Two Types Of Infectious Disease Model Stability Analysis, And Vaccination Strategies

With the rapid development of world science and technology, the gradualimprovement of the level of medical,There are some infectious diseases has beencompletely eliminated, such as leprosy, polio and smallpox.But some viruses also inchange, upgrade, there are still some infectious disease, threatening the survival ofhuman beings, such as influenza, HIV/AIDS, SARS and so on.And spread of infectiousdiseases prevention and control law became the research hot spot, through the law of thespread of infectious diseases, route of transmission, and to explore the optimal methodof prevention and control of infectious diseases has very realistic significance.On thebasis of previous studies, this paper studies the SIR model and SIQRS model, the maincontents are as follows:This article is divided into four parts, the first part first introduces the developingcourse of infectious diseases and infectious diseases influence on human development,secondly introduces the model of the infectious diseases and the development trend ofthe research achievements of recent years, finally the need to use some of the basictheorems and lemma, reasoning has carried on the brief explanation.The second partmainly studies the incidence has a standard vaccination of susceptible people andneonatal SIR epidemic model, have no disease equilibrium and the endemic equilibriumcondition of global asymptotic stability and the controller is designed based onLyapunov method, at the time R01，the conditions of the disease-free equilibriumglobal asymptotic stability.The third part studies a class of SIR model of neonatalcontinuous inoculation, and pulse vaccination for the susceptible person, using thetheory of dynamics of infectious diseases, the differential equation stability theory andthe discrete dynamic system of stroboscopic map theory, discuss the global dynamicbehavior of the model, prove the existence and stability of the disease-free periodicsolution.The fourth part, the research has a vertical infection and SIQRS infectiousdisease model of nonlinear infection rate, under the condition of pulse vaccination,through the theory of impulsive differential equation, analyses the existence andstability of the disease-free periodic solution, as well as the system’s consistentcontinued survival.