A Class Of Epidemic Models With Dispersal

In this paper, the basic concepts on epidemic models and the method of modeling an SIS epidemic model are introduced briefly, two SIS epidemic models with dispersal are established on different demographic and epidemiological assumptions. And, these models are studied and analyzed by the limiting system theory, Liapunov function, Dulac criterion, and so on.For the first model, based on the assumptions that the per capita birth rate is a Logistic function and the per capita natural death rate is a constant, and that the infected individuals can not disperse and breed offsprings, the disease incidence is bilinear. The conditions of the global asymptotical stability of the disease-free equilibrium and endemic equilibrium are studied. The uniform persistence of the system is proved. The basic reproduction number, R₀, is obtained for the Model. And besides, the theoretical conclusions are used in numerical computation. The results of numerical computation show that the changes of the dispersal rate can make the threshold change from less than one to more than one. While if R₀ > 1, then the infectious disease exists persistently under some appropriate conditions, which shows that even if the infected individuals are strictly restricted, the changes of the dispersal rate can result in prevailing of the disease. For the second model, based on the assumptions that the infected individuals can disperse and their newborn infants are not infected, the disease incidence is a standard type. The sufficient conditions of the global asymptotical stability of the disease free equilibrium and endemic equilibrium of the system are gained.