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 R (0) = 1, there exhibits a backward bifurcation, if R∗ < 1 and R (0) = 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.