Research On Infectious Diseases Models Spreading In Multiple Patches

The existence of infectious diseases has always been a very common phe-nomenon, it brings us a very large disaster. Therefore, mathematical model can beused to analyze the infectious diseases law and the key factors and to help the relevantdepartments develop a proper control and treatment programs. In this thesis, researchon infectious diseases models spreading in multiple patches are studied, this thesis isorganized as follows:Chapter1concentrates on the significance of researches on infectious diseases,and recent development of this field. In chapter2, we introduce the basic knowledgein the model used in this thesis.In chapter3, an SIS epidemic model with population dispersal is studied, inthe model the birth and death rates are both Logistic function, and all individualscan migrating freely between patches. The basic reproduction number R0is obtained,When R0<1, the disease-free equilibrium is globally asymptotically stable. WhenR0>1, the endemic equilibrium is globally asymptotically stable.In chapter4, we mainly consider a class of discrete SIS epidemic model. Basedon the rational assumption, some conclusions are given according to the birth func-tions, when the basic reproduction number R0≤1, disease-free equilibrium is glob-ally stable. when the basic reproduction number R0>1, endemic equilibrium existsand it is globally stable.