艾滋病动力学模型的稳定性分析

AbstractAIDS has become now the medical history of more concern of the infectious disease.In recent years,caused by HIV AIDS infection is increasing and the death rate is very high,so the prevention and treatment of AIDS is also always people to explore and researchhotspot.In this context,the establishment and analysis of important value for the study ofAIDS model always,it is also a hot topic of concern,different scientists committed toresearch its mechanism from different angles,in the aspects of the model.The mathematicalmethod has become an important tool in the research of infectious diseasesThe first two chapters of this article mainly describe the research background,researchsignificance and research status of AIDS,and introduce the general propagation model ofinfectious diseases and some basic theoretical knowledge neededThe third chapter studies the stability of a class of SEI model with latent period ofAIDS,divides people susceptible to lurk,and infected.First of all,the application oftheoretical knowledge of the second chapter calculate the basic reproduction number,secondly,through Hurwitz criterion proved that the local stability of the disease-freeequilibrium and the endemic equilibrium.Finally,by constructing a Lyapunov function toprove the global stability of the disease-free equilibrium.Keywords:infectious diseases;AIDS;basic reproductive number;stability