectious diseases with a long incubation period. Influenza has a short incubation period, which means that the surveillance methods and reporting systems [21] also have to be adjusted, if influenza simulation models are to be useful during ongoing outbreaks. While verification of a simulation program concerns whether the program runs as the developers expect it to, its validation refers to whether the simulation is an acceptable model of the real world [22]. Regarding verification, the present prototype was developed using repeated formative evaluations, from which the outputs were recorded and compared to both changes made and previous results. The code could in this way be improved, and the processing time be reduced by a factor of twenty. Two particular problems with validating the output against public health data and practice were experienced during the development, both being related to the lack of empirical data from virus outbreaks in the communities under study. First, without such data, it is not possible to completely validate any of the models included in the simulation environment with regard to missing parameters. In other words, there may be critical factors during a future outbreak that are not reproduced in the models. Second, abstract models and outputs are difficult to use by public health practitioners in outbreak response programs. For instance, due the theoretical nature of the basic reproduction number, Ro, it has to be closely interpreted before it can be used to inform program actions, and it is also hard to identify empirical data sets for its validation, Modeling of community characteristics is a central component in the simulation environment. During the design analysis, we found it necessary to critically evaluate the definition of ‘community’ in the context of epidemiological modeling. In the public health setting, ‘community’ is often defined by the geographical area covered by a particular unit or agency in terms of surveillance and interventions. However, it has been pointed out that ‘community’ may account for a broader range of aspects, from pure territory to transcendence to a holistic spirit throughout the population [23]. Between these levels, structures, values, rituals, and behaviours take hold. Clearly, many factors beyond geopolitical boundaries are important for influenza transmission and disease control. These factors are residing in the civic or social network level of community, e.g. inter-family contacts and willingness to adapt life-style in order to care for others. It is a challenge for further research to include also factors describing the more particular civic life in environments simulating transmission of contagious diseases. In summary, complex models of infectious disease transmission are today used to combine multi-source data to study equally complex outcomes. Even though these models can be simplified to calculation of the basic reproduction number, a theoretical concept describing the average number of people expected to become infected when an infectious person enters a totally susceptible population [24], the usability of such
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models for public health practitioners preparing for disease outbreaks and bioterrorist attacks has heretofore been limited [25]. In this study, we have displayed how a simulation environment can be useful for public health practitioners by proactively computing the basic reproductive number. We have also identified issues necessary to render the simulation models user friendly and effective in public health settings. Further research on population models for use in simulations of influenza outbreaks is particularly warranted.
Acknowledgments
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This work was supported by the Swedish Emergency Management Agency (KBM) under contract 0700/2004.
[15] Nicholson K, Webster R G, Hay AJ. Textbook of Influenza. Malden, Massachusetts: Blackwell Science, 1998.
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[email protected]
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