Stochastic analysis of COVID-19 by a SEIR model with Lévy noise

We propose a Lévy noise-driven susceptible-exposed-infected-recovered model incorporating media coverage to analyze the outbreak of COVID-19. We conduct a theoretical analysis of the stochastic model by the suitable Lyapunov function, including the existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium; we deduce a stochastic basic reproduction number R₀ ^s for the extinction of disease, that is, if R₀ ^s≤1, the disease will go to extinction. Particularly, we fit the data from Brazil to predict the trend of the epidemic. Our main findings include the following: (i) stochastic perturbation may affect the dynamic behavior of the disease, and larger noise will be more beneficial to control its spread; (ii) strengthening social isolation, increasing the cure rate and media coverage can effectively control the spread of disease. Our results support the feasible ways of containing the outbreak of the epidemic.