Behavior Analysis Of HTLV-? Infection Model With Stochastic Perturbations

Human T-cell leukaemia virus type-I(HTLV-?)is a human retrovirus that mainly infects CD4+T cells.HTLV-? is the causative agent of HTLV-?-associated myelopathy/tropical spastic paraplegia(HAM/TSP),adult leukemia and other eyes diseases.The pathogenesis of HTLV-? is still unclear,and there is no effective treatment,which poses a serious threat to human health.Therefore,studying the HTLV-? infection model with stochastic perturbations has practical significance.This article focuses on the following three parts:(1)The general HTLV-? infection model assumes that healthy CD4+T cells enter the blood at a constant rate l,which is reasonable only if the virus spreads faster and the host's environment remains unchanged.Therefore,it is more realistic to consider the growth of healthy cells in Logistic form.A HTLV-? infection model with Logistic growth and nonlinear immune response is established.The basic reproduction number0 R and the basic reproduction number1 R are obtained.The existence conditions of equilibrium are discussed by analysis.The global asymptotic stability of the equilibrium is obtained by Liapunov function.Numerical simulation further proves our results.(2)Due to the differences in constitution,living environment and medical treatment degree of HTLV-? infected patients;the stochastic model is more close to the actual situation of human body infected with HTLV-? infection.Based on the deterministic model of previous part,the stochastic perturbations are introduced,and a HTLV-? infection stochastic model is established.Firstly,the global existence and uniqueness of the positive solution of the model are proved by the It(?) formula and Liapunov function method.Then the extinction of the infected cells is studied.Finally,the sufficient conditions for the stable distribution of the model are obtained by the ergodic theory.(3)With the further development of scientific research,it has been found that healthy CD4+T cells remain latent after being infected by the virus,and are converted into infected cells only after transcription activation.Therefore,a four-dimensional HTLV-? infection model with nonlinear immune response and latent period is established.Based on the deterministic model,the stochastic perturbations are introduced and the stochastic model is studied.The existence and uniqueness of the positive solution of the model are given,and the sufficient conditions for the extinction of infected cells are obtained.Finally,the stochastic model has a stable distribution and it is ergodicity.