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Abstract <p>This study develops compartmental epidemic models based on systems of ordinary and delayed differential equations to investigate the transmission dynamics of COVID-19. A normalized model incorporating a discrete time delay associated with the latent period of infection is analyzed, and the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_0\)</EquationSource> </InlineEquation> is derived to examine its influence on the stability of disease-free and endemic equilibria. It is shown that the disease-free equilibrium is locally asymptotically stable when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R_0 &lt; 1\)</EquationSource> </InlineEquation>, whereas the endemic equilibrium is stable for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R_0&gt; 1\)</EquationSource> </InlineEquation>, independently of the length of the delay. The model is subsequently extended to include vaccination, allowing the impact of different vaccination rates on disease transmission to be examined. Numerical simulations are presented to support the analytical results and to illustrate how time delay and vaccination jointly affect the system dynamics. The results highlight the critical role of vaccination in reducing the basic reproduction number below unity and achieving disease elimination. The framework provides a theoretical basis for designing time-sensitive vaccination policies in future pandemics.</p>

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Modeling the role of latent period and vaccination in COVID-19 dynamics

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Padma Bhushan Borah,
  • Kaushik Dehingia,
  • Evren Hinçal,
  • Ausif Padder,
  • Hemanta Kumar Sarmah

摘要

Abstract

This study develops compartmental epidemic models based on systems of ordinary and delayed differential equations to investigate the transmission dynamics of COVID-19. A normalized model incorporating a discrete time delay associated with the latent period of infection is analyzed, and the basic reproduction number \(R_0\) is derived to examine its influence on the stability of disease-free and endemic equilibria. It is shown that the disease-free equilibrium is locally asymptotically stable when \(R_0 < 1\) , whereas the endemic equilibrium is stable for \(R_0> 1\) , independently of the length of the delay. The model is subsequently extended to include vaccination, allowing the impact of different vaccination rates on disease transmission to be examined. Numerical simulations are presented to support the analytical results and to illustrate how time delay and vaccination jointly affect the system dynamics. The results highlight the critical role of vaccination in reducing the basic reproduction number below unity and achieving disease elimination. The framework provides a theoretical basis for designing time-sensitive vaccination policies in future pandemics.