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ScanLag: High-throughput Quantification of Colony Growth and Lag Time
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Dynamics and Persistence of a Generalized Multi-strain SIS Model.

Scott Greenhalgh1, Tabitha Henriquez2, Michael Frutschy3

  • 1Department of Mathematics, Siena University, 515 Loudon Road, Loudonville, NY, 12211, USA. sgreenhalgh@siena.edu.

Bulletin of Mathematical Biology
|September 10, 2025
PubMed
Summary

This study introduces a novel mathematical model for infectious disease spread, accounting for time-varying factors. The model offers analytical solutions for disease persistence and stability, improving epidemiological predictions.

Keywords:
Akaike information criteriaFloquet theoryForecast skill scoreOrdinary differential equationsStability analysisSyphilis

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Autonomous compartmental models are widely used but struggle to incorporate time-varying factors like seasonal changes.
  • Non-autonomous models can address these limitations by including time-dependent parameters, though analysis is often restricted to numerical methods.
  • Existing analytical techniques for non-autonomous models are limited, hindering a deeper understanding of disease dynamics.

Purpose of the Study:

  • To develop a novel n-strain generalized Susceptible-Infectious-Susceptible (SIS) compartmental model with time-varying recovery rates.
  • To derive analytical expressions for Floquet exponents, enabling theoretical analysis of model properties.
  • To characterize the persistence and stability of the n-strain SIS model and provide a closed-form solution for the single-strain case.

Main Methods:

  • Developed a generalized n-strain SIS compartmental model with a time-varying recovery rate.
  • Derived algebraic expressions for Floquet exponents, allowing for analytical tractability.
  • Characterized model persistence and stability properties for n >= 1.
  • Obtained a closed-form solution for the single-strain SIS model with general infectious period distributions.

Main Results:

  • The n-strain generalized SIS model yields Floquet exponents as algebraic expressions, a rare analytical outcome.
  • Complete characterization of persistence and stability properties for the n-strain model is achieved.
  • A closed-form solution for the single-strain SIS model is derived, accommodating diverse infectious period distributions.
  • The model's applicability was demonstrated using US syphilis incidence data, with Akaike Information Criteria and Forecast Skill Scores used for evaluation.

Conclusions:

  • The developed non-autonomous SIS model provides a tractable framework for analyzing infectious disease dynamics with time-varying parameters.
  • The analytical solutions enhance understanding of disease persistence and stability, offering advantages over purely numerical approaches.
  • The model's successful application to real-world data highlights its potential for accurate epidemiological forecasting and public health decision-making.