Impacts of media awareness on a stage structured epidemic model
The authors establish a stage-structured epidemic model including the effect of media awareness and assuming that the disease can be transmitted only among the mature populations. They identify the equilibria and the basic reproduction number. Castillo-Chavez's method is used to show global asymptotic stability of the disease-free equilibrium for \(R_0<1\), while the geometrical approach by Li and Muldowney is applied to show global asymptotic stability of the endemic equilibrium for \(R_0>1\) under some additional conditions. Using media awareness as a control parameter, the authors formulate an optimal control problem, which is solved analytically by applying Pontryagin's maximum principle. Several numerical examples illustrate the analytical results. The main conclusion of this work is that although media awareness alone is not sufficient to eradicate the disease, it can help disease management by decreasing extinction time and reducing the number of infected.
scientific article; zbMATH DE number 7350426
scientific article