Abstract
In this paper, we present the following stochastic hepatitis B epidemic model driven by a standard Brownian motion and Lévy jump noise and we discuss the impact of infinite Lévy jumps by the definition of the new threshold. Large time estimates are established based on Kunita’s inequality rather than Burkholder–Davis–Gundy inequality for continuous diffusions. We prove the existence of a unique global positive solution. The impact of stochasticity and the effect of vaccination is taken into consideration in the formulation of sufficient conditions for the extinction and persistence of Hepatitis B. We illustrate our theoretical results by numerical simulations.
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