Modeling And Analysis On Dengue Fever Dynamics With Re-infection And Age-structure

Dengue fever and malaria are infectious diseases caused by vector-borne viruses in tropical and subtropical areas around the world.The World Health Organization(WHO)report shows that about 390 million people are infected with dengue virus annually,of which 1/3 are asymptomatic.The repeated infection for asymptomatically infected persons and different strains poses an important challenge to control the spread of dengue fever.As an important tool for people to predict and analyze the development trend of infectious diseases,mathematical model has been widely used in the prevention and control of dengue fever.This paper mainly uses the theories of age structured epidemic dynamic system and numerical simulation to explore the dynamic characteristics of a kind of model with repeated infection in the transmission of dengue fever.The main contents are as follows:In chapter 1,we mainly introduces the significance and research status of modeling of vector-borne diseases such as dengue fever,as well as some basic mathematical knowledge involved.In chapter 2,according to the characteristics of repeated infection of different strains of dengue fever and the influence of infection age on the disease transmission dynamics,we established a two-strain dengue fever dynamics model with repeated infection and infection age.In the model,we first give the threshold reproduction number of strain prevalent in the system,and analyze the condition of strain eradication and existence of strain dominance equilibrium in the system.Secondly,the global asymptotic stability of the disease-free equilibrium state,the local asymptotic stability of the dominant strain equilibrium and the uniform persistence of the disease in the system are proved,and the conditions for the establishment of the competitive exclusion principle of the strain in the system are given.Finally,the existence of the coexistence equilibrium state of strains in the system is briefly discussed.In chapter 3,according to the characteristics of the population's susceptibility and recovery ability,which depend on the physiological age of the population,combined with the role of asymptomatic infections in the process of disease transmission,a dengue fever model with repeated infection and the physiological age of the population was established.Firstly,the model is normalized,the basic reproduction number of disease is analyzed and given,and the locally and globally asymptotic stability of disease-free equilibrium are proved.Secondly,we explore the existence conditions of the endemic equilibrium diseases in the system,and give the necessary conditions for the occurrence of backward bifurcation in the system.Finally,we use MATLAB to verify our theoretical results.