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The effect of stochasticity with respect to reinfection and nonlinear transition states for some diseases with relapse
Author(s) -
El Fatini Mohamed,
El Khalifi Mohamed,
Lahrouz Aadil,
Pettersson Roger,
Settati Adel
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6903
Subject(s) - mathematics , uniqueness , extinction (optical mineralogy) , stationary distribution , persistence (discontinuity) , nonlinear system , disease , statistical physics , mathematical analysis , statistics , medicine , markov chain , biology , physics , quantum mechanics , paleontology , geotechnical engineering , pathology , engineering
In this paper, we consider a stochastic epidemic model with relapse, reinfection, and a general incidence function. Using stochastic tools, we establish a stochastic thresholdR s 0and 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 whenR s 0 > 1 . Moreover, we prove the existence and uniqueness of a stationary distribution. Finally, numerical simulations are presented to show the effectiveness of theoretical results.