On a Reaction-Diffusion Model of COVID-19

Nowadays mathematical models play a major role in epidemiology since they can help predicting the spreading and evolution of diseases. Many them are based on ODEs assumption that populations being studied homogenous sets fixed points (individuals) but actually far from people constantly moving. In fact, thanks to science progresses, distances no longer what used be past disease travel reach out even most remote places globe matter hours. HIV Covid-19 outbreaks perfect illustrations how fast now spread. When it comes studying spatio-temporal disease, instead dynamic Reaction-Diffusion ones best suited. They inspired by second Fick’s law physics getting more used. this article we make study COVID-19. We first present our SEIR model, find two equilibrium an expression for basic reproduction number (R0), use additive compound matrices show only one condition is necessary local stability like traditionally done, conditions DFE (Disease Free Equilibrium point) EE (Endemic globally asymptotically stable. Then construct diffusive model previous investigate existence traveling wave connecting monotone iterative method give minimal speed. last section remains stable when diffusion added whereas there will appearance Turing instability once added. The conclusion emphasizes importance barrier gestures fact tested better governments able handle tackle disease.