Modeling And Research For The Transmission Of A Emerging Disease With Impact Of Media

When a emerging diseases spread in a region,it will bring a large number of illness.Meanwhile,the media will report the disease.The media will affect the propagation.A disease model with impact of media is constructed. It is shown that the global dynamical behavior of this model is completed determined by Ro, that is, the disease free equilibrium is global asymptotical stable if R0<1, in this case,the disease will die out; The endemic equilibrium is global asymptotical stable if R0>1, in this case, the disease will persist in population. Numerical simulators are given to support the theoretical results obtained. At last,The control model of the malignant disease with impact of media is also formulated by introducing a control variable. The existence and explicit expression of the optimal control is given and proven, respectively.