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The effect of stochasticity with respect to reinfection and nonlinear transition states for some diseases with relapse

In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic threshold Rs0 and prove the extinction of the disease when its value is equal or less than unity. We also show the persistence in mean...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-12, Vol.43 (18), p.10659-10670
Main Authors: El Fatini, Mohamed, El Khalifi, Mohamed, Lahrouz, Aadil, Pettersson, Roger, Settati, Adel
Format: Article
Language:English
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Summary:In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic threshold Rs0 and prove the extinction of the disease when its value is equal or less than unity. We also show the persistence in mean of the disease when Rs0>1. Moreover, we prove the existence and uniqueness of a stationary distribution. Finally, numerical simulations are presented to show the effectiveness of theoretical results.
ISSN:0170-4214
1099-1476
1099-1476
DOI:10.1002/mma.6903