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<p>This paper examines the asymptotic dynamics of an age-structured SIR model featuring nonlinear incidence and distributed delay. The dynamical behavior of the model is analysed via linearisation by means of semigroup and spectral methods. Initially, we establish the existence of equilibria and linearize the nonlinear system around these equilibria. Then, under the framework of operator semigroup, we obtain the well-posedness of the linearized system by transforming it into an abstract Cauchy problem. Based on the well-posedness result, we further establish additional regularity properties, which allow us to investigate the dynamical behavior, including stability/instability/Hopf bifurcation for the equilibria. Sufficient conditions for these phenomena are also derived. At last, some numerical simulations are provided to demonstrate the obtained results.</p>

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Dynamics of An Age-Structured SIR Model with Nonlinear Incidence and Distributed Delay

  • 期刊论文

  • 发表日期：

    2025年6月16日

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  • Yuan Yuan,
  • Dongxue Yan

摘要

This paper examines the asymptotic dynamics of an age-structured SIR model featuring nonlinear incidence and distributed delay. The dynamical behavior of the model is analysed via linearisation by means of semigroup and spectral methods. Initially, we establish the existence of equilibria and linearize the nonlinear system around these equilibria. Then, under the framework of operator semigroup, we obtain the well-posedness of the linearized system by transforming it into an abstract Cauchy problem. Based on the well-posedness result, we further establish additional regularity properties, which allow us to investigate the dynamical behavior, including stability/instability/Hopf bifurcation for the equilibria. Sufficient conditions for these phenomena are also derived. At last, some numerical simulations are provided to demonstrate the obtained results.