Mathematical Analysis Of A Kind Of Spreading Malaria Model With Mosquito Net Usage Rate

Malaria is one of the most serious mosquito-borne infectious diseases,according to the World Heath Organization(WHO),about 3.4 billion people around the world are at risk of malaria infection.For mosquito-borne diseases such as malaria,medical reasons for the disease and the characteristics of the virus can be studied,measures such as improving treatment and new vaccines are being used to treat infected people,but these studies and treatments often lag behind the spread and outbreak of disease.To predict,control,and even eliminate such infections,we need to understand the spread of malaria,we also need to know how malaria continues to survive in the population and how to control disease incidence at a certain level.Based on the traditional SIS v.s.SI model of malaria,this paper studies the influence of self-protective factors on the spread of malaria.In the build of the model,we use the bed nets as a measure of protection,together with the basic reproduction number,we analyze the transmission dynamics of the malaria virus.The dissertation contains five chapters.Chapter 1 introduces the background and research status concerning the development of malaria modeling,as well as the inspiration of research problems.Also,the main contents of this paper are briefly introduced.Chapter 2 is devoted to the malaria model with mosquito net utilization in homogeneous space,the basic reproduction number is proposed by using the next generation matrix method.With the help of characteristic equation,we obtain the local stability of the disease-free equilibrium and the endemic equilibrium.The global stability of the disease-free equilibrium and the endemic equilibrium under a certain conditions is obtained by constructing the Lyapunov function and the upper and lower solutions method respectively.Chapter 3 deals with the diffusion malaria model with the use of the bed nets in a heterogeneous environment.The expression of the basic reproduction number is given by the characteristic problem of the corresponding linear equation.The local and global stability of the disease-free equilibrium and the endemic equilibrium is discussed.In Chapter 4,numerical simulations(with Matlab)have been given to both of the malaria models with mosquito net utilization in homogeneous environment and the diffusive malaria model in heterogeneous environment.Graphs have been plotted to verify the theoretical conclusions.In Chapter 5,the major contents of the problems discussed above are summarized,and ecological explanations to the corresponding research outputs are provided.Some further problems related to the topic is also discussed.