Dynamics and Persistence of a Generalized Multi-strain SIS Model.

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.