Global Dynamics Of Dengue Epidemic Models

As one of the important infectious diseases threatening human health,the impact of vector-borne diseases cannot be ignored.Dengue fever is an acute infectious disease caused by dengue virus,which is transmitted by aedes mosquitoes.It is listed by WHO as one of the most potentially threatening diseases in the world in 2019.Dengue Fever is likely to lead to widespread outbreaks and will seriously harm people's physical and mental health.Therefore,it is of great theoretical and practical significance to study the transmission law and control strategy of dengue fever.Based on the transmission mechanism of dengue fever,we focuses on analyzing the influence of human-to-human direct transmission,incubation period and cycle environment on the transmission of dengue virus among people,and thus establish different mathematical models.Furthermore,the stability and durability of the model are analyzed comprehensively and meticulously.Combined with the actual prevalence data in Japan,the basic reproduction number of dengue transmission is estimated using statistical probability method.The above analysis provides a theoretical basis for accurate disease prevention and control.The structure of the paper is as follows:In Chapter 1,by introducing the research background and current status of the dengue infectious disease transmission model,the research value and significance of the dengue infectious disease model are given.In Chapter 2,the main background knowledge needed for the research of this paper is given,including some related basic concepts,stability theories and research methods.In Chapter 3,the transmission of a single-strain dengue virus is taken as an example,according to its transmission characteristics,it is important to consider that the virus can be transmitted directly in the population without the vector,and the corresponding dynamics model is established.By using Lyapunov stability method,La Salle invariant set principle and the related theory of monotonic systems,the global stability of the model is discussed.It is concluded that the disease-free equilibrium of the model is globally asymptotically stable when the basic reproduction number is less than 1 and the endemic equilibrium of the model is globally asymptotically stable when the basic reproduction number is greater than 1.In Chapter 4,the latent period of dengue transmission in human population is considered,and mosquitoes are divided into larval and adult stages to establish an infectious disease model,and then their dynamic behavior is studied.By introducing the limit system of the original system,it is obtained that the model is uniformly persistent.Furthermore,the relevant theory of monotonic system is used to prove that the endemic equilibrium of the model is globally asymptotically stable when ₀R(29)1.In Chapter 5,on the basis of Chapter 4,the influence of periodic environment on the spread of dengue fever is introduced,and a model with latency effect is established in periodic environment,furthemore,the uniformly persistence of the system is obtained.Numerical simulations show that the solution of the system oscillates periodically with time.In Chapter 6,based on the actual dengue fever data in Japan,combined with the branching process theory,the offspring distribution of the disease is considered as a common statistical probability distribution,and the Metropolis-Hastings sampling algorithm in the Monte Carlo Markov Chain(MCMC)method is used to estimate the basic reproduction number of dengue fever.In Chapter 7,we summarize the main results of this paper on the dengue infectious disease transmission models,and the issues that need to be studied in future is expected.