Research And Control Of Several Variable Coefficients Epidemic Dynamics Model

The infection had brought tremendous mischance to people in history.And then,how to prevent the outbreak of epidemic periodically will become very important and forever problems.Epidemic Models were established to forecast the trend of illness development,in order to offer the evidence to the medical and government partmentfor making policy and resisting the disease better.and then,To a greater extent to ensure the safety of the people’s life, maintaining social harmony and stability.Firstly, we analyze an Epidemic Model. The threshod data R0is obtained, which determines the existence of an infectious disease. when R0<1,disease-free equilibrium is globally and asymptotically stable and the disease always dies out eventually. When R0>1,There exist two equilibrium pionts,the disease-free equilibrium Eowhich is unstable and the endemic equilibrium E1which is globally and asymptotically stable and the disease is uniformly persistent.Secondly, we consider an SEIS epidemic mode with nonlinear contagious rate, The threshold data R0is obtained, which determines the existence of an infectious disease.When R0<1,disease-free k0equilibrium is globally and asymptotically stable. WhenR0>1,the disease-free equilibriumk0is unstable and the unique endemic equilib-rium K*is locally and asymptotically stable.Thirdly, we consider an SEIR epidemic model with seasonal forcing in transmission rate. Furthermore, an man-made tracking control method is used to control chaotic motions in the SEIR epidemic model. A feedback controller is designed to achieve tracking of an ideal output. And then, the disease can gradually disappear.And then, matlab numerical simulation illustrates that the method is effective.Finally, we consider an SEIR epidemic model with variable eoefficients. Fur-thermore, according to the principles of variable structure control, a variable structure controller is designed to achieve tracking of an ideal output. And then, it prevent the outbreak of epidemic periodically. Finally, matlab numerical simulation illustrates that the method is effective.