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Modeling epidemic dynamics in variable environments using nonlinear perturbation methods
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DOI：10.1007/s11071-026-13033-2.png)
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Abstract
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This paper develops and analyzes a deterministic and stochastic SIR epidemic model incorporating logistic population growth, a non-monotone incidence rate, and treatment limited by hospital-bed capacity. The deterministic analysis establishes conditions for disease extinction and persistence, derives the basic reproduction number, and reveals complex dynamics through the study of transcritical, saddle-node, Hopf, and Bogdanov–Takens bifurcations. The stochastic model developed incorporating the effect of environmental noise, proving the existence of positive solutions, extinction and persistence criteria, stationary distributions, and probability density function. Stochastic sensitivity analysis and confidence ellipses are employed to quantify the influence of environmental fluctuations on disease dynamics and to identify regions of heightened vulnerability to random perturbations. The findings highlight how limited healthcare resources and environmental fluctuations influence epidemic outcomes.
Keywords:
Limited hospital beds
Bogdanov–Takens bifurcation
Stationary distribution
Confidence ellipse
Stochastic sensitivity
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6
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1.4W
Citations:
4.1W
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Scientific Reports
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Scientific ReportsIF3.9
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