Study On Pattern Formations Of Epidemic Models Using Reaction-diffusion

Epidemic models using reaction-diffusion is to predict how diseases distribute in thespace and how they transit in the space. This paper investigates the pattern formation ofthree different types of epidemic models with space structures.In the first chapter, we give the significance about investigating epidemic models usingreaction-diffusion and present the previous work on it. Also, we give the main work in thispaper.In the second chapter, we investigate an epidemic model with nonlinear incidence rates.We obtain the Hopf and Turing critical line and give the exact Turing space. By usingcomputer simulations, we get rich spatial dynamics including spotted, stripe and coexistenceof the both.In the third chapter, we study an epidemic model with nonlinear incidence rates in-cluding crowding effects. By using mathematical analysis and computer simulations, we findsuch model has stationary pattern.In the fourth chapter, we investigate the effect of noise on epidemic models. We findthat, as the noise intensity increases, the direction of the pattern changes. Also, we showthe space-time plot and time series with respect to noise intensity.