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Abstract: Mathematical modelling is playing an increasing role in developing an understanding of the dynamics of communicable disease and assisting the construction and implementation of intervention strategies. The threat of novel emergent pathogens in human and animal hosts implies the requirement for methods that can robustly estimate epidemiological parameters and provide forecasts. Here, a technique called variational data assimilation is introduced as a means of optimally melding dynamic epidemic models with epidemiological observations and data to provide forecasts and parameter estimates. Using data from a simulated epidemic process the method is used to estimate the start time of an epidemic, to provide a forecast of future epidemic behaviour and estimate the basic reproductive ratio. A feature of the method is that it uses a basic continuous-time SIR model, which is often the first point of departure for epidemiological modelling during the early stages of an outbreak. The method is illustrated by application to data gathered during an outbreak of influenza in a school environment. [Copyright &y& Elsevier]

Abstract: Recently, evidence has been presented to suggest that there are significant heterogeneities in the transmission of communicable diseases. Here, a stochastic simulation model of an epidemic process that allows for these heterogeneities is used to demonstrate the potentially considerable effect that heterogeneity of transmission will have on epidemic outbreak size distributions. Our simulation results agree well with approximations gained from the theory of branching processes. Outbreak size distributions have previously been used to infer basic epidemiological parameters. We show that if superspreading does occur then such distributions must be interpreted with care. The simulation results are discussed in relation to measles epidemics in isolated populations and in predominantly urban scenarios. The effect of three different disease control policies on outbreak size distributions are shown for varying levels of heterogeneity and disease control effort. [Copyright &y& Elsevier]