In this paper, we present an extension of our novel microsimulation technique, as applied to biological infection spread, to estimate the underlying causal parameters driving an infectious process. The underlying simulation framework, Simulacron, was developed in order to understand the development and course of, response to and recovery from single and multiple threats on community populations. Such threats include a range of natural (such as disease spread in communities, fire, flood etc.) and manmade events (such as terrorism, including the use of biological agents, money laundering, smuggling as well as accidents etc.). These threats can cause serious disruption to modern society and the optimal approaches to prevention, mitigation, response and recovery are little understood. Furthermore, assumptions currently used cannot otherwise be readily tested.
A case study of the 1920 influenza outbreak at the Royal Naval School, Greenwich has previously been used to demonstrate the feasibility of the simulator. This case is well documented and has detailed information about the typical education schedules and the physical locations within the school as well as documentation on the disease spread. It also has the advantage of being a semi-closed environment with about 1,000 pupils at any one time in the school; a manageable size for simulation on a single processor. One significant issue which arose during this study is the difficulty of equating traditional epidemiological measures of disease virulence (reproduction number, etc.) with the causal parameters (infection timings, cross-infection probability, etc.) used in our model This paper describes two programs, developed for use with the simulator, to estimate the causal parameters that best fit these traditional measures. Refinery, given an initial range for each causal parameter, performs Monte Carlo sampling to produce a set of candidate parameter instances. Refinery then performs simulated annealing in order to refine the causal parameter estimate ranges. Monotony then performs multiple simulations tor each of these instances, varying only in random seed. Once complete, values for the statistical measures are computed for each instance.
Three results from the simulation in which the infection parameters and the number of Susceptibles in the population were chosen randomly from a normal population are shown in Figure I. The 1920 outbreak is superimposed assuming one infection cycle as an offset. It is possible that one case went undetected prior to the historical observations of the outbreak in those runs shown. The mean time to isolation from infection was 41.7±0.2 hours and the mean time to infection by a person already infected was 30.2±2.9 hours.
The reproduction number calculated by this method agrees with a simple SIR calculation on the historical data. The simulation gives an average hero time of 7 hours before discovery and isolation. As a result the infectious time is 22 hours which is similar to the 24 hours in the literature. The one parameter that does not match assumptions on influenza data is the latent time. The simulation is giving a value of 20 hours compared to literature values of 35 to 45 hours. Figure Ib shows the minimum fitness as a function of latent and asymptomatic times indicating that the results obtained sit in a minimum that practically rules out other values for the latent time.