Abstract:

This paper considers the SIS stochastic epidemic model on the simplex complex under the influence of noise, the difference in stochastic stability and stochastic bifurcation of models with 1 simplex contagion strength ($\lambda$) or 2 simplex contagion strength ($\lambda_{\triangle}$) perturbed by noise is compared. The results show that the threshold of the stochastic model infectious disease extinction with probability 1 after the noise acts on the low-order term where $\lambda$ is located is related to the noise intensity, and vice versa when it acts on the high-order term where $\lambda_{\triangle}$ is located has no effect; increasing $\lambda_{\triangle}$ causes the point near 1 of the steady-state probability density function appearing peak, larger the pear value or nearing the 1 point, that is, increasing $\lambda_{\triangle}$ promotes the outbreak of the disease.

Key words: Simplex complexes, SIS epidemic model, Stochastic stability, Stochastic bifurcation