Dynamics of a time fractional order spatio-temporal [formula omitted] with vaccination and temporary immunity

Abstract

The principal aim of this work it to study and analyze a spatio-temporal fractional Susceptible–Infected–Recovered SIR infection model. We will assume vaccination of susceptible population as well as the temporary immunity of the recovered. The dynamics of the infection is described by three partial differential equations with a fractional derivative order and diffusion for each equation. First, we will prove the existence, uniqueness and boundedness of the solutions. The infection-free equilibrium point and the endemic equilibrium point have been presented as function of the basic reproduction number R0. Next, we will concluded that the local stability of the each equilibrium depends mainly on the basic reproduction number. Finally, the theoretical results are verified by numerical simulations.