Fractional Model Analysis Of A HIV Model With Cell-to-cell Transmission

AIDS is an infectious disease in the late stage of individual infection with human immunodeficiency virus（HIV）.HIV can attack CD4⁺T cells in two ways:virus-cell and cell-to-cell,resulting in different degrees of immune deficiency in human body.In recent years,the use of fractional-order to study virus dynamics models has attracted widespread attention from researchers.Compared with integer-order models,fractional-order differential equations have the characteristics of describing memory and genetic material,which provides a new direction for describing HIV dynamics with memory transmission process.Therefore,this thesis establishes and studies two kinds of fractional-order HIV infection kinetic models with intercellular transmission.The main contents are as follows:In Chapter 1,we introduce the basics and significance of HIV dynamics and fractional-order differential equation,the current status of research,and relevant background.In Chapter 2,considering that susceptible cells have Logistic proliferation and latently infected cells,we develop a fractional-order HIV model with cell-to-cell transmission and Logistic proliferation.Firstly,the existence,uniqueness,positivity and boundedness of the solution are proved.Secondly,the global stability and consistent persistence of the disease-free equilibrium point of the model are proved.Thirdly,the discrete numerical schemes of the three operators are given,and the sensitivity of the basic reproduction number of the model is performed by PRCCs.Finally,the theoretical results are illustrated by numerical simulation.In Chapter 3,by asssuming different degrees of attenuation rates of the virus,we establish a fractional-order HIV model with antibody immunity and cell-to-cell transmission.Firstly,the positive and boundedness of the model’s solution are proved.Secondly,we define the basic reproduction number R₀^*and immune reproduction number R_Aof the model,and prove that the model has three equilibrium points,infection-free equilibrium point P₀,immune-free equilibrium point P₁ and immune equilibrium point P₂.We study the global stability of the model’s equilibrium point.Again,these theoretical results are demonstrated with numerical simulations.