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Parametric dependence in model epidemics. II: Non-contact rate-related parameters
1Department of Ecology and Evolutionary Biology, The University of Arizona, Tucson, AZ 85721, USA. wms@u.arizona.edu
This study explores how non-contact parameters in SEIR models influence epidemic dynamics. Varying these factors shifts resonance patterns but preserves the overall bifurcation structure, aiding real-world epidemic modeling.
Area of Science:
- Mathematical epidemiology
- Dynamical systems theory
Background:
- Previous work analyzed SEIR bifurcation structures focusing on transmission parameters (contact rate, seasonality magnitude).
- The study characterized global parametric dependence via subharmonic resonances and period-doublings of the annual cycle.
Purpose of the Study:
- Extend SEIR bifurcation analysis to non-contact-related parameters.
- Investigate the impact of latency, infection, immunity periods, and mortality/reproduction rates on epidemic dynamics.
- Assess how these changes affect previously identified resonance and period-doubling patterns.
Main Methods:
- Numerical continuation
- Brute force simulation
- Analysis of SEIR (Susceptible-Exposed-Infectious-Recovered) equations
Main Results:
- Varying non-contact parameters introduces new dynamical complexity.
- The previously reported global bifurcation pattern is preserved.
- Non-contact parameters primarily displace bifurcation curves in the contact rate-seasonality plane.
- Regions of resonance and period-doubling are expanded or contracted.
Conclusions:
- The fundamental bifurcation structure of seasonal SEIR models is robust to changes in non-contact parameters.
- Understanding these parameter effects aids in refining real-world epidemic modeling.
- Displacement of bifurcation curves offers insights into epidemic predictability.
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