Spatial effects on viral disease in plankton system

Abstract

We consider a three dimensional mathematical model in virus infected phytoplankton and zooplankton system with the help of reaction-diffusion equations to study stability under diffusion. The analytical explanation provide for understanding phytoplankton dynamics with three population classes: susceptible phytoplankton (P_s), infected phytoplankton (P_i) and zooplankton (Z). In this model we assume that the rate of disease transmission by including a saturation effect for higher number of infective in place of mass action law. Our aim is to provide a qualitative analysis of the system without diffusion and with diffusion. We also study global stability of positive equilibrium point by using LaSalle's principle. The analytical findings are supported by the numerical results. It has been observed that incorporate of diffusion stabilize the system more rapidly. Also all the species coexist with homogeneous biomass distribution.