Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study

A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.