Effect of Movement on the Early Phase of an Epidemic
1Department of Mathematics and Data Science Nexus, University of Manitoba, Winnipeg, MB, Canada.
Bulletin of Mathematical Biology
|September 23, 2022
Abstract:
The early phase of an epidemic is characterized by a small number of infected individuals, implying that stochastic effects drive the dynamics of the disease. Mathematically, we define the stochastic phase as the time during which the number of infected individuals remains small and positive. A continuous-time Markov chain model of a simple two-patch epidemic is presented. An algorithm for formalizing what is meant by small is presented, and the effect of movement on the duration of the early stochastic phase of an epidemic is studied.
Insights
Stochastic effects dominate early epidemics when infected numbers are small. Movement between populations can alter the duration of this critical early epidemic phase.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Science
Background:
- Early epidemic phases are driven by random events (stochastic effects) due to low infection numbers.
- Understanding this stochastic phase is crucial for predicting disease spread.
- Previous models often overlooked the detailed dynamics of this initial period.
Purpose of the Study:
- To mathematically define and analyze the early stochastic phase of an epidemic.
- To investigate how population movement influences the duration of this phase.
- To develop a method for quantifying 'small' numbers of infections.
Main Methods:
- Developed a continuous-time Markov chain model for a two-patch epidemic system.
- Created an algorithm to formally define the 'small' number of infected individuals.
- Simulated epidemic spread to assess the impact of inter-patch movement.
Main Results:
- The duration of the stochastic phase is sensitive to the rate of movement between populations.
- Movement can either prolong or shorten the stochastic phase depending on parameters.
- The study provides a framework for analyzing early epidemic dynamics.
Conclusions:
- Population movement is a significant factor affecting the early stochastic dynamics of epidemics.
- Mathematical modeling, like Markov chains, is essential for understanding disease emergence.
- Quantifying the stochastic phase aids in targeted public health interventions during outbreaks.
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