Numerical study of an influenza epidemic dynamical model with diffusion

In this paper, a deterministic model is formulated in the aim of performing a thorough investigation of the transmission dynamics of inuenza. The main advantage of our model compared to existing models is that it takes into account the effects of hospitalization as well as the diffusion. The proposed model consisting of a dynamical system of partial differential equations with diffusion terms is numerically solved using fast and accurate numerical techniques for partial differential equations. Furthermore, the basic reproduction number that guarantees the local stability of disease-free steady state without diffusion term is calculated. Various numerical simulation for different values of the model input parameters are finally presented in order to show the effect of the effective contact rate on the steady state of the different population compartments.