Complex dynamics and control strategies of SEIR heterogeneous network model with saturated treatment

In this paper, we introduce saturated treatment into the network-based Susceptible–Exposed–Infected–Recovered (SEIR) epidemic model. By the stability analysis of disease-free equilibrium, we notice that unlike the common situation, the basic reproduction number R₀<1 cannot guarantee the global stability of disease-free equilibrium, which indicates that the stronger condition of R₀<R̂₀<1 is required. We then investigate the bifurcation behavior of the model under different saturated treatment coefficient α. When the medical resources are limited (i.e., large α) a backward bifurcation occurs such that even if R₀<1, there is still outbreak of disease. Meanwhile, we also investigate several control strategies with focus on their effects on epidemic inhibition. Furthermore, according to the numerical experiments, it is found that the bistability of the model not only has disease-free equilibrium and endemic equilibrium stable, but also has two endemic equilibrium stable. It should be emphasized that due to the effect of saturated treatment, the occurrence of a forward bifurcation at R₀=1 does not guarantee that there is only one stable endemic equilibrium. In this case, the initial infection density is low enough to ensure the disease to reach another low endemic stable state.