A numerical study on an influenza epidemic model with vaccination and diffusion

A vaccinated diffusive compartmental epidemic model is developed to explore the impact of vaccination as well as diffusion on the transmission dynamics of influenza. The basic reproduction numbers with and without vaccination are obtained. Sensitivity analysis of the reproduction number based on parameters involved in the system has been investigated. Stability analysis of the points of equilibrium has also been investigated. Using the combined effect of the vaccine efficacy and vaccination rate, the model is analysed to determine criteria for control of influenza epidemic. The roles of vaccine efficacy and vaccination rate are compared. It is shown that higher levels of vaccine efficacy and vaccination rate lead to a decrease in the epidemic size. It is also shown that an accurate estimation of the efficiency of vaccine is necessary to control the spread of influenza and thus vaccination strategy needs to be implemented carefully.