GLOBAL ANALYSIS OF A TIME-FRACTIONAL ORDER IN SPATIO-TEMPORAL BASIC VIRUS DYNAMIC MODELING

Abstract

The main objective of this study is to investigate and analyze a spatio-temporalmodel of viral infection including a fractional derivative order. This model represents the dynamics of infection through partial differential equations integrating spatial diffusion todepict the spread of viruses. We assume in our model, the diusion of the free viruses. First,we establish the existence, uniqueness and limits of solutions. The infection-free equilibrium points and the endemic equilibrium point are given in terms of the basic reproduction number. We conclude then that the overall stability of each equilibrium is mainly determined by this number. After validating our the oretical results by numerical simulations, we also madea numerical comparison between two schemes: one using a normal derivative and the other using a fractional derivative. It has been observed that the order of fractional derivatives has no impact on the stability of equilibria, but only on the speed of convergence towards stable states.