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Competitive Exclusion, Viral Persistence, and Stochastic Coexistence in a Two-Species Chemostat with SIR-Structured Infection

  • Jialu Zhu [1] ; Tao Feng [2] ; Zhipeng Qiu [1]
    1. [1] Nanjing University of Science and Technology

      Nanjing University of Science and Technology

      China

    2. [2] Yangzhou University

      Yangzhou University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 4, 2026
  • Idioma: inglés
  • Enlaces
  • Resumen

    • We study a two-species stochastic chemostat with a single limiting nutrient, in which one competitor is subject to a viral infection with an SIR-type compartmental structure.

      Our analysis yields verifiable sufficient criteria for competitive exclusion, viral extinction or persistence, and stochastic coexistence. First, we introduce stochastic average break-even nutrient concentrations for the two competitors and use them to derive explicit sufficient conditions for competitive exclusion. Under these conditions, the competitor with the larger stochastic nutrient requirement becomes extinct, while the other persists. Second, for the infection dynamics, we analyze an auxiliary boundary system for the nutrient and susceptible class, define a noise-dependent invasion index through its ergodic invariant measure, and obtain sufficient criteria for viral extinction and persistence. Under an additional balance condition involving dilution, growth, and noise intensities, we further establish the existence and uniqueness of a stationary distribution for the full system, which characterizes stochastic coexistence in the interior state space. Euler–Maruyama simulations support the theoretical results and suggest that environmental noise, together with viral transmission, can promote coexistence in parameter regimes where the corresponding deterministic model does not.

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