Abstract
In a previous paper, we discussed the bifurcation structure of SEIR equations subject to seasonality. There, the focus was on parameters that affect transmission: the mean contact rate, β(0), and the magnitude of seasonality, ε(B). Using numerical continuation and brute force simulation, we characterized a global pattern of parametric dependence in terms of subharmonic resonances and period-doublings of the annual cycle. In the present paper, we extend this analysis and consider the effects of varying non-contact-related parameters: periods of latency, infection and immunity, and rates of mortality and reproduction, which, following the usual practice, are assumed to be equal. The emergence of several new forms of dynamical complexity notwithstanding, the pattern previously reported is preserved. More precisely, the principal effect of varying non-contact related parameters is to displace bifurcation curves in the β(0)-ε(B) parameter plane and to expand or contract the regions of resonance and period-doubling they delimit. Implications of this observation with respect to modeling real-world epidemics are considered.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 231-248 |
| Number of pages | 18 |
| Journal | Journal of Biological Dynamics |
| Volume | 1 |
| Issue number | 3 |
| State | Published - Jul 2007 |
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ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics
- Ecology
Cite this
Parametric dependence in model epidemics. II : Non-contact rate-related parameters. / Schaffer, William M; Bronnikova, T. V.
In: Journal of Biological Dynamics, Vol. 1, No. 3, 07.2007, p. 231-248.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Parametric dependence in model epidemics. II
T2 - Non-contact rate-related parameters.
AU - Schaffer, William M
AU - Bronnikova, T. V.
PY - 2007/7
Y1 - 2007/7
N2 - In a previous paper, we discussed the bifurcation structure of SEIR equations subject to seasonality. There, the focus was on parameters that affect transmission: the mean contact rate, β(0), and the magnitude of seasonality, ε(B). Using numerical continuation and brute force simulation, we characterized a global pattern of parametric dependence in terms of subharmonic resonances and period-doublings of the annual cycle. In the present paper, we extend this analysis and consider the effects of varying non-contact-related parameters: periods of latency, infection and immunity, and rates of mortality and reproduction, which, following the usual practice, are assumed to be equal. The emergence of several new forms of dynamical complexity notwithstanding, the pattern previously reported is preserved. More precisely, the principal effect of varying non-contact related parameters is to displace bifurcation curves in the β(0)-ε(B) parameter plane and to expand or contract the regions of resonance and period-doubling they delimit. Implications of this observation with respect to modeling real-world epidemics are considered.
AB - In a previous paper, we discussed the bifurcation structure of SEIR equations subject to seasonality. There, the focus was on parameters that affect transmission: the mean contact rate, β(0), and the magnitude of seasonality, ε(B). Using numerical continuation and brute force simulation, we characterized a global pattern of parametric dependence in terms of subharmonic resonances and period-doublings of the annual cycle. In the present paper, we extend this analysis and consider the effects of varying non-contact-related parameters: periods of latency, infection and immunity, and rates of mortality and reproduction, which, following the usual practice, are assumed to be equal. The emergence of several new forms of dynamical complexity notwithstanding, the pattern previously reported is preserved. More precisely, the principal effect of varying non-contact related parameters is to displace bifurcation curves in the β(0)-ε(B) parameter plane and to expand or contract the regions of resonance and period-doubling they delimit. Implications of this observation with respect to modeling real-world epidemics are considered.
UR - http://www.scopus.com/inward/record.url?scp=84871872958&partnerID=8YFLogxK
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M3 - Article
VL - 1
SP - 231
EP - 248
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
SN - 1751-3758
IS - 3
ER -