Asymptotic Behavior Of A Stochastic Hepatitis C Virus Infection Model With Mixed Switching

Globally,hepatitis C viral disease is one of the main causes of human morbidity and death.However,in real life,the spread and evolution of hepatitis C infection virus is often disturbed by various random factors,such as environmental temperature,humidity,seasonal changes and other factors.Therefore,study the dynamics of random factors on the hepatitis C infection virus model The influence of the nature of science has certain theoretical and practical significance.This paper uses stochastic differential equations,Markov chains,and stochastic analysis to study the asymptotic behavior of random hepatitis C infection virus models.The first chapter mainly introduces the relevant background and significance of the random hepatitis C virus infection model,as well as some prerequisite knowledge for the study.The second chapter mainly studies the extinction and persistence of the stochastic hep-atitis C virus infection model(HCV model)with mixed switching.First,the existence and uniqueness of the solution of the stochastic HCV model is proved;secondly,the existence and uniqueness of the invariant probability measure of the stochastic HCV model is proved by using the Feller property,the invariant control set and the Krylov-Bogoliubov's theorem.Finally,using the strong ergodicity theorem,the Borel-Cantelli lemma and the iterative logarithm law and other theories,the conditions for the extinction and persistence of the stochastic HCV model are obtained.The third chapter mainly studies the progressive nature of the random hepatitis C virus infection model with mixed switching.First,By constructing a N-truncated process,using Ito's lemma and control convergence theorem and other theories,it is proved that the stochastic HCV model has a strong Feller property;Secondly,the Lyapunov exponential function was cleverly constructed,and the generalized Ito's formula,strong Markov property and strong Feller property and other related theories were used to prove that the stochastic HCV model has recurrence;Finally,using the characteristic function and mixed diffusion theory and other related knowledge,the conditions for the stochastic HCV model to have positive recurrence and zero recurrence are obtained.