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Effects of quasiperiodic forcing in epidemic models
Shakir Bilal1, Brajendra K Singh2, Awadhesh Prasad1
1Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India.
Chaos (Woodbury, N.Y.)
|October 27, 2016
Summary
This study explores how changing transmission rates in epidemic models affect disease spread dynamics. We found that quasiperiodic modulation can lead to strange nonchaotic attractors, offering potential for predictable epidemic growth.
Area of Science:
- Mathematical epidemiology
- Dynamical systems theory
- Nonlinear dynamics
Background:
- Compartmental epidemic models are crucial for understanding disease transmission.
- Temporal modulation of transmission rates can significantly alter epidemic dynamics.
- Previous studies focused on periodic forcing, leaving quasiperiodic effects less explored.
Purpose of the Study:
- To investigate bifurcations in seasonally driven compartmental epidemic models with temporally modulated transmission rates.
- To characterize the transition from periodic to chaotic dynamics under different modulation types (periodic vs. quasiperiodic).
- To explore the emergence and implications of strange nonchaotic attractors (SNAs) in epidemic modeling.
Main Methods:
- Analysis of bifurcations in seasonally driven compartmental epidemic models.
- Simulation of model dynamics under periodic and quasiperiodic modulation of the transmission rate.
- Identification of period-doubling bifurcations and torus doublings leading to chaos.
- Characterization of strange nonchaotic attractors (SNAs) at the chaos-torus boundary.
Main Results:
- Periodic modulation leads to dynamics ranging from periodic to chaotic, often via period-doubling bifurcations.
- Quasiperiodic modulation results in the creation of tori and chaos via finite torus doublings.
- Strange nonchaotic attractors (SNAs) emerge at the boundary between chaotic and torus dynamics.
- Multistability decreases with increasing quasiperiodic modulation strength.
Conclusions:
- Quasiperiodic modulation introduces complex dynamics, including SNAs, in epidemic models.
- The presence of SNAs suggests a degree of asymptotic predictability in epidemic growth, even in chaotic regimes.
- This research advances understanding of nonlinear dynamics in epidemiological modeling.
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