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<p>To investigate the impact of time delay and booster vaccinations on pertussis transmission, this paper establishes a model of pertussis infection incorporating the incubation delay of pertussis and the effect of control measures based on the mechanisms of pertussis spread. Through theoretical analysis, we demonstrate that when the control reproduction number is less than 1, the disease-free equilibrium of the system is globally asymptotically stable. When the control reproduction number exceeds 1, the system possesses a unique endemic equilibrium that is globally asymptotically stable. Furthermore, sensitivity analysis indicates that reducing the effective contact rate, increasing first-dose vaccination coverage and enhancing early detection and treatment of confirmed cases are crucial for reducing transmission. Numerical simulation results reveal: (a) the peak size of pertussis infections decreases as the time delay increases, and the peak onset time is delayed accordingly; (b) when the treatment recovery rate increases from 0.5 to 0.9, the peak size of the total infected population decreases by 92.4<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\%\)</EquationSource> </InlineEquation>; (c) when the coverage rate of the first vaccine dose is raised from 0.6 to 0.9, the peak size of total infections decreases by 8.58<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\%\)</EquationSource> </InlineEquation>; in contrast, an increase in the booster dose coverage from 0.2 to 0.5 resulted in a 1.57<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\%\)</EquationSource> </InlineEquation> reduction in the peak size of total infected individuals. The findings suggest that increasing first-dose and booster vaccine coverage, as well as improving timely treatment rates, are all effective strategies for significantly reducing pertussis transmission.</p>

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Global dynamics of a pertussis transmission model with time delay and vaccine boosters

  • 期刊论文

  • 发表日期：

    2026年7月21日

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  • Xiaojing Wang,
  • Kun Liu,
  • Yucan Tang,
  • Maoxing Liu

摘要

To investigate the impact of time delay and booster vaccinations on pertussis transmission, this paper establishes a model of pertussis infection incorporating the incubation delay of pertussis and the effect of control measures based on the mechanisms of pertussis spread. Through theoretical analysis, we demonstrate that when the control reproduction number is less than 1, the disease-free equilibrium of the system is globally asymptotically stable. When the control reproduction number exceeds 1, the system possesses a unique endemic equilibrium that is globally asymptotically stable. Furthermore, sensitivity analysis indicates that reducing the effective contact rate, increasing first-dose vaccination coverage and enhancing early detection and treatment of confirmed cases are crucial for reducing transmission. Numerical simulation results reveal: (a) the peak size of pertussis infections decreases as the time delay increases, and the peak onset time is delayed accordingly; (b) when the treatment recovery rate increases from 0.5 to 0.9, the peak size of the total infected population decreases by 92.4 \(\%\) ; (c) when the coverage rate of the first vaccine dose is raised from 0.6 to 0.9, the peak size of total infections decreases by 8.58 \(\%\) ; in contrast, an increase in the booster dose coverage from 0.2 to 0.5 resulted in a 1.57 \(\%\) reduction in the peak size of total infected individuals. The findings suggest that increasing first-dose and booster vaccine coverage, as well as improving timely treatment rates, are all effective strategies for significantly reducing pertussis transmission.