Schistosomiasis Transmission Model With The Effects Of Immigration And Reinfection

In this paper,we study mostly mathematical models of schistosomiasis.The first is the model of the schistosomiasis transmission in two susceptible groups,including bilinear incidence rate and standard incidence rate.The second is the effects of reinfection for schistosomiasis transmission model and its optimal control.Because the different impact of immigration and local population on the schistosomiasis transmission,in the second chapter we establish the mathe-matical model of the bilinear incidence of schistosomiasis in two susceptible groups,the existence of equilibrium and the stability are studied.Sensitivity analysis are conducted for the impact of the initial value of the two type sus-ceptible on the threshold value,the theoretical results are confirmed by some numerical simulations.In the third chapter we establish the mathematical model of the standard incidence of schistosomiasis in two susceptible groups,since the existence of equilibrium is very complex,in this chapter,by using inequality techniques are used to discuss the existence of endemic equilibrium and the results are confirmed by the center manifold theory.In the fourth chapter,based on the actual data about the reinfection phenomenon in the recovery,a model of schistosomiasis is established.The basic reproduction number is calculated,the existence of endemic equilibrium and stability of the disease free equilibrium are studied.Subsequently,we present the corresponding optimal control problem and obtain the optimal solution.Through sensitivity analysis of reinfection,the result shows that the greater the rate of reinfection,the number of patients with schistosomiasis will be more and more.In addition,a large number of numerical simulations show that to reduce human and snail contact and to control snail are better to control the transmission of schistosomiasis.Among them,to control snail is the best.