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<p>Early diagnostic testing is a critical tool for controlling COVID-19 transmission, enabling rapid case detection and isolation. This study develops an SPAQR (Susceptible, Pre-symptomatic, Asymptomatic, Quarantined, Recovered) compartmental model to investigate the impact of PCR-based screening on epidemic dynamics. We derive the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak{R}_{0}\)</EquationSource> </InlineEquation> as a threshold for disease extinction or persistence and analyze the local and global stability of the disease-free and endemic equilibria in terms of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak{R}_{0}\)</EquationSource> </InlineEquation>. Sensitivity analysis identifies the detection rate <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation> as the most influential parameter governing <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathfrak{R}_{0}\)</EquationSource> </InlineEquation>. Numerical simulations confirm that increasing the PCR testing rate substantially lowers <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathfrak{R}_{0}\)</EquationSource> </InlineEquation>, flattens the epidemic peak, and preserves a larger susceptible population. The results underscore the vital role of large-scale early diagnostic testing and prompt isolation in achieving effective and sustainable epidemic control.</p>

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The impact of early diagnostic tests in controlling COVID-19 disease, a mathematical study

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Salah Eddine Bessayeh,
  • Nacera Helal,
  • Mohamed Helal,
  • Abdelkader Lakmeche

摘要

Early diagnostic testing is a critical tool for controlling COVID-19 transmission, enabling rapid case detection and isolation. This study develops an SPAQR (Susceptible, Pre-symptomatic, Asymptomatic, Quarantined, Recovered) compartmental model to investigate the impact of PCR-based screening on epidemic dynamics. We derive the basic reproduction number \(\mathfrak{R}_{0}\) as a threshold for disease extinction or persistence and analyze the local and global stability of the disease-free and endemic equilibria in terms of \(\mathfrak{R}_{0}\) . Sensitivity analysis identifies the detection rate \(\delta\) as the most influential parameter governing \(\mathfrak{R}_{0}\) . Numerical simulations confirm that increasing the PCR testing rate substantially lowers \(\mathfrak{R}_{0}\) , flattens the epidemic peak, and preserves a larger susceptible population. The results underscore the vital role of large-scale early diagnostic testing and prompt isolation in achieving effective and sustainable epidemic control.