Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis

Boukanjime, Brahim; Fatini, Mohamed El; Laaribi, Aziz; Taki, Regragui

doi:10.1016/j.physa.2019.122321

Cited by 21 publications

(10 citation statements)

References 14 publications

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“…In fact, the COVID-19 epidemic model is unavoidably subjected to the environmental noise, which made the parameters involved in the system often fluctuate randomly around some average values as the surrounding environment fluctuation. See [1] , [2] , [3] , [5] , [6] , [7] , [16] , [25] and references therein for epidemic models with environmental noise. Therefore, it is necessary to include random fluctuations in the process of COVID-19 modelling.…”

Section: Model and Preliminariesmentioning

confidence: 99%

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Boukanjime

Caraballo

Fatini

et al. 2020

Chaos, Solitons & Fractals

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In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and telegraph noise incorporating general incidence rate. Firstly, we investigate the existence and uniqueness of a global positive solution. Then, we establish the stochastic threshold for the extinction and the persistence of the disease. The data from Indian states, are used to confirm the results established along this paper.

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Section: Model and Preliminariesmentioning

confidence: 99%

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Boukanjime

Caraballo

Fatini

et al. 2020

Chaos, Solitons & Fractals

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“…Recently, the research on modelling two types of infectious diseases draw many applied mathematicians' attention [6][7][8][9][10][11]. In [6], the authors discussed an epidemic model with double hypothesis combined two different transmission mechanisms.…”

Section: Introductionmentioning

confidence: 99%

An Stochastic Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

xunyang,

Shi,

canyun

et al. 2024

Preprint

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In this paper, a stochastic epidemic model with two different types of infectious diseases that spread through both horizontal and vertical transmission is investigaed. By constructing suitable Lyapunov functions and applying Itˆ o’s formula as well as Chebyshev’s inequality, the sufficient conditions for stochastic ultimate boundedness and permanence are established. The reliability of theoretical results are further illustrated by numerical simulations.

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“…The effect of environmental variabilities due to the water temperature, humidity, and floods was ignored in the above model. There is a growing interest in considering the environmental perturbations in epidemiology model since it has turned out that the stochastic model can describe real-life problems in a more accurate way [19][20][21][25][26][27]. To date, there are different ways to include the stochastic effects in the model.…”

Section: Introductionmentioning

confidence: 99%

Stationary distribution and probability density function of a stochastic waterborne pathogen model with saturated direct and indirect transmissions

Liu

2023

Math Methods in App Sciences

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We investigate the dynamical behavior of deterministic and stochastic waterborne pathogen models with saturated incidence rates. In particular, the indirect transmission via person–water–person contact is half‐saturated and the direct transmission by person–person contact takes the saturated form. Possible equilibrium points of the model are investigated, and their stability criterion is discussed. Basic reproduction number of the model is obtained through the next‐generation matrix method. It has been shown that the disease‐free equilibrium is locally stable when and unstable for . Furthermore, a stochastic Lyapunov method is adopted to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the proposed stochastic model, which reveals that the infection will persist if . We also obtain an exact expression of the probability density function near the quasi‐endemic equilibrium of stochastic system. Finally, numerical simulations are carried out to support our analytical findings. Results suggest that saturation constants in both direct and indirect transmissions play a positive role in controlling disease. Our results may provide some new insights for the elimination of waterborne disease.

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Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis

Cited by 21 publications

References 14 publications

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

An Stochastic Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission

Stationary distribution and probability density function of a stochastic waterborne pathogen model with saturated direct and indirect transmissions

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