Asymptotic behavior of a stochastic SIR model with general incidence rate and nonlinear Lévy jumps

Yang, Qingxiong; Zhang, Xinhong; Jiang, Daqing

doi:10.1007/s11071-021-07095-7

Cited by 17 publications

(8 citation statements)

References 57 publications

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“…Then, random fluctuations affect the distribution of infectious diseases since this type of epidemic spreads randomly. Therefore, some authors have expressed the random effect in their deterministic models by employing the direct perturbation of parameter approach [32][33][34][35]. For example, El Koufi et al in [26] have assumed that the stochastic perturbations are of white noise type and affect the transmission rate of disease.…”

Section: Model Formulationmentioning

confidence: 99%

The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

Koufi

Bennar

et al. 2022

Journal of Applied Mathematics

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At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value Π s of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results.

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Section: Model Formulationmentioning

confidence: 99%

The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

Koufi

Bennar

et al. 2022

Journal of Applied Mathematics

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“…The basic reproduction number in the SIR network model with the contact network provides a threshold for global stability for disease-free equilibrium (R 0 < 1) [7,8]. The basic reproductive number R 0 is one of the parameters to quantify the evolution of the endemic and can be treated as a critical point for mutations, which determines the prevalence of infectious diseases at temporal scale [4,5,[9][10][11][12][13]. Globalization results movement of infected individuals across boundaries, and therefore, spatial dynamics along with temporal dynamics of spread become critical [14].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

et al. 2023

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The world is facing Covid-19 waves and the overall pattern of confirmed cases shows periodic oscillations. In this paper, we investigate the spatio-temporal spread of Covid-19 in the network-organized SIR model with an extrinsic incubation period of the driving factors. Firstly, Our analysis shows the occurrence of Hopf bifurcation and periodic outbreaks which is consistent with the actual spread of Covid-19. And we investigate periodic waves on spatial scales using Turing instability, and the spread of infected individuals increases the localized hot spots. We study the effect of the incubation period, more incubation periods generate Turing instability resulting in periodic outbreaks. There is an occurrence of bursting states at peaks of periodic waves due to small diffusion of infected and susceptible, which means stable and unstable areas try to convert each other due to high competition among nodes. Also, We note the disappearance of these bursts when infected and susceptible individuals' movements are easier, thus dominance of infected individuals prevails everywhere. Effective policy interventions and seasonality can cause periodic perturbations in the model, and therefore we study the impact of these perturbations on the spread of Covid-19. Periodic perturbations on the driving factors, infected individuals show co-existing spatial patterns. Chaotic outbreak becomes periodic outbreaks through alternating periodic or period-2 outbreaks as we regulate the amplitude and frequency of infected individuals. In short, regulations can erase period-2 and chaotic spread through policy interventions.

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“…In recent years, several epidemiological models have been proposed to describe the impact of environmental noise on the dynamics of infectious diseases [10,11,12,13]. For instance, Cai et al [14] investigated the dynamics of a stochastic SIRS model with general infection force under intervention policy in which linear white noise was assumed to perturb the disease transmission coefficient.…”

Section: Introductionmentioning

confidence: 99%

Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants

Shi

Jiang

2023

Preprint

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As it is widely known, the spread of infectious diseases can result in significant socioeconomic consequences and pose a threat to public health. However, biologically plausible models that incorporate stochastic interference and dual epidemic hypotheses have received limited attention. This paper aims to bridge this gap by examining a stochastic dual epidemic hypothesis model that incorporates Ornstein-Uhlenbeck processes to perturb the nonlinear incidence rate. We provide a rigorous analysis of the model, first proving the existence and uniqueness of global solution. We also analyze sufficient conditions for the extinction or persistence of each disease. Additionally, we establish the existence of an ergodic stationary distribution and derive expressions for the normal distribution followed by the global solution around the endemic equilibrium. Finally, using several numerical experimental examples, we validate our theoretical results with the case of dual variants of SARS-CoV-2 that can simultaneously infect humans. This paper contributes to the understanding of stochastic dual epidemic hypotheses and provides a foundation for future research in this field.

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Asymptotic behavior of a stochastic SIR model with general incidence rate and nonlinear Lévy jumps

Cited by 17 publications

References 57 publications

The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants

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