Jv. Greenman et Pj. Hudson, INFECTED COEXISTENCE INSTABILITY WITH AND WITHOUT DENSITY-DEPENDENT REGULATION, Journal of theoretical biology, 185(3), 1997, pp. 345-356
Numerical studies of two-host shared pathogen systems, using nonlinear
dynamical models, have suggested that there are a set of simple rules
governing the possible number of stable equilibria. In this paper we
show by counterexample that these rules are not universally valid, whe
ther or not the system is subject to density-dependent regulation. The
analysis of diverse counterexamples reveals a variety of structures,
including models with no relevant stable equilibria or with multiple s
table infected coexistence equilibria. In the former case, asymptotic
behaviour is characterised by single or multiple limit cycles, generat
ing sustained oscillations. It has also been found possible to have li
mit cycles and stable equilibria coexisting in the same model. The par
ameter values defining the counterexamples reflect exceptional but, in
most cases, plausible situations and provide insight into the mechani
sms by which stability fails to be achieved. One biological implicatio
n of this analysis is that long-lived infective stages are not necessa
ry to produce oscillations in the numbers of forest living invertebrat
es. (C) 1997 Academic Press Limited.