Parametric dependence in model epidemics. II: Non-contact rate-related parameters

W. M. Schaffer, T. V. Bronnikova

Research output: Contribution to journalArticle

1 Scopus citations

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, β0, and the magnitude of seasonality, ϵB. 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 β0−ϵB 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 languageEnglish (US)
Pages (from-to)231-248
Number of pages18
JournalJournal of biological dynamics
Volume1
Issue number3
DOIs
StatePublished - Jul 2007

Keywords

  • Bifurcations
  • Continuation
  • Epidemiology
  • Mathematical models
  • SEIR Equations

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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