The Existence Of Traveling Wave Solutions Of A Class Of Cholera Model

Cholera is a very serious infectious disease.It is of great theoretical significance and application value to characterize the transmission mechanism of cholera by reaction-diffusion equation.Aiming at the cholera epidemic problem in Haiti,the existence and nonexistence of traveling wave solutions for a class of reaction-diffusion SIRW are studied by using qualitative,stability theory,Schauder fixed point theorem and Laplace transformation.The specific research content is as follows:Firstly,by constructing appropriate upper and lower solutions and using Schauder fixed point theorem,the existence of traveling wave solutions is obtained,and then the existence of weak traveling wave solutions is obtained by using the persistence theory.Secondly,by constructing appropriate Lyapunov functional,the existence of strong wave solutions of the system under certain conditions is obtained.Finally,Laplace transform is used to prove that,under certain conditions,traveling wave solutions do not exist.The above research results provide theoretical reference for people to better understand the transmission mechanism of such infectious diseases.