Time fractional order spatio-temporal $SIR$ model with therapy: Global analysis

Résumé

In this work, we will study a time fractional order spatio-temporal $SIR$ model with therapy and vaccination. The model is described by a system of reaction-diffusion equations incorporating a fractional derivative. The therapy will be added to the model in order to describe the effect of treatment on the population dynamics. The existence, boundedness and uniqueness of the solution are proved. The global stability of the equilibria is established. Numerical simulations are curried out in order to show the equilibria stability and the effect of therapy.