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

Marina Bershadsky () and Leonid Shaikhet ()
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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

Mathematics, 2025, vol. 13, issue 14, 1-14

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.

Keywords: white noise; Ito’s stochastic differential equation; the general method of constructing Lyapunov functionals; stability in probability; linear matrix inequalities (LMIs) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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