Modeling and analysis of SIR epidemic model concerning nonlinear incidence rate, births and deaths on simplicial complexes

To capture the intracommunity epidemic transmission process, this paper presents a SIR epidemic model incorporating nonlinear incidence rates alongside birth and death rates on the 2-order simplicial complexes. Firstly, the existence and stability of equilibrium points are analyzed. Meanwhile, we derive the basic reproduction number, two epidemic outbreak thresholds related to the bistability region, and the critical value for higher-order enhancement factor. Theoretical findings indicate that the system produces the bistable state. In addition, when the higher-order enhancement factor exceeds the critical value and the contagion coefficient exceeds two epidemic thresholds, the system exhibits discontinuous transitions. Furthermore, the sensitivity analysis reveals that recovery rate and the pairwise transmission rate have a significant impact on the propagation threshold. Simulation results demonstrate that as the birth rate and higher-order enhancement factors increase, and as the natural and disease mortality rates decrease, the system transitions from a forward bifurcation to a backward bifurcation.