Dynamical Modeling Of Infectious Diseases And Stability Analysis

It is well known, infectious diseases have a huge perniciousness to the development of humanbeing, social and health. The research of infectious diseases in the world is the urgent thing forthe famous researchers and scholars. Dynamical modeling of epidemics is the important way toresearch infectious diseases. It mainly research the mechanism about spread of infectious dis-eases. According mathematical model which describe the mechanism about spread of infectiousdiseases and dynamic state of pathogene, and then use knowledge of math to analysis analyze thedevelopment regularity of infectious diseases so as to provide important theory way and bases ofmaking a strategic decision for controlling spread of infectious diseases .In this paper, which is divided into three parts. The first part, it mainly introduce the perni-ciousness of infectious diseases, and some base concepts and models about infectious diseases.The second part, it mainly make a integration for differential equations about SIS, SIR,SIRS models with vertical inheritance to differential form and find the liapunov function of SIS,SIR, SIRS models to analyze stability of their equilibrium point. In this part, we find a liapunovfunction for SIS, SIR, SIRS models by using variable substitution and obtain a stable result.As R0 < 1, the free equilibrium point exists and is global stability, and as R0 > 1, the endemicequilibrium point exists and is global stability.The third part, it mainly describe unreasonable of assumed condition in epidemiological mod-els. we differentiate for S + I = N or S + I + R = N to analyze SIS,SIR,SIRS modelsand obtain some results about unreasonable of assumed condition in epidemiological models, andthen we apply differential equations about stability theory to analyze stability of SIS,SIR,SIRSmodels with nonconstant population.The study in this paper are the important part in dynamic epidemiological models field. Theways and the results in this paper will play a role of guideline for studying and controlling spreadof infectious diseases.