Research On Several Classes Of Vector-borne Disease And COVID-19 Dynamic Models

In recent years,the prevention and control of the occurrence and prevalence of infectious diseases have been the goal of health organizations all over the world,especially vector-borne diseases such as dengue fever,malaria,cholera,yellow fever,west nile fever and the ongoing epidemic of COVID-19.As an important tool for quantitative study of infectious diseases,the dynamic model of infectious diseases has gradually received extensive attention from experts and scholars at home and abroad.Based on pathogen diversity,individual difference,seasonal impact,spatial heterogeneity and population mobility,this thesis establishes and in-depth studies three types of vector-borne disease models with age structure,seasonal influence and spatial spread,and a class of COVID-19 patch model to explore the impact of different control strategies on eliminating disease transmission.The full text can be summarized as follows:In the first chapter,we first introduce the hazards and transmission characteristics of some diseases,especially dengue fever,avian influenza and COVID-19.Secondly,the research status and problems of age structure infectious disease model,vector-borne infectious disease model with seasonal influence,spatial spread infectious disease model and COVID19 transmission model are presented.Through the introduction and summary of the research status,we finally give the starting point of this thesis and the main purpose of the research.In the second chapter,based on the diversity of pathogens and the complexity of transmission,a multi-strain dengue transmission model with incubation age and cross-immune age is established to explore its impact on the prevention and control of dengue transmission.In this chapter,we discuss the positivity,boundedness and asymptotic smoothness of the solution of the model.At the same time,the basic reproduction number of the model R0=max{R1,R2} is defined by using the next generation matrix method,where Ri is the basic reproduction number of strain i(i=1,2).In addition,the global asymptotic stability of the disease-free equilibrium state of the model is obtained,and it is proved that the local stability of the strain dominate equilibrium,and the persistence of the model and the existence and stability of the coexistence equilibrium are obtained.Finally,some numerical simulations are used to verify our theoretical results and interesting opening question.In the third chapter,consider the mosquito the important influence to the spread of mosquito-borne diseases and mosquito aquatic phase(eggs,larvae and pupae)on the sensitivity of the seasonal succession,in this chapter,we establish a mosquito-borne infectious diseases model with mosquito aquatic stage(eggs,larvae and pupae)and seasonal succession for tropical monsoon climate region,this model is a periodic discontinuous differential system.In this chapter,we discuss the existence and uniqueness of the disease-free periodic solution.Then,by means of the next generation operator method,we define the basic reproduction number R0 of the model,and prove the stability of the disease-free periodic solution.In addition,when R0>1,the uniform persistence of the model and the existence of positive periodic solution of the model are obtained.Finally,some numerical simulations are given to verify our main theoretical results.The simulation results suggest that ignoring the effects of seasonal succession may overestimate or underestimate the risk of mosquito-borne diseases.In the forth chapter,we establish a degenerate reaction-diffusion avian influenza virus transmission model,and the model uses some time-dependent parameters to depict the effect of temperature on the survival time of avian influenza virus in the environment.Firstly,we discuss the existence and boundedness of the model solution,and obtain the existence of the global attractor of the model solution mapping by using the Kuratowski noncompact measure.Then,in a spatially heterogeneous environment,the basic reproduction number R0 of the model is defined,and the threshold dynamics of avian influenza virus transmission is discussed.In addition,in the case of autonomous and homogeneous space,we study the threshold dynamics of the model by using Lyapunov function and invariant principle.Finally,numerical simulation is used to verify our theoretical results.In the fifth chapter,in order to understand the impact of border control strategies and local non-pharmaceutical interventions on the transmission and control of COVID-19,we present a COVID-19 patch model with border control measures and non-pharmaceutical interventions.In this chapter,we first discuss the dynamic behavior of independent patch models for the case of border closure.Then,the two-patch model after reopening the border is discussed,and the basic reproduction number of the model is obtained,and the existence and stability of the boundary equilibria and coexistence equilibrium of the model are proved.Numerical simulations conclude that reopening the border would not lead to a local epidemic in the absence of disease in the second patch and with strict control measures in place at the immigration department.In addition,when there is not quarantined the virus carriers to enter the second patch(or loose border control lead to virus carriers into the second patch),the number of infected people in the second patch will decrease with the border control efforts,but the epidemic or extinction of final state will not be changed,can only rely on the local non-pharmaceutical intervention measures to change the final state of the disease.