Stability Analysis Of Vector-borne Diseases Model

Vector-borne diseases have been endangering the health of the people. So pathogenesis、 infectious regularity and control strategy of vector-borne diseases has become one of the world’s urgent need to solve a major problem. This paper involves three classes of vector-borne diseases model. It is based on Hurwitz criterion, V function, Dulac function, the limit equation theory and the theory of compound matrices. At the same time the stability of the equilibrium of the model makes a complete analysis of results. This paper is divided into five chapters.In the first section, it is introduction, and it mainly involves the background and the significance of infectious disease and introduces the dynamics of infectious diseases of the research results, some basic theory of vector-borne diseases studied in this paper and the main work in this paper.In the second section, it mainly involves some basic theory of vector-borne diseases studied in this paper.In the third section, the SvIvSpIp epidemic model with the Logistic birth is investigated. Using Hurwitz criterion, eliminating periodic solution in two-dimensional systems and Dulac function analysis of the stability of the model.In the fourth section, the SvIvSpIpHpRp epidemic model with the Logistic birth is investigated. Using Hurwitz criterion, the limit equation theory and the theory of compound matrices analysis of the stability of the model.In the fifth section, the SpIpSvIvSHIH epidemic model with the constant immigration is investigated. Using Hurwitz criterion, eliminating periodic solution in two-dimensional systems and Dulac function analysis of the stability of the model.