Research On An Age-infection-structured HIV Model With Antiretroviral Therapy

Infectious diseases are diseases caused by viruses or bacteria,and can spread among a population,it is characterized by easy outbreak,fast transmission rate and great harm to health.It threatens the survival of human beings and brings huge losses to social economy.Therefore,it is a necessary and arduous task to control the epidemic of infectious diseases.AIDS is a very harmful infectious disease,caused by infection with HIV,its characteristic is that the infectivity of infected individuals is affected by the age of infection and anti-drug therapy.Currently,there is no effective vaccine against AIDS,one of the effective ways is antiretroviral therapy,it can effectively and long-term inhibit human immunodeficiency virus?HIV?infection.This paper is based on the characteristics of the spread of AIDS,the crowd is divided into three categories:susceptible class,infection class and pathogenesis class,and HIV models with age of infection and antiretroviral therapy is established.The existence and uniqueness of the system solutions are proved by using the semigroup theory of bounded operators.By constructing Lyapunov function,the stability of infection-free steady state and infection steady state is discussed.It is proved that if R₀?1,the infection-free steady state is globally asymptotically stable.And get if R₀>1,the infection steady state is globally asymptotically stable.