Qualitative Analysis Of Epidemic Models Under Environmental Impact

To effectively control the spread of disease,infectious diseases can be analyzed in depth from mathematics as the entry point,and new theoretical foundations can be proposed through in-depth analysis of infectious disease models,which can also provide guidance from measures to be taken in reality.Based on the transmission mechanism of tuberculosis and influenza,this paper establishes an infectious disease model under the influence of the environment.This paper is divided into four parts,and the specific work is as follows.The first chapter analyzes the necessity of studying infectious diseases from the perspective of mathematical modeling,and the progress of research on infectious disease models under environmental influence,and briefly summarizes the work of this paper.In Chapter 2,according to the mechanism of tuberculosis transmission,we establish an SVEIRB model under environmental impact and vaccination(?)Using next generation matrix theory,the basic regeneration number 0 of the model is calculated.Using Lyapunov function and La Salle invariant set principle,we prove the global asymptotic stability of the equilibrium.At the end of the chapter,simulations are performed using matlab to verify the theoretical results obtained.The third chapter considers the impact of quarantine and environmental impact on influenza transmission,and we build the following model(?)According to the next generation matrix theory,the basic regeneration number of the disease is obtained,and using construct Lyapunov function and La Salle invariant set principle,we prove the global asymptotic stability of the equilibrium.Conducting numerical simulation to intuitively reflect the influence of various parameters in the process of disease transmission.Chapter 4 summarizes the results of the research in this thesis and puts forward my own views on the follow-up work.