The Dynamics Models Analysis Of HIV And West Nile Fever

In recent years,infectious diseases have become one of the main factors that threaten human health,the control and prevention of infectious diseases are also become one of the hot spots in the research of scholars.At present,the research methods of infectious diseases include of description,analyses,experimentation and theoretical research.The dynamics models of infectious diseases as One of the main methods of theoretical research.and it is popular in scholars because of its accuracy,intuition and conciseness.This paper focuses on the two hot issues of HIV and West Nile fever,and provides two dynamics models to investigate the transmission of HIV and West Nile fever.We analyze the dynamical behavior and provide serval measures to control the diseases.First of all,we establish a high risk infection model of HIV with vertical infection because the high risk items is very significance on the transmission of HIV.The effect of p on the spread of disease is discussed and the threshold of disappearance of R0 is given by using the method of regenerated matrix.The disease-free equilibrium is always existed and it is globally asymptotically stable if R0<1.However,there exists a globally asymptotically stable local equilibrium if R0>1.we also simulate-the reported data of HIV by using the estimated parameter values.By carrying out the sensitivity analysis of the basic reproduction number R0,we get serval suggestions to control the transmission of HIV.The second part discuss the effect of sterile mosquitoes on the spread of West Nile virus in birds.In this part,according to the literature[1],we introduce the sterile mosquito into our differential equation model which is main about the transmission of West Nile virus in birds.We analyze the influence of sterile mosquitoes on West Nile virus’s transmission in birds and calculate The basic reproduction number R1.the existence and stability of the equilibrium point are also discussed in this part and the conditions for the existence of the backward branch are given.Based on the results of sensitivity analysis and numerical simulation conclusion,we put forward the control of wild mosquitoes,natural birth rate per unit time and improve the number of bites,corvids and non-corvids recovery rate to control of West Nile fever in bird.