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Stability Analysis of a Mathematical Model for Infection Diseases with Stochastic Perturbations

Author

Listed:
  • Marina Bershadsky

    (Department of Computer Science, Shamoon College of Engineering (SCE), Beer Sheva 8410802, Israel)

  • Leonid Shaikhet

    (Department of Mathematics, Ariel University, Ariel 40700, Israel)

Abstract

A well-known model of infectious diseases, described by a nonlinear system of delay differential equations, is investigated under the influence of stochastic perturbations. Using the general method of Lyapunov functional construction combined with the linear matrix inequality (LMI) approach, we derive sufficient conditions for the stability of the equilibria of the considered system. Numerical simulations illustrating the system’s behavior under stochastic perturbations are provided to support the thoretical findings. The proposed method for stability analysis is broadly applicable to other systems of nonlinear stochastic differential equations across various fields.

Suggested Citation

  • Marina Bershadsky & Leonid Shaikhet, 2025. "Stability Analysis of a Mathematical Model for Infection Diseases with Stochastic Perturbations," Mathematics, MDPI, vol. 13(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:14:p:2265-:d:1701064
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    References listed on IDEAS

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    1. Settati, A. & Caraballo, T. & Lahrouz, A. & Bouzalmat, I. & Assadouq, A., 2025. "Stochastic SIR epidemic model dynamics on scale-free networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 246-259.
    2. Zhou, Yanli & Zhang, Weiguo, 2016. "Threshold of a stochastic SIR epidemic model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 204-216.
    3. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. M. Bershadsky & M. Chirkov & A. Domoshnitsky & S. Rusakov & I. Volinsky, 2019. "Distributed Control and the Lyapunov Characteristic Exponents in the Model of Infectious Diseases," Complexity, Hindawi, vol. 2019, pages 1-12, November.
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