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Related Experiment Video

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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Published on: September 23, 2025

Threshold dynamics in a time-delayed epidemic model with dispersal.

Michael C White¹, Xiao-Qiang Zhao

¹Department of Mathematics and Statistics, Memorial University of Newfoundland, PO Box 4200, St. John's, NL, Canada A1C 5S7. mikewhite@nl.rogers.com

Mathematical Biosciences

|July 1, 2009

Summary

This study shows that diseases persist when the basic reproduction number exceeds one, even with population dispersal between two areas. A small initial infected population helps the disease die out if the basic reproduction number is below one.

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Area of Science:

Mathematical Biology
Epidemiology
Population Dynamics

Background:

Investigates the global dynamics of a time-delayed mathematical model.
Considers population dispersal between two distinct patches.

Purpose of the Study:

To analyze disease persistence and extinction in a spatially structured population.
To determine the role of the basic reproduction number and initial conditions.

Main Methods:

Application of persistence theory for a general class of birth functions.
Mathematical modeling of disease spread with time delays and dispersal.
Numerical simulations using biologically relevant birth functions.

Main Results:

Disease persistence is proven when the basic reproduction number (R0) is greater than one.
Disease extinction is demonstrated if R0 is less than one and the initial infected population is small.
Dispersal's relevance to disease dynamics is illustrated.

Conclusions:

The basic reproduction number is a critical threshold for disease persistence.
Initial population size significantly influences disease extinction dynamics.
Population dispersal plays a key role in the spatial spread of diseases.