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<p>The growing frequency and complexity of simultaneous infectious disease outbreaks underscore the urgent need for more precise models that capture the inherent randomness of epidemic dynamics. This study introduces a novel stochastic framework modeling the interaction of two co-circulating infectious diseases, combining both SIR and SIRS transmission structures. To realistically reflect the unpredictable nature of epidemics, the model incorporates Brownian motion to represent continuous environmental fluctuations and Lévy jumps to account for abrupt shocks. We establish sufficient conditions under which the diseases either die out, persist, or coexist amid stochastic influences. Notably, our results demonstrate that stochastic effects can drive disease extinction even when deterministic reproduction numbers indicate potential endemicity. Numerical simulations are provided to validate the theoretical findings, and a sensitivity analysis on the stochastic parameters is conducted to explore their impact on epidemic outcomes.</p>

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A stochastic model of co-circulating diseases with distinct immunity profiles incorporating Lévy jumps

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • T. Tamil Selvan,
  • Mahesh Kumar

摘要

The growing frequency and complexity of simultaneous infectious disease outbreaks underscore the urgent need for more precise models that capture the inherent randomness of epidemic dynamics. This study introduces a novel stochastic framework modeling the interaction of two co-circulating infectious diseases, combining both SIR and SIRS transmission structures. To realistically reflect the unpredictable nature of epidemics, the model incorporates Brownian motion to represent continuous environmental fluctuations and Lévy jumps to account for abrupt shocks. We establish sufficient conditions under which the diseases either die out, persist, or coexist amid stochastic influences. Notably, our results demonstrate that stochastic effects can drive disease extinction even when deterministic reproduction numbers indicate potential endemicity. Numerical simulations are provided to validate the theoretical findings, and a sensitivity analysis on the stochastic parameters is conducted to explore their impact on epidemic outcomes.