@article{Zhao2026, 
author = {Yanfei Zhao and Yongkun Li},
title = {Asymptotic behaviors and dynamical bifurcation of a stochastic multi-strain epidemic model with jump diffusion},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14915-14952},
keywords = {multi-strain epidemic model, Lévy noise, invariant measure, dynamical bifurcation},
url = {https://www.sciopen.com/article/10.3934/math.2026614},
doi = {10.3934/math.2026614},
abstract = {This paper investigated the asymptotic behavior and dynamical bifurcation of a stochastic multi-strain epidemic model with jump diffusion. We defined a threshold parameter    λ as the Lyapunov exponent of the total infected population, which incorporates the stationary distribution of strain proportions on the disease-free boundary and a jump-induced correction term arising from the Lévy noise:     λ  =      ∫          Δ            [        ∑          i      =      1        n        (        β    i        y    i    −  (      γ    i    +      μ    i    +      η    i    )      y    i        )    −      1    2        (        ∑          i      =      1        n        σ          2      i            y    i              )        2        ]        μ    ∗    (  d  y  )  +      ∫                  Y                  [    ln  ⁡      (    1  +      ∑          i      =      1        n        y    i        f          2      i        (  u  )      )    −      ∑          i      =      1        n        y    i        f          2      i        (  u  )      ]    ν  (  d  u  )  .This threshold provides a necessary and sufficient condition for overall disease persistence (   λ  >  0) versus extinction (   λ  ≤  0). Moreover, we introduced strain-specific thresholds        λ    i   and established a competitive exclusion principle: The strain with the largest        λ    i   dominates, while strains with smaller        λ    i   go extinct; when two or more strains share the same maximal        λ    i  , they can coexist. Furthermore,    λ serves as a dynamical bifurcation point: When    λ  ≤  0, the unique invariant measure is concentrated on the extinction set; when    λ  >  0, this measure loses stability and a new invariant measure supported on the positive orthant emerges. Numerical simulations confirmed the critical role of    λ and illustrated competitive exclusion between strains under different noise intensities.}
}