Analysis Of A Multi-state HIV Model With Incomplete Vaccine Immunization

AIDS has been a major global public health problem since its emergence in the1980s.HIV-infected individuals go through multiple stages of infection,ranging from years to decades.An effective vaccine can curb the AIDS pandemic,therefore,combining the national and international research results on HIV model transfer analysis,this paper aims to explore the model analysis of multiple infection states when vaccine efficacy is limited.Traditional model analysis usually considers three stages of HIV infection,namelyI₁,I₂ and AIDS stages,in which susceptible individuals who are not vaccinated and susceptible individuals who are vaccinated but whose vaccine protection has diminished or even failed may enter stageI₁ due to infection,and stageI₁ may progress to stageI₂ as the disease progresses.At the same time,patients may regress from stageI₂ toI₁ with drug intervention and remission,and may repeat between stagesI₁ andI₂ several times.However,once the patient enters the AIDS stage,he or she cannot regress to the two previous stages,which means that the patient is in a situation of terminal disease and can no longer be treated by any means.This model takes into account too few stages of disease progression and does not fully match the objective facts of pathology,so it needs to be expanded.In this paper,a multi-stage HIV model is developed and used to analyze the potential impact of a non-complete vaccine immunization.It is known from medical fundamentals that a vaccine has several desirable properties such as prevention of infection,bypassing the primary infection stage,and therapeutic effects that alter the infection status of the disease,such as a vaccine that reverses AIDS from the final stage of development to the asymptomatic stage.This model first briefly describes the model parameters and builds the model,and verifies the good definition and positive invariance of the model in turn.The concept of basic reproduction number is further introduced using the next generation matrix approach.Following that,the Lyapunov function is used to demonstrate that the multi-infection stage model has a globally asymptotically stable disease-free equilibrium solution when the basic reproduction number is less than one.In addition,the multi-infection stage model has a unique local equilibrium solution when the basic reproduction number is greater than 1.And under certain assumption restrictions,this local equilibrium solution is globally asymptotically stable.The epidemiological implication of these results is that a non-complete vaccine could eliminate HIV from an area if it could keep the basic reproduction number below 1;otherwise,when time tends to infinity,the infected population would persist in the population at a constant rate for a long time.In addition,an HIV vaccine would allow vaccinated individuals to bypass primary infection,thereby reducing the prevalence of HIV and producing a positive therapeutic effect.