Dynamic analysis of a SIV Filippov system with media coverage and protective measures

This study aims to analyze a class of SIV systems considering the transmission rate influenced by media coverage and protective measures, in which the transmission rate is represented by a piecewise-smooth function. Firstly, for the SIV Filippov system, we take the dynamic behaviors of two subsystems into consideration, and obtain the basic reproduction number and the equilibria of the subsystems respectively. Secondly, based on the Filippov convex method, we calculate the sliding domain and the sliding mode equation, and further analyze the global dynamic behaviors of the system, through which we verify that there is no closed orbit in the system. Furthermore, we prove the global asymptotical stability of the disease-free equilibrium, two real equilibria, and the pseudo-equilibrium under certain conditions. The results demonstrate that the threshold value, the protective measures, and the media coverage could affect the number of infected individuals and the final scale of the disease. To prevent the spread of the disease, it is necessary to select an appropriate threshold and take applicable protective measures combined with media coverage. Lastly, we verify the validity of the results by numerical simulations.