Media coverage campaign in Hepatitis B transmission model

In this paper, we consider a transmission model of hepatitis B virus by taking into account media coverage. First, we formulate the model and find the basic reproduction number R0 by using the next generation matrix method. We show that the disease free equilibrium is locally asymptotically stable for R0<1 and unstable if R0>1. We also prove that the system is globally asymptotically stable for R0<1. In order to control the spread of this disease in community, we devise an optimal control problem by introducing three control functions, that is, the educational campaign, vaccination and the media coverage. To do this, we solve analytically the control problem with characterization of control variables using the Portraying's Maximum Principle. Finally, we present some numerical illustrations.