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A stochastic SIS epidemic model which is characterized by Lévy noise on a network is established to study how these two factors work together in the spread of diseases. First, the existence of a unique positive solution is proved. Next, the stability in probability and  p -th moment asymptotic stability of the disease-free equilibrium are investigated, and the sufficient condition for persistence in the mean of the disease is obtained. The synergy between the network and Lévy noise in which the heterogeneity of the network can amplify the effect of the noise can suppress the disease outbreak by increasing the disease extinction threshold. Finally, numerical simulations are carried out to illustrate our results.

Stochastic SIS epidemic model on network with Lévy noise