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The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case

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  • Sabbar, Yassine
  • Kiouach, Driss
  • Rajasekar, S.P.
  • El-idrissi, Salim El Azami

Abstract

This study concentrates on the analysis of a stochastic SIC epidemic system with an enhanced and general perturbation. Given the intricacy of some impulses caused by external disturbances, we integrate the quadratic Lévy noise into our model. We assort the long-run behavior of a perturbed SIC epidemic model presented in the form of a system of stochastic differential equations driven by second-order jumps. By ameliorating the hypotheses and using some new analytical techniques, we find the exact threshold value between extinction and ergodicity (persistence) of our system. The idea and analysis used in this paper generalize the work of N. T. Dieu et al. (2020), and offer an innovative approach to dealing with other random population models. Comparing our results with those of previous studies reveals that quadratic jump-diffusion has no impact on the threshold value, but it remarkably influences the dynamics of the infection and may worsen the pandemic situation. In order to illustrate this comparison and confirm our analysis, we perform numerical simulations with some real data of COVID-19 in Morocco. Furthermore, we arrive at the following results: (i) the time average of the different classes depends on the intensity of the noise (ii) the quadratic noise has a negative effect on disease duration (iii) the stationary density function of the population abruptly changes its shape at some values of the noise intensity.

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  • Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003204
    DOI: 10.1016/j.chaos.2022.112110
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    2. Yassine Sabbar & Asad Khan & Anwarud Din, 2022. "Probabilistic Analysis of a Marine Ecological System with Intense Variability," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    3. Yassine Sabbar & Mohammad Izadi & Aeshah A. Raezah & Waleed Adel, 2024. "Nonlinear Dynamics of a General Stochastic SIR Model with Behavioral and Physical Changes: Analysis and Application to Zoonotic Tuberculosis," Mathematics, MDPI, vol. 12(13), pages 1-17, June.
    4. Elaiw, A.M. & Alsaedi, A.J. & Hobiny, A.D. & Aly, S., 2023. "Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    5. Ye, Yong & Zhao, Yi & Zhou, Jiaying, 2022. "Promotion of cooperation mechanism on the stability of delay-induced host-generalist parasitoid model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

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