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<p>In this paper, a novel age-structured epidemiological model that simultaneously considers multiple viral strains is proposed. We develop a numerical framework for the study of the dynamics and optimal control by a linearly implicit Euler method, in which the biological meaning is unconditionally preserved. The first order convergence of numerical solutions in a finite time is derived from a uniform numerical boundedness. Moreover, the numerical dynamics are determined by a numerical basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="285_2024_2180_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_h\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>h</mi> </msub> </math></EquationSource> </InlineEquation>, which reflects the asymptotic stability of the equilibrium points. The abstract framework offers an effective and unified approach to study the long-time behaviour of multi-strain epidemic models that cover a wide variety of well-known models, which also provides a numerical optimal control strategy of the multi-strain age-structured SIR model. Finally, some numerical simulations illustrate the verification and the efficiency of our results.</p>

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Numerical dynamics and optimal control for multi-strain age-structured epidemic model

  • 期刊论文

  • 发表日期：

    2025年1月16日

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  • Zhijie Chen,
  • Hanmeng Feng

摘要

In this paper, a novel age-structured epidemiological model that simultaneously considers multiple viral strains is proposed. We develop a numerical framework for the study of the dynamics and optimal control by a linearly implicit Euler method, in which the biological meaning is unconditionally preserved. The first order convergence of numerical solutions in a finite time is derived from a uniform numerical boundedness. Moreover, the numerical dynamics are determined by a numerical basic reproduction number \(R_h\) R h , which reflects the asymptotic stability of the equilibrium points. The abstract framework offers an effective and unified approach to study the long-time behaviour of multi-strain epidemic models that cover a wide variety of well-known models, which also provides a numerical optimal control strategy of the multi-strain age-structured SIR model. Finally, some numerical simulations illustrate the verification and the efficiency of our results.