scholarly journals Asymptotic properties of a stochastic SIQR epidemic model with Lévy Jumps and Beddington-DeAngelis incidence rate

2021 ◽  
pp. 104472
Author(s):  
Amine El Koufi ◽  
Abdelkrim Bennar ◽  
Nouhaila El Koufi ◽  
Noura Yousfi
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Asymptotic Properties ◽  
Lévy Jumps

The long-time behavior of a stochastic SIR epidemic model with distributed delay and multidimensional Lévy jumps

2021 ◽  
Author(s):  
Driss Kiouach ◽  
Yassine Sabbar
Keyword(s):  
Epidemic Model ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Time Behavior ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Long Run ◽  
Long Time ◽  
Lévy Jumps

This paper reports novel theoretical and analytical results for a perturbed version of a SIR model with Gamma-distributed delay. Notably, our epidemic model is represented by Itô–Lévy stochastic differential equations in order to simulate sudden and unexpected external phenomena. By using some new and ameliorated mathematical approaches, we study the long-run characteristics of the perturbed delayed model. Within this scope, we give sufficient conditions for two interesting asymptotic properties: extinction and persistence of the epidemic. One of the most interesting results is that the dynamics of the stochastic model are closely related to the intensities of white noises and Lévy jumps, which can give us a good insight into the evolution of the epidemic in some unexpected situations. Our work complements the results of some previous investigations and provides a new approach to predict and analyze the dynamic behavior of epidemics with distributed delay. For illustrative purposes, numerical examples are presented for checking the theoretical study.

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

scholarly journals Modeling and sensitivity analysis of HBV epidemic model with convex incidence rate

2021 ◽  
Vol 22 ◽  
pp. 103836
Author(s):  
Amir Khan ◽  
Rahat Zarin ◽  
Ghulam Hussain ◽  
Auwalu Hamisu Usman ◽  
Usa Wannasingha Humphries ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Incidence Rate ◽  
Epidemic Model

scholarly journals Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yakui Xue ◽  
Tiantian Li
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Endemic Equilibrium ◽  
Logistic Growth ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Sir Epidemic Model ◽  
Globally Asymptotically Stable ◽  
Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

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