Dynamic Behavior Of Several Infectious Disease Models Under Threshold Policy

In this thesis,a kind of Filippov plant infectious disease model with one economic threshold,a type of Filippov plant infectious disease model with two economic thresholds and a class of SIR computer virus model with two thresholds are studied.In order to prove the relevant conclusions,we use the plane equation stability theory and qualitative theory and the theory of discontinuous differential equations on the right,moreover,combine with LaSalle invariance principle,generalized Lyapunov method,Bendixson-Dulac criterion,differential inequality technique,Filippove convex combination and other methods.The full text consists of five chapters.In Chapter 1,the research background,significance and development status of plant infectious disease models and computer virus models are introduced.The main research contents of this paper are addressed as well.In Chapter 2,introduces some basic mathematical concepts and theoretical knowledge used in this thesis.In Chapter 3,base on that principle of pursuing maximum economic benefit,a kind of Filippov plant infectious disease model with one economic threshold was analyzed from the point of view of planting susceptible plants.According to the threshold value,the generalized Lyapunov method is used to obtain the global dynamic behavior of the system in three cases.In chapter 4,based on the model analyzed in chapter 3,we analyzed a type of Filippov plant infectious disease model with two economic thresholds.In the analysis of the global dynamic behavior of the system,five types of equilibrium are obtained by changing the size of two economic thresholds.A continuous non-smooth Lyapunov function is constructed and the generalized Lyapunov method is used to prove that the equilibrium point of the system is globally asymptotically stable under each parameter.In Chapter 5,considering the economic cost in the actual process,we control the spread of computer virus in the network by installing anti-virus software and reinstalling the system.We mainly analyze a class of computer virus model with two thresholds.In the analysis of the global dynamic behavior of the system,the Bendixson-Dulac criterion is used to prove that the system does not cross the limit cycle,and the vector field analysis shows that the system does not have the sliding mode limit cycle.Combined with the limit set theory,the global dynamics result of the system is obtained.At the end of the thesis,the research is summarized and the future researches are prospected.