Effects of quasiperiodic forcing in epidemic models

We study changes in the bifurcations of seasonally driven compartmental epidemic models, where the transmission rate is modulated temporally. In the presence of periodic modulation of the transmission rate, the dynamics varies from periodic to chaotic. The route to chaos is typically through period...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2016-09, Vol.26 (9), p.093115-093115
Main Authors: Bilal, Shakir, Singh, Brajendra K., Prasad, Awadhesh, Michael, Edwin
Format: Article
Language:English
Subjects:
Bifurcations
Chaos theory
Computer Simulation
Disease Susceptibility
Epidemics
Humans
Models, Biological
Modulation
Nonlinear Dynamics
Period doubling
Periodicity
Regular
Time Factors
Toruses
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Summary:We study changes in the bifurcations of seasonally driven compartmental epidemic models, where the transmission rate is modulated temporally. In the presence of periodic modulation of the transmission rate, the dynamics varies from periodic to chaotic. The route to chaos is typically through period doubling bifurcation. There are coexisting attractors for some sets of parameters. However in the presence of quasiperiodic modulation, tori are created in place of periodic orbits and chaos appears via finite torus doublings. Strange nonchaotic attractors (SNAs) are created at the boundary of chaotic and torus dynamics. Multistability is found to be reduced as a function of quasiperiodic modulation strength. It is argued that occurrence of SNAs gives an opportunity of asymptotic predictability of epidemic growth even when the underlying dynamics is strange.
ISSN:1054-1500
1089-7682
1054-1500
DOI:10.1063/1.4963174