Role of limited medical resources in an epidemic model with media report and general birth rate

Abstract

This paper formulates an SEIRSHM epidemic model with general birth rate, media report and limited medical resources. Firstly, the well-posedness of the solutions and the extinction of the disease are discussed. Then, the existence of the endemic equilibrium is discussed and we find when R∗ > 1 and R₀ = 1, there exhibits a backward bifurcation, if R∗ < 1 and R₀ = 1, there exhibits a forward bifurcation. Finally, numerical simulations are carried out to illustrate the main results and show that media report and limited medical resources have a great impact on disease transmission.