Dynamical analysis of simplicial epidemic model with demographic and aware effect

The prolonged spread of infectious diseases inevitably leads to changes in public awareness and behavior, including heightened preventive awareness and the implementation of containment strategies. Moreover, the interplay between demographic and awareness further complicates the dynamics of disease transmission, presenting significant challenges for epidemiological modeling. We propose a simplicial susceptible-aware-infected-susceptible (sSAIS) propagation model with demographic and aware effect on the simplicial network. Individuals are influenced by external information, which itself is modulated by the density of infected individuals, thereby improving self-protection and becoming the aware to avoid being infected.We establish the boundedness and invariant set of the model deriving stability theorems for all equilibria.Through numerical simulations, we capture the discontinuous phase transition phenomenon, bistable phenomenon, and the existence of periodic solutions of the system. Furthermore, we find that in addition to the first-order infection rate and the average degree of the network, the birth rate and the death rate are the two most influential parameters in the model of the outbreak. An increase in the birth rate significantly elevates infection density and lowers the outbreak threshold, while an increase in the death rate has the opposite effect. The increase in information execution rate and the decrease in information failure rate have a positive effect on the improvement of disease control and outbreak threshold. Therefore, controlling the birth rate and the death rate, increasing the probability of individual exposure to disease prevention and control information and reducing the information failure rate can become effective control strategies.