Stability Study Of Several Types Of Infectious Disease Model

The emergence and continuous spread of infectious diseases threaten the life and health of biology such as human beings,and affect all aspects of high-quality development such as the economy.At the same time,the classification of infectious diseases is not only compli-cated,but also has the possibility that its pathogenic pathogens can change their infectious characteristics due to mutation in the process of transmission.In terms of theory,the de-velopment trend of infectious diseases can be judged by studying the dynamics of infectious disease models,which provides a strong support for formulating effective and reasonable infectious disease control strategies in practice.Therefore,in order to meet the risks and challenges brought by various infectious diseases,the application of infectious disease dy-namics plays an important realistic significance role in studying the dynamic behavior of various infectious disease models.Based on the theory of infectious disease dynamics,this paper mainly studies the sta-bility of three types of infectious disease models,and the main contents are as follows:The first chapter is the prolegomenon,which mainly introduces the research background and significance of this paper,the main research and development status of infectious disease dynamics at home and abroad,the main work and preparatory knowledge of this paper.In the second chapter,the stability of the epidemic model with vertical transmission is studied.The basic reproduction number R₀is obtained by using the next-generation matrix method.When R₀<1,the local asymptotic stability of the system at the disease-free equilibrium is obtained by the Routh–Hurwitz criterion.The global asymptotic stability of the system at the disease-free equilibrium is proved by constructing Lyapunov function.When R₀>1,the system exists a unique endemic equilibrium point.The conditions of the local asymptotic stability of the system at the endemic equilibrium point are obtained according to the Routh criterion.Finally,the rationality of the conclusion is verified by numerical simulation.In the third chapter,we study the stability of a epidemic model with saturation incidence and environmental infection.The basic reproduction number R₀and equilibrium points are calculated.When R₀<1,the local asymptotic stability and global asymptotic stability of the system at disease-free equilibrium point are analyzed by stability theory.When R₀>1,the sufficient conditions of the local asymptotic stability of the system at the endemic equilibrium point are discussed and the global asymptotic stability of the system is proved.Finally,the main conclusions of stability and the effect of vaccination rate on the basic regeneration number are numerically simulated.In the fourth chapter,the stability of a mpox virus infectious disease model with vac-cine immunity and environmental infection is studied.The basic reproduction numbers of human and animal are obtained by using matrix theory.The disease-free equilibrium and the condition for the existence and uniqueness of endemic equilibrium are given.The local asymptotic stability of the disease-free equilibrium point is obtained by the Routh-Hurwitz criterion.By constructing Lyapunov function,the system is proved to be globally asymp-totically stable at disease-free and endemic equilibrium points.