Mathematical Models Of AIDS And Rabies And Their Kinetics

Epidemic models have a long history dating back to Daniel Bernoulli's analysis of smallpox in 1760.In the middle twentieth century.There have a great development of the epidemic dynamics.The symbol work is the published of mathematical epidemiology written by Baily in 1957,and later republished.In recent years,the development is also very fast.Many mathematical models were used to analysis various disease.Meanwhile some mainly focused on measles flu.So we can divide the following four cases in the point of view mathematical models:one is described by ODE,the second is described by PED,the third is described by ODE and PDE. mainly include the age-structured epidemic models,and the fourth is described by stochastic models. we can add stochastic disturbance in ODE or use Monte Carlo simulation by markov chain. In this paper, we mainly established the ODE models of AIDS and rabies.AIDS is a malignant infections disease with high death rate that caused by Human immuno-deficiency virus .Rabies is an virulent contagious disease which transmit between people and animals .When infected,the deathrate is 100%. This paper based on some pathological facts .Mathematical models were established. We studied the dynamic behavior of the models through mathematical analysis and numerical simulation,we obtained the following results:1.When the force of infection in assumed to be nonlinears.We find the main factor of which determining the stability of the system's Periodic solutions and it's Period.2.we studied the outbreak of rabies and established the mathematical model based on the reality of our country. We not only focued on the rabies transmitted in the dogs but also considered people infected by exposed dogs, infected dogs and "sound dogs" carrying virus. We found out the basic reproduction number and compared the efficiency of the three strategies for controlling the rabies: culling, vaccination, culling and vaccination. The results of analysis and simulation indicate that the strategy of culling is the most efficiency strategies, vaccination is the intermediate and culling and vaccination is the worse. Meanwhile, as the inbalance between city and country, we stated that vaccination in the city and culling and vaccination in the country are recommended for controlling the rabies. Our study provides a theoretical basis for controlling the rabies in our country.