Qualitative analysis of a nonautonomous stochastic $ SIS $ epidemic model with L$ \acute {e} $vy jumps

Lv, Long; Yao, Xiaojuan

doi:10.3934/mbe.2021071

MBE

2021

DOI: 10.3934/mbe.2021071

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Qualitative analysis of a nonautonomous stochastic $ SIS $ epidemic model with L$ \acute {e} $vy jumps

Long Lv

Xiaojuan Yao

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Cited by 3 publications

References 28 publications

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Effect of seasonally forced noisy environment on aquatic prey–predator model with water level fluctuations

Sarkar

Pal

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, the impact of environmental noise on prey–predator interactions with seasonal fluctuations in water levels has been studied. Both intensity of noise and water level variations together play a significant role in the dynamics of an aquatic prey–predator system. Analytically, we have shown the existence of a positive solution and its uniqueness, the ultimate bound of the system’s solutions, and the global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go into extinction are derived and their biological significance is also discussed. The sufficient condition of stochastic permanence is also analyzed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic systems and observed some significant dynamics in the considered system.

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Effect of seasonally forced noisy environment on aquatic prey–predator model with water level fluctuations

Sarkar

Pal

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

Liu

et al. 2023

Int. J. Biomath.

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To investigate the effect of information transmission, Lévy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic, a stochastic SIQR epidemic model with non-monotone incidence rate and Lévy jumps on scale-free networks is constructed. At first, the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov functions. Then the stochastic model is made in accordance with the ecological significance, the existence and uniqueness of the global positive solution of the stochastic SIQR model is manifested. Next, by constructing suitable stochastic Lyapunov functions and applying Itô formula with jump, the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is checked. At last, the correctness of the analytical results is verified by numerical simulations.

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Global dynamics and density function in a class of stochastic SVI epidemic models with Lévy jumps and nonlinear incidence

Wang¹,

Wang²,

Teng

2023

MATH

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<abstract><p>The paper studies the global dynamics and probability density function for a class of stochastic SVI epidemic models with white noise, Lévy jumps and nonlinear incidence. The stability of disease-free and endemic equilibria for the corresponding deterministic model is first obtained. The threshold criteria on the stochastic extinction, persistence and stationary distribution are established. That is, the disease is extinct with probability one if the threshold value $ R_{0}^{s} < 1 $, and the disease is persistent in the mean and any positive solution is ergodic and has a unique stationary distribution if $ R_{0}^{s} > 1 $. Furthermore, the approximate expression of the log-normal probability density function around the quasi-endemic equilibrium of the stochastic model is calculated. A new technique for the calculation of the probability density function is proposed. Lastly, the numerical examples and simulations are presented to verify the main results.</p></abstract>

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Qualitative analysis of a nonautonomous stochastic $ SIS $ epidemic model with L$ \acute {e} $vy jumps

Cited by 3 publications

References 28 publications

Effect of seasonally forced noisy environment on aquatic prey–predator model with water level fluctuations

Effect of seasonally forced noisy environment on aquatic prey–predator model with water level fluctuations

Asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

Global dynamics and density function in a class of stochastic SVI epidemic models with Lévy jumps and nonlinear incidence

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