Dynamic Model Analysis Of Acute And Chronic Infectious Diseases

The article sets up two models.According to the transmission feature of acute and chronic diseases,a model of hepatitis C with two stages of acute infection and chronic infection is established.In addition,an acute and chronic infectious disease model with time delay is also built.We analyze models by using the Routh-Hurwitz criterion and the Lyapunov function method.Details as follows:First part,in the light of characteristics of hepatitis C virus infection.Acute hepatitis C patients could step into the recovered class,for which it could eliminate the virus by themselves.On the contrary,patients with chronic hepatitis C,which could not automatically eliminate the virus,could not enter into the recovered class,so the hepatitis C patients eventually develop cirrhosis or liver cancer.Therefore,an epidemiological model of hepatitis C with acute and chronic stages is established.We calculate the basic reproduction number of the model,and the stability of the model is analyzed by using Routh-Hurwitz criterion and constructing V function.Second part,to study the transmission mechanism of diseases,a delay model with acute and chronic infectious diseases is built.Compared with the typical dynamic model of HCV infection,this paper introduces two time delays.One describes the required time for a susceptible person to become an acute or chronic infected person;the other describes that time it takes for an acute infected person to become a chronic infected person.We obtained the basic reproductive number of the model.According to the stability theory of delay differential equations,the existence and uniqueness of solutions are testifid.The global appeal of the equilibrium point is obtained by constructing proper Lyapunov function and through the hypothesis model.