Stability of an SEIR epidemic model with independent stochastic perturbations

Witbooi, Peter J.

doi:10.1016/j.physa.2013.06.025

Cited by 57 publications

(21 citation statements)

References 18 publications

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“…In most cases, it has been observed in [12,13] that introducing a stochastic perturbation into an unstable disease-free equilibrium model system of ordinary differential equation may lead to a system being stable in sde. Stochastic differential equation models for various diseases have been studied and similar work has been done in [11,12,[14][15][16].…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

A Stochastic TB Model for a Crowded Environment

Vyambwera

Witbooi

2018

Journal of Applied Mathematics

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We propose a stochastic compartmental model for the population dynamics of tuberculosis. The model is applicable to crowded environments such as for people in high density camps or in prisons. We start off with a known ordinary differential equation model, and we impose stochastic perturbation. We prove the existence and uniqueness of positive solutions of a stochastic model. We introduce an invariant generalizing the basic reproduction number and prove the stability of the disease-free equilibrium when it is below unity or slightly higher than unity and the perturbation is small. Our main theorem implies that the stochastic perturbation enhances stability of the disease-free equilibrium of the underlying deterministic model. Finally, we perform some simulations to illustrate the analytical findings and the utility of the model.

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Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

A Stochastic TB Model for a Crowded Environment

Vyambwera

Witbooi

2018

Journal of Applied Mathematics

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“…In the last decade, many applied mathematicians have been interested in the study of infection dynamics under perturbations based on stochastic compartmental models; see for example [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. The main idea here is that contacts between susceptible and infected populations are unpredictable.…”

Section: Introductionmentioning

confidence: 99%

Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach

et al. 2019

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Mass vaccination campaigns play major roles in the war against epidemics. Such prevention strategies cannot always reach their goals significantly without the help of media and awareness campaigns used to prevent contacts between susceptible and infected people. Feelings of fear, infodemics, and misconception could lead to some fluctuations of such policies. In addition to the vaccination strategy, the movement restriction approach is essential because of the factor of mobility or travel. However, anti-epidemic border measures may also be disturbed if some infected travelers manage to escape and infiltrate into a safer region. In this paper, we aim to study infection dynamics related to the spatial spread of an epidemic in interconnected regions in the presence of random perturbations caused by the three above-mentioned reasons. Therefore, we devise a stochastic multi-region epidemic model in which contacts between susceptible and infected populations, vaccination-based and movement restriction optimal control approaches are all assumed to be unpredictable, and then, we discuss the effectiveness of such policies. In order to reach our goal, we employ a stochastic maximum principle version for noised systems, state and prove the sufficient and necessary conditions of optimality, and finally provide the numerical results obtained using a stochastic progressive-regressive schemes method.

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“…Many authors have been introduced random effects into population systems by different techniques (see, e.g., [25][26][27][28][29][30][31][32][33][34]). Furthermore, in the study of the dynamical behavior of the epidemic models, we are interested in two situations.…”

Section: Introductionmentioning

confidence: 99%

Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals

Kiouach

Sabbar

2018

Discrete Dynamics in Nature and Society

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The aim of this paper is to generalize the nonlinear incidence rate of a stochastic SIRS (susceptible-infected-recovered-susceptible) epidemic model. Our basic model was enriched with the hypotheses of vertical transmission and transfer from infected to susceptible individuals, to approach the reality. Our analysis showed that the model is well-posed. Under some conditions imposed on the intensity of the white noise perturbation, the global stability of the system is proven. Furthermore, the threshold of our model which determines the extinction and persistence of the disease is established. Numerical examples are realized to prove the rigor of our theoretical results.

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Stability of an SEIR epidemic model with independent stochastic perturbations

Cited by 57 publications

References 18 publications

A Stochastic TB Model for a Crowded Environment

A Stochastic TB Model for a Crowded Environment

Role of Media and Effects of Infodemics and Escapes in the Spatial Spread of Epidemics: A Stochastic Multi-Region Model with Optimal Control Approach

Stability and Threshold of a Stochastic SIRS Epidemic Model with Vertical Transmission and Transfer from Infectious to Susceptible Individuals

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