Stability Analysis Of Two Classes Of Infectious Disease Model With Transport-related Infection

With the development of society, infectious diseases pose a great threat to human beings. We can derive the conditions on the extinction or persistence of infectious disease by using the theory of differential equations. This provides an important theoretical basis for the precautions, prediction and control of infectious disease. This paper mainly study the following two classes of infectious disease models with transport-related infection.In first part, based on SIS infectious disease model,we consider the factors on the transport-related infection and nonlinear infectious rate)1/(iiiibISIS ++ i=)2,1(.By using the basic reproduction number and the eigenvalue of the linear system, we obtain threshold conditions on stability of the disease-free equilibrium and the endemic equilibrium effects. That is, if 10R￡, the disease-free equilibrium is locally and asymptotically stable; while the endemic equilibrium is locally and asymptotically stable if0 R >1.In second part, on the basis of the model given in the first part, we further consider two new groups including Healthy people( R) and infected person of the entry is isolation treatment(Q). We firstly establish the SIQRS infectious disease model by using the compartment model. The threshold conditions on local stability of the disease-free equilibrium and the endemic equilibrium are given.That is, if0 R <1, the disease-free equilibrium is locally and asymptotically stable; while the endemic equilibrium is locally and asymptotically stable if0 R >1.