Dynamics Modeling And Analysis Of Mosquito-Borne Diseases With Immunity And Age Structure

Vector-borne diseases are caused by parasites,viruses and bacteria transmitted by mosquitoes,ticks and lice.Every year,vector-borne infectious diseases such as malaria,dengue fever and schistosomiasis cause more than 700,000 deaths worldwide,placing a huge burden on global public health.There is still a lack of effective vaccines for many vector-borne infectious diseases.Therefore,the spread of vector diseases brings a great threat to human life and health.Mathematical models play a more and more important role in correctly understanding the law of disease transmission,preventing and controlling the occurrence of diseases.In this paper,the dynamic model of malaria transmission is established by using the theory and method of age-structured infectious disease dynamics,and the dynamic characteristics of disease transmission in the system are analyzed.The specific contents are as follows:In the first chapter,the research background and related basic knowledge of this paper are introduced.In the second chapter,according to the infectivity and transmission characteristics of malaria,the immune response in the host,and the growth process of malaria parasite in mosquitoes,a kind of immune-infectious disease dynamics model with age structure is established in this chapter.By using the theory and method of infectious disease dynamics,firstly,the immune regeneration number in the host and the basic reproduction number to control malaria transmission are obtained.Secondly,the global dynamics of the model is analyzed,and the threshold dynamics of malaria transmission is obtained.Finally,the effects of the immune dynamics in the host and the disease dynamics in mosquitoes on the disease transmission in the population are analyzed,and the conditions for the sustainable survival of the disease are obtained.In the third chapter,according to the characteristics of vector-transmitted diseases,firstly,the dynamics model of vector-borne diseases with infection age is analyzed by using the age-structured dynamics theory and methods of infectious diseases and the methods and techniques of constructing appropriate Lyaunov functions,and the dynamics of threshold for controlling the spread of vector-borne diseases is obtained,that is,when the basic reproductive number R0> 1,the endemic equilibrium in the system is globally asymptotically stable,and when R0< 1,the uninfected equilibrium in the system is globally asymptotically stable.At the same time,the persistence of diseases in the system is obtained by using the persistence theory of infinite dimensional dynamical systems when the basic reproductive number R0> 1.Secondly,the vector infectious disease model with susceptible age is modeled and studied,the dynamic characteristics of the system are studied by using similar theories and methods,and the influence of direct transmission between hosts on mosquito-borne diseases is analyzed.Finally,the biological significance of the conclusion is expounded.