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  3. Post-peak Dynamics And Epidemic Overshoot In Sir-type Frameworks.
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  3. Post-peak Dynamics And Epidemic Overshoot In Sir-type Frameworks.

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Post-peak dynamics and epidemic overshoot in SIR-type frameworks.

Zhimin Li1, Yijun Lou2, Zhen Jin3

  • 1Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China; School of Science, Chang'an University, Xi'an, 710064, China.

Mathematical Biosciences
|June 19, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study provides analytical results for cumulative infections and deaths post-epidemic peak using the SIR model. It offers tools for assessing post-peak risks and planning public health interventions.

Keywords:
DeclineOvershootPost-peak dynamicsSIR model

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Existing disease transmission models focus on pre-peak dynamics and reducing the reproduction number.
  • Post-peak cumulative infections and deaths are critical but understudied aspects of epidemic control.

Purpose of the Study:

  • To systematically investigate post-peak epidemic indices within the Susceptible-Infected-Recovered (SIR) model.
  • To derive analytical results for cumulative infections and deaths after the epidemic peak.
  • To provide practical tools for assessing post-peak risks and informing public health interventions.

Main Methods:

  • Derivation of explicit analytical results for cumulative infections and deaths in the SIR model.
  • Development of closed-form expressions for the epidemic peak and its timing.
  • Establishment of rigorous upper bounds for post-peak cumulative infections and deaths.
  • Validation of theoretical findings using numerical simulations on real-world epidemic data.

    • Main Results:

    • Closed-form expressions for epidemic peak timing and magnitude derived.
    • Sharp upper bounds established for cumulative infections and deaths post-peak.
    • Theoretical results validated against real-world epidemic scenarios, demonstrating applicability across diverse incidence rates.

    Conclusions:

    • The study advances the theoretical understanding of post-peak epidemic dynamics in SIR models.
    • Provides practical tools for accurate post-peak risk assessment and resource planning.
    • Highlights limitations in deriving exact analytical expressions for cumulative post-peak outcomes in extended models.