Existence Of Traveling Wave Solutions For Two Kinds Of Hantavirus Transmission Models

This paper is divided into four chapters and mainly studies the existence of traveling wave solutions of two kinds of hantavirus transmission models.In Chapter 1,we introduces the research background,related developments and some existing research results of Hantavirus transmission model,and then elaborates the research work of this paper.In Chapter 2,Hantavirus transmission model with reaction-diffusion considering killing factors was studied where S(t,x),I(t,x)are the densities of susceptible mice and infected mice at t time,x position respectively,N=S+I,d is the diffusion rate of mice,b is the natural birth rate of mice,d0 is the natural mortality rate of mice,e is the hunting rate,K is the environmental capacity,? is the transmission coefficient of infected mice to susceptible mice.b,d,d0,e,K,? are all positive constants and 6>d0+e.The existence of traveling wave solutions for non-monotone systems can be studied by using Schauder s fixed point theorem and analytical techniques[1].We'll take a similar approach and give our main conclusions of system(1).The existence of traveling wave solutions is obtained by Schauder's fixed point theorem and the minimal wave speed is given.The nonexistence of traveling wave solutions is obtained by introducing a negative one-sided Laplace transform.In Chapter 3,we consider the effect of viruses in the environment on the transmission of hantavirus,a model of Hantavirus transmission with reaction-diffusion under indirect infection was studied where S(t,x)and I(t,x)are the densities of susceptible mice and infected mice at t time,x position respectively,N(t,x)is the total number of mice,N=S +I.D1 and D2 are the diffusion rates of susceptible mice and infected mice,b1 is the natural birth rate of mice and d1 is the natural mortality rate of mice,d2 is the hunting rate of humans to mice,d3 is the mortality due to illness,d4 is the mortality of viruses in the environment,K is the environmental capacity,?I is the transmission coefficient of infected mice to susceptible mice,?W is the infection rate of the virus carried in the environment to susceptible mice,m is the conversion rates.D1,D2,b1,d1,d2,d3,d4,K,?I,?W m are all positive constants.In this chapter,we will prove the existence and nonexistence of traveling wave solutions by using Schauder fixed point theorem and negative one-sided Laplace,and the model is simulated numerically.Chapter 4 Summarize the results of the previous two chapters and give the direction of the the future research.