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SIS epidemic attractors in periodic environments
John E Franke1, Abdul-Aziz Yakubu
1Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA. franke@math.ncsu.edu
Journal of Biological Dynamics
|August 11, 2012
Summary
In periodic environments, demographic dynamics do not always drive disease spread in susceptible-infected-susceptible (SIS) models. Chaotic attractors and infinitely complex basins of attraction were discovered, impacting epidemic modeling.
Area of Science:
- Epidemiology
- Mathematical Biology
- Dynamical Systems Theory
Background:
- Demographic dynamics typically influence disease spread in stable environments.
- Periodic environmental fluctuations can alter established relationships between population changes and disease transmission.
Purpose of the Study:
- To investigate if demographic dynamics consistently drive disease dynamics in periodically forced epidemic models.
- To explore the complexity of attractors and their basins of attraction in such models.
Main Methods:
- Analysis of a Susceptible-Infected-Susceptible (SIS) epidemic model with periodic forcing.
- Demonstration of a chaotic attractor within the model.
- Mathematical proof regarding the structure of coexisting attractors' basins of attraction.
Main Results:
- Demographic dynamics do not always drive disease dynamics in periodic environments.
- A chaotic attractor was identified in an SIS model with asymptotically cyclic demographic dynamics.
- The basins of attraction for coexisting attractors in periodically forced SIS models possess infinitely many components.
Conclusions:
- The interplay between demography and disease is more complex in periodic environments than previously assumed.
- The existence of chaotic attractors and intricate basin structures necessitates advanced modeling approaches for accurate epidemic prediction.
- Findings challenge the universality of demographic drivers in epidemic dynamics under fluctuating conditions.
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