Research On The Epidemic Models And Controlling Strategy Of Epidemic Diseases

According to The World Health Organization report, infective diseases are still the first killer for the human. The human are confronted with the menace of infective diseases for long-term. For the experimental methods are not permitted on study of the infective diseases, the theoretic analysis and simulation technology are required for mechanism of epidemic, law of spread and tendency of the epidemic diseases. The dynamic models have been taken an important role in studying infective disease. In this paper, the establishment of the epidemic diseases models and controlling strategy are studied.The paper is departed into four parts. In the second part, the four SIS models are investigated; the four SIRS models with nonlinear incidence rate are studied in the third part; In the forth part, the SEIS and SI₁I₂R model are researched. Important results obtained in this paper as following:1. Some epidemic diseases have the characteristic of transmission by mother to baby and contact. Up till now, the diseases are studied by the dynamic models with bilinear incidence rate and standard incidence rate under the hypothesis of the infective individuals having no fertility. The model with general incidence rate is established firstly under the hypothesis of the infective individuals having fertility and some proportion of the baby infected and the basic reproduction number is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when R₀ is not greater than one; the disease-free equilibrium is unstable, and endemic equilibrium is globally asymptotically stable when R₀ is greater than one. According the results above, the suggestions following are put forward:1) Raising the death rate and recover rate of the infective individuals. If the infective individuals are birds or domestic animals, we can catch and kill them to increase the death rate. If the infective individuals are human, we must quicken the tempo of research and development of specific medicine to decrease the recovery rate.2) Decreasing the fertility of infective individuals and proportion of the infected babies. This purpose can be realized by the vaccination of newborn etc. to obstruct the way of mother—baby.2 Some infective diseases have the characteristic of periodic attacks such as flu and bird flu. To introduce the cyclic parameters into the model has important significance. For the model with cyclic parameters epidemic model complexity, there is a little research paper. The basic reproduction number and globally asymptotical stability of the model with cyclic parameters are first founded in this paper.3. The incidence rate is a very important item in the epidemic models. In the classical epidemic disease models, bilinear incidence rate and standard incidence rate have been frequently used. Actually, they are two extreme types and can not explain better the complex phenomena of disease transmission. In this paper, bilinear incidence rate and standard incidence rate are improved intononlinear type as and was introduced into the four SIRS models.By constructing Liapunov function and Dulac function, the threshold of existence of the endemic equilibrium and disease-free equilibrium are obtained. According the globally stable results obtained of the four models, the controlling epidemic disease strategy that inducing the immigration and increasing the recovery rate and death rate is put forward.