Stability Analysis Of Several Types Of Infectious Disease Models

Infectious disease model has been the main content of mathematical biology research,based on the dynamic analysis and numerical simulation can show the process of development of infectious diseases,propagation reveal and prediction of infectious diseases,analysis of the causes of disease outbreaks and the key factors,so as to find the optimal strategy for the prevention and control of infectious disease.The main contents of this paper are as follows:Firstly,a kind of hepatitis B virus model with CTL immunity is established,and the dynamic stability of the equilibrium point is analyzed,the threshold of disease prevalence is obtained,that is,the basic reproduction number Ro.When R₀ ? 1,by constructing Lyapunov function,it is proved that the disease-free equilibrium is globally asymptotically stable by using Lassalle invariance principle;When R₀?1,the system has a unique endemic equilibrium and is locally asymptotically stable at the local equilibrium point.Then,the theoretical results are verified by numerical simulation with appropriate parameters.Secondly,a class of hepatitis B virus model with delay and saturation incidence is studied.Considering the recovery rate of infected cells,the threshold of disease is determined R₀,by constructing Lyapunov function,The Hurwitz criterion is used to prove when R₀?1,for any delay,the disease-free equilibrium is globally asymptotically stable,at this point the disease died out.When R₀?1,the system has a unique endemic equilibrium and is locally asymptotically stable at the local equilibrium point.Then,the theoretical results are verified by numerical simulation with appropriate parameters.Finally,an epidemic model with nonlinear incidence rate is studied,the dynamic stability of the equilibrium point of the model is obtained,the threshold of disease is determined R₀.Assume that all inputs are susceptible,When R₀?1,by constructing Lyapunov function,it is proved that the disease-free equilibrium is globally asymptotically stable;When R₀?1,the system has a unique endemic equilibrium and is locally asymptotically stable at the local equilibrium point.The theoretical results are verified by numerical simulation with appropriate parameters.