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A multi-season epidemic model with random genetic drift and transmissibility
Tom Britton1, Andrea Pugliese2
1Department of Mathematics, Stockholm University, Stockholm, Sweden. tom.britton@math.su.se.
Journal of Mathematical Biology
|November 12, 2025
Summary
This study models influenza-like disease spread, showing how viral genetic drift and transmissibility impact epidemics. Community immunity evolves predictably, allowing prediction of epidemic size using early growth rates and immunity status.
Area of Science:
- Epidemiology
- Mathematical Biology
- Virology
Background:
- Influenza-like diseases exhibit seasonal patterns influenced by viral evolution and population immunity.
- Understanding the interplay between viral genetic drift, transmissibility, and host immunity is crucial for predicting epidemic dynamics.
Purpose of the Study:
- To develop a mathematical model for influenza-like disease spread considering seasonal viral genetic drift and transmissibility changes.
- To analyze the long-term behavior of community immunity and its impact on epidemic outcomes.
- To establish a method for predicting epidemic size based on early outbreak characteristics.
Main Methods:
- A stochastic model was developed to simulate disease transmission across seasons.
- Community immunity status was modeled as an ergodic Markov chain converging to a stationary distribution.
- Analytical solutions were derived for a simplified case with single-season immunity.
- The relationship between effective reproduction number and initial growth rate was investigated.
Main Results:
- The model demonstrates that community immunity status follows a predictable Markovian process, reaching a stable distribution over time.
- For single-season immunity, stationary distributions for key epidemic parameters (effective reproduction number, infection fractions) were characterized.
- A strong correlation was found between the effective reproduction number and the initial exponential growth rate of an outbreak.
- The conditional distribution of infection fractions given the effective reproduction number was derived.
Conclusions:
- The long-term immunity status of a community can be modeled as a stationary Markov chain.
- Early epidemic growth rates, alongside current immunity levels, can be leveraged to predict the final epidemic size.
- This modeling approach offers valuable insights for public health interventions and preparedness strategies for influenza-like illnesses.
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