| Malaria is caused by a parasite called Plasmodium, which is transmitted via the bites of infected mosquitoes. Approximately half of the world’s population is at risk of malaria. To reduce malaria incidence, various control strategies have been taken. Among of these strategies, mathematical modeling would play a special role. Through the analysis of these models and model parameters, we can obtain some control strategies to reduce malaria prevalence and prevalence levels. In this paper, we consider the stability of mathematical model of malaria transmission with relapse. Further, a deterministic mathematical model for the co-infection of HIV and malaria is presented and analyzed.In Chapter1, we introduce the background and development situation of the subject, and give some theoretical tools and preliminaries serving the discussion in the paper.In Chapter2, a more realistic mathematical model of malaria transmission with relapse is introduced, the humans population is divided into susceptible, infected and recovered, mosquitoes into susceptible and infected, and assume that the recovered humans have low levels of parasite in their blood streams and can pass the infection to mosquitoes. The basic reproduction number R0is calculated by next generation matrix method. Then we prove the global stability of the disease-free equilibrium by construct Lyapunov function. Using the persistence theory of dynamical system to show the uniform persistence of the disease. At the same time, some numerical simulations are performed to illustrate our analytic results.In Chapter3, a deterministic mathematical model for the co-infection of HIV and malaria is constructed. A qualitative analysis about positivity, boundedness, existence, uniqueness of the model is carried out. There are three possible endemic equilibria:the case where there is HIV only, the case where there is malaria only and when both HIV and malaria co-exist. Finally, some numerical simulations are given to conform the analytic results. |
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