Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea

• We present stochastic methods for computation of influenza transmission models.
• We use the moment closure method that reduces computational load much.
• We find quantitative differences between deterministic and stochastic solutions.
• We investigate the impact of various vaccination and antiviral treatment scenarios.

In this paper, we present stochastic methods for computation of influenza transmission models. First, SEIR type deterministic epidemiological models are revisited and stochastic modeling for those models are introduced. The main motivation of our work is to present computational methods of the stochastic epidemic models. In particular, the moment closure method (MCM) is developed for some influenza models and compared with the results under the standard stochastic simulation algorithm (SSA). All epidemic outcomes including the peak size, the peak timing and the final epidemic size of both methods are in a good agreement, however, the MCM has reduced the computational time and costs significantly. Next, the MCM has been employed to model the 2009 H1N1 influenza transmission dynamics in South Korea. The influenza outcomes are compared under the standard deterministic approach and the stochastic approach (MCM). Our results show that there is a considerable discrepancy between the results of stochastic and deterministic models especially when a small number of infective individuals is present initially. Lastly, we investigate the effectiveness of control policies such as vaccination and antiviral treatment under various scenarios.