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A stochastic SIRI epidemic model with Lévy noise

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  • Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not acquit permanent immunity but return to infectious class. Such diseases are modeled by SIRI models. In this paper, we establish the existence of a unique global positive solution for a stochastic epidemic model with relapse and jumps. We also investigate the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we present some numerical results to support the theoretical work.

    Mathematics Subject Classification: 92B05, 60G51, 60H30, 60G57.


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  • Figure 1.  rajectories of the solutions to the systems (1.1) and (1.3) for Moroccan zoonotic tuberculosis with $\mathcal{R}_0\leq 1$.

    Figure 2.  Trajectories of the solutions to the systems (1.1) and (1.3) for bovine tuberculosis [5] with $\mathcal{R}_0>1$, $N = \mu = 0.1,\;\beta = 0.6\;and\;\gamma = \delta = 0.5$.

    Figure 3.  Trajectories of the solutions to the systems (1.1) and (1.3) with various relapse rate $\delta$: $0.14, 0.2, 0.4$.

    Figure 4.  Trajectories of the solutions to the systems (1.1) and (1.3) with a various recovery rate $\gamma$: $0.09, 0.18, 0.22$

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