A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

Berrhazi, Badr-eddine; Fatini, Mohamed El; Laaribi, Aziz; Pettersson, Roger; Taki, Regragui

doi:10.1016/j.chaos.2017.10.007

Cited by 52 publications

(17 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…then the diffusion matrix is A(X) = diag(σ 2 1 S 2 , σ 2 2 I 2 , σ 2 3 R 2 ). Besides for all (S, I, R) ∈Ū, ξ ∈ R 3 + , there is M = min(σ 2 1…”

Section: Lemma 52 ( [14]mentioning

confidence: 99%

“…In the real world, epidemic dynamics is unavoidably perturbed by some kind of environmental noise. 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.…”

mentioning

confidence: 99%

See 1 more Smart Citation

A stochastic SIRI epidemic model with relapse and media coverage

Caraballo¹,

Fatini²,

Pettersson³

et al. 2018

DCDS-B

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…then the diffusion matrix is A(X) = diag(σ 2 1 S 2 , σ 2 2 I 2 , σ 2 3 R 2 ). Besides for all (S, I, R) ∈Ū, ξ ∈ R 3 + , there is M = min(σ 2 1…”

Section: Lemma 52 ( [14]mentioning

confidence: 99%

mentioning

confidence: 99%

A stochastic SIRI epidemic model with relapse and media coverage

Caraballo¹,

Fatini²,

Pettersson³

et al. 2018

DCDS-B

Self Cite

View full text Add to dashboard Cite

show abstract

“…The dynamic effects of time delays and stochastic noise on disease outcomes in populations are important research themes in mathematical epidemiology (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein). Models incorporating systems of delay differential equations have been shown to exhibit more complex dynamics and capture more of the observed biology underlying disease transmission and persistence (see [11,[15][16][17] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Stochastic dynamics in a delayed epidemic system with Markovian switching and media coverage

Liu

Heffernan

2020

Adv Differ Equ

View full text Add to dashboard Cite

A stochastic SIR system with Lévy jumps and distributed delay is developed and employed to study the combined effects of Markovian switching and media coverage on stochastic epidemiological dynamics and outcomes. Stochastic Lyapunov functions are used to prove the existence of a stationary distribution to the positive solution. Sufficient conditions for persistence in mean and the extinction of an infectious disease are also shown.

show abstract

“…As we all know that the spreading of disease is unpredictable due to the impact of environmental variations, proper and realistic stochastic differential equation models are proposed for studying the spreading of disease under various environmental conditions. [5][6][7][8] An increasing number of researchers investigate and improve the stochastic SIRS models, such as one susceptible individual with one infectious individual, [9][10][11][12][13][14][15] two susceptible individuals with one infectious individual, 16 and multiple susceptible individuals with one infectious individual. 17 In the previous papers, the susceptible individuals be infected with only a disease, whether multifarious or onefold species.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a kind of stochastic SIRS models with two different nonlinear incidences

Huang

Wei

et al. 2019

Advances in Mechanical Engineering

View full text Add to dashboard Cite

A new kind of stochastic SIRS models with two different nonlinear incidences are extended. The obtained results can be expressed in two dimensions. In mathematics, the threshold values R s 1 and R s 2 which ensure permanent or extinct disease are presented, respectively. More concretely, when R s i .1(i = 1, 2), the two diseases are persistence in mean. When R s i \1 or R s i .1(i = 1, 2), the two diseases will either be extinct or be permanent, respectively. What's more interesting is the numerical results which show that the two diseases go to extinction at a large time, when R s 1 = 1 and R s 2 = 1. Furthermore, the sufficient conditions for the diseases that are extinct and permanent are given. In addition, the stochastic boundedness of the model is investigated. Epidemiologically, we can conclude that large noise fluctuations can effectively prevent the outbreak of disease, which can supply us beneficial methods to control the spreading of two diseases. Finally, a few numerical simulations are presented to demonstrate and verify the findings obtained.

show abstract

A stochastic SIRS epidemic model incorporating media coverage and driven by Lévy noise

Cited by 52 publications

References 25 publications

A stochastic SIRI epidemic model with relapse and media coverage

A stochastic SIRI epidemic model with relapse and media coverage

Stochastic dynamics in a delayed epidemic system with Markovian switching and media coverage

Dynamics of a kind of stochastic SIRS models with two different nonlinear incidences

Contact Info

Product

Resources

About