A simplicial SSIS epidemic model with the outgoing pressure

A new simplicial epidemic model that considers the pressure of out-going is proposed to describe the characteristics of clustering on disease transmission more accurately. In addition, the probability evolution equations of nodes in each state are obtained by the quenched mean-field method. Furthermore, we analyze the conditions of the existence and the stability of the equilibrium points. Subsequently, the sensitivity analysis of the parameters is investigated, and it can be concluded that the degree about pairwise transmission rate has great impact on the propagation threshold. Our simulation results indicate that the system produces forward bifurcation or backward bifurcation via the one-parameter bifurcation diagram, and the bistable state of the system appears under certain conditions. Meanwhile, we obtain the transition conditions of the system from the disease-free equilibrium state to the bistable state through the divisional diagram. It is also noticed that the pressure of out-going plays a crucial role in the spreading process of diseases. On the one hand, the increasing of the pressure of out-going leads to the decreasing of the disease transmission threshold and a faster outbreak of disease. On the other hand, an increase in the individuals without the pressure of out-going causes the increasing of transmission threshold and a slower outbreak of disease.