August 17, 2025Open Access

SIRS model for computer viruses propagation with time dependent delay and jumps

MDMilica DjordjevicUniversity of Nis JÐJasmina ÐorđevićUniversity of Nis

Key Points

Extinction conditions from the unique stochastic SIRS model for computer viruses are identified, demonstrating that the viruses can vanish from the system.
Theoretical proof confirms the global and positive nature of the model's solution, featuring two independent computer viruses under stochastic influences.
Assessment includes numerical simulations that illustrate theoretical results, employing the Euler-Maruyama method for validation.
This research suggests conditions for strong persistence in mean populations of viruses, indicating robustness against extinction.

Abstract

In this paper we propose stochastic SIRS model which describes propagation of two independent computer viruses. Randomness is introduced in the model by perturbing transmission rates via Brownian motion and Poisson jump. For this model, we theoretically prove that its solution is unique, global and positive. Furthermore, we derive conditions under which viruses become extinct from population. Also, conditions for stochastic strong persistence in mean of viruses will be obtained. In the end, we will present numerical simulations to illustrate our theoretical results using Euler-Maruyama method.

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