The Research On A Wild-type And Drug-resistant HIV Infection Model

Infectious diseases have always been a threat to human health since ancient times.It is reported that about a quarter of the world's deaths are caused by infectious diseases every year.Hence,understanding the mechanism of the diffusion of infectious virus plays an important role in the prevention and control of virus transmission.This paper has investigated the global dynamic behavior in a wild-type and drug-resistant HIV infection model.The main contents and frame of the article is as follows:1.In the first part(Section 2),a wild-type and drug-resistant HIV infection model with saturated incidence is established,and the wild-type strain can mutate and become drug-resistant during the process of reverse transcription(SR conver-sion,for short).Firstly,the positivity and boundedness of solutions of model are established,and the basic reproduction number is also obtained.Then the thresh-old condition of the existence of equilibria is established.The threshold criteria on the local and global stability of equilibria and the uniform persistence of model are gained by using the linearization method,Lyapunov functional method and the theory of persistence in dynamical systems.Lastly,the main results show that if the saturation coefficients are zero,then there is competitive exclusion mechanism in wild-type and drug-resistant strains when there is not SR conversion.That is,the drug-resistant can not invade the wild-type strain if drug-resistant strain re-production number R_r less than the wild-type strain reproduction number R_s,and otherwise,the drug-resistant strain is able to invade and out-compete the wild-type strain;if both saturation coefficients are not zero,then there is not only the com-petitive exclusion mechanism,but also the global coexistence phenomenon in wild-type and drug-resistant strains.When there is SR conversion,the model may have positive equilibria which is globally asymptotically stable,and using the numerical examples to verify the correctness of theorem and the rationality of inference.2.In the second part(Section 3),the wild-type and drug-resistant strain HIV infection model with saturated incidence and distributed latent delay is established.Firstly,the delays T_s and T_r,representing the incubation period of wild-type and drug-resistant strains infect susceptible cells in the host,respectively.The positivity and boundedness of solutions for model are established by comparison principle and method of variation of constants,the threshold conditions for the existence of equilibria are further obtained according to the basic reproduction numbers.Then the threshold criterion on the local and global stability of equilibria are established by using the linearization method and the Lyapunov functional.The main results show that there is not only the competitive exclusion,but also the global coexistence phenomenon in wild-type and drug-resistant strains when there is not SR conversion.The threshold condition on the uniform persistence of model is obtained by the theory of persistence in dynamical systems when there is SR conversion.Lastly,the numerical simulation verifies the correctness of the conclusion.