A cluster-based model of COVID-19 transmission dynamics
1Theoretical and Applied Mechanics, Mechanical and Aerospace Engineering, Cornell University, Ithaca 14853, New York, USA.
Chaos (Woodbury, N.Y.)
|December 9, 2021
Summary
A new mathematical model explains sudden COVID-19 waves, even with preventive measures. It highlights how transmission within social clusters, not just overall spread, drives epidemic surges, a phenomenon termed cryptogenic instability.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Dynamics
Background:
- COVID-19 trajectories often show sudden epidemic waves despite consistent preventive measures.
- Classical epidemiological models struggle to explain these non-classical disease progression patterns.
Purpose of the Study:
- To develop a mathematical model explaining sudden, severe epidemic waves.
- To identify the mechanisms behind non-classical disease spread dynamics.
Main Methods:
- Construction of a deterministic, discrete-time, discrete-population mathematical model named the cluster seeding and transmission model.
- Hypothesizing that transmission primarily occurs within closed social clusters (e.g., families, friends).
- Analyzing the impact of intra-cluster versus inter-cluster transmission on epidemic trajectories.
Main Results:
- Identified 'cryptogenic instability': infrequent inter-cluster transmission can destabilize low-case plateaus into large epidemic waves.
- Demonstrated that this instability can occur even with a small contribution to the overall population-averaged spreading rate.
- Observed a 'critical mass effect' where stochasticity at low case counts can temporarily suppress instability.
Conclusions:
- The cluster seeding and transmission model explains sudden epidemic surges not captured by conventional models.
- Inter-cluster transmission dynamics are crucial for understanding and managing epidemic outbreaks.
- Emergent phenomena like cryptogenic instability and critical mass effect challenge current epidemic management strategies.
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