Stochastic stability and instability of an epidemic model with relapse

Fatini, Mohamed El; Lahrouz, Aadil; Pettersson, Roger; Settati, Adel; Taki, Regragui

doi:10.1016/j.amc.2017.08.037

Cited by 35 publications

(25 citation statements)

References 19 publications

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“…In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions. In the real world, epidemic dynamics is inevitably perturbed by the environmental noise, see references for white noise [3,7,17,24,20] and [6,31] for Lévy noise. Stochastic models possess some inherent randomness.…”

mentioning

confidence: 99%

A stochastic threshold for an epidemic model with isolation and a non linear incidence

Caraballo¹,

Fatini²,

Sekkak³

et al. 2020

Communications on Pure &Amp; Applied Analysis

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In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a stochastic threshold for the model without any sharp sufficient assumptions on model parameters as compared to existing works. Firstly, we establish the uniqueness of the global positive solution according to Lyapunov function method. Secondly, we prove stochastic permanence of the solutions. Then, we establish sufficient condition for the extinction. Thirdly, we investigate necessary and sufficient conditions for persistence in mean of the disease. Finally, we provide some numerical simulations to illustrate our theoretical results.

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mentioning

confidence: 99%

A stochastic threshold for an epidemic model with isolation and a non linear incidence

Caraballo¹,

Fatini²,

Sekkak³

et al. 2020

Communications on Pure &Amp; Applied Analysis

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“…To reveal the effects of stochasticity, many authors have introduced randomness into epidemic models [2,12,13,18,21,22,26,36,41]. Amongst authors who studied SIRI epidemic model, we can cite [19] for an epidemic model perturbed by white noise, [39] for a nonautonomous periodic SIRI model, [9] where authors discussed stability and instability for an epidemic model with relapse, and [3] for a stochastic SIRI model driven by lévy noise. Then to make model (1.1) more reasonable and realistic, we introduce a corresponding stochastic perturbation as follows:…”

mentioning

confidence: 99%

A stochastic SIRI epidemic model with relapse and media coverage

Caraballo¹,

Fatini²,

Pettersson³

et al. 2018

DCDS-B

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This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we show the existence of a stationary distribution. Numerical simulations are presented to confirm the theoretical results.

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“…The NFDM is able to maintain the properties of the exact solution of the original ODE or PDE. The numerical scheme is called NFDM if at least one of the following conditions are satisfied [10][11][12][13][14][15][22][23][24][25][26][27][28]]:…”

Section: A Nonstandard Theta Milstein Methodsmentioning

confidence: 99%

“…Recently, many interesting studies were presented to the stochastic tuberculosis (TB) model such as [11][12][13][14]. Also, several papers considered modeling tuberculosis (TB) [15][16][17][18][19][20]; however, the proposed model introduces several factors in spreading TB, for instance, the fast infection, the exogenous reinfection, and secondary infection along with the resistance factor [21].…”

Section: Introductionmentioning

confidence: 99%

Nonstandard theta Milstein method for solving stochastic multi-strain tuberculosis model

Sweilam

AL–Mekhlafi

2020

J Egypt Math Soc

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In this article, a novel stochastic multi-strain tuberculosis model is presented. Numerical simulations for this model are the main aim of this work. A non-standard theta Milstein method is constructed to study the proposed model, where the proposed method is based on choosing the weight factor theta. The main advantage of this method is it can be explicit or implicit with large stability regions using the idea of the weighed step introduced by R.E. Mickens. Mean-square stability of nonstandard theta Milstein method is studied. The new scheme shows a greater behavior compared to the theta Milstein method. It is concluded that the proposed scheme preserves the positivity of the solution and numerical stability in larger region than the standard method.

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Stochastic stability and instability of an epidemic model with relapse

Cited by 35 publications

References 19 publications

A stochastic threshold for an epidemic model with isolation and a non linear incidence

A stochastic threshold for an epidemic model with isolation and a non linear incidence

A stochastic SIRI epidemic model with relapse and media coverage

Nonstandard theta Milstein method for solving stochastic multi-strain tuberculosis model

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