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Analysis of a COVID-19 Epidemic Model with Seasonality
1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada. zhiminl@mun.ca.
Bulletin of Mathematical Biology
|November 11, 2022
Summary
This study models seasonal COVID-19 transmission, finding that a higher basic reproduction number indicates persistent disease with periodic outbreaks. Numerical analysis confirms a stable, recurring pattern for COVID-19 cases.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Dynamics
Background:
- COVID-19 cases show seasonal patterns globally.
- Understanding these fluctuations is crucial for public health interventions.
Purpose of the Study:
- To develop a mathematical model for COVID-19 transmission incorporating seasonality.
- To analyze the impact of the basic reproduction number on disease dynamics.
Main Methods:
- Formulation of a compartmental epidemic model with seasonal forcing.
- Analytical determination of disease-free equilibrium stability.
- Investigation of disease persistence and periodic solutions using bifurcation theory.
- Numerical simulations and case study using US COVID-19 data.
Main Results:
- The disease-free equilibrium is globally asymptotically stable when the basic reproduction number is below a critical threshold.
- When the basic reproduction number exceeds this threshold, the disease becomes uniformly persistent.
- Existence of at least one positive periodic solution demonstrated theoretically.
- Numerical simulations indicate a globally asymptotically stable positive periodic solution under specific conditions.
Conclusions:
- Seasonality significantly influences COVID-19 transmission dynamics.
- The basic reproduction number is a critical determinant of disease persistence and epidemic patterns.
- The model provides insights into recurring COVID-19 outbreaks, validated by US data.
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