Analysis of final size and peak time for SIR epidemic model on simplicial complexes

The Susceptible–Infected–Recovered $\left(\mathrm{SIR}\right)$ epidemic model based on a simplicial complex is investigated, incorporating higher-order network topology and nonlinear incidence rates. We derive theoretical results for the basic reproduction number, the final size, and the epidemic peak of the mean-field model. Furthermore, we provide a theoretical estimate for the peak time of an epidemic. Numerical simulations reveal that higher-order interactions significantly impact the dynamics of epidemic transmission. Specifically, as the strength of higher-order interactions increases, both the final size and the epidemic peak heighten, while the peak time is shortened. These findings highlight the importance of considering higher-order structures in modeling epidemic spread.