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https://www.selleckchem.com/products/epacadostat-incb024360.html 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.Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done numerically, the interesting dynamics that have emerged, and the largely unsuccessful attempts that have been made to analytically treat the evolution of densities in differential delay equations. We also present a new approach to the problem and illustrate it with a simple example.Propagation of rays in 2D and 3D corrugated waveguides is performed in the general framework of stability indicators. The analysis of stability is based on the Lyapunov and reversibility error. It is found that the error growth follows a power law for regular orbits and an exponential law for chaotic orbits. A relation with the Shannon channel capacity is devised and an approximate scaling law found for the capacit

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