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Interaction of maturation delay and nonlinear birth in population and epidemic models 总被引：16，自引：0，他引：16
A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e−
d
1
T−dN(t) governs the adult population, with the death rate in previous life stages d
1≧0. Standard assumptions are made on B(N) so that a unique equilibrium N
e
exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d
1>0, as T increases the equilibrium N
e
can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease
that does not cause death is introduced into the population, a threshold parameter R
0 is identified. When R
0<1, the disease dies out; when R
0>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations
indicate that oscillations can also be induced by disease related death in a model with maturation delay.
Received: 2 November 1998 / Revised version: 26 February 1999 相似文献
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IUMS NewsInternational Union of Microbiological Societies Newsletter 相似文献
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Ficus burtt-davyi, like most other fig species (Ficus, Moraceae), is exclusively pollinated by its own unique species of fig wasp, in this caseElisabethiella baijnathi (Chalcidoidea, Agaonidae). Because fig crop development on any one tree is usually synchronised, the small and short-lived
female wasps have to migrate and find other trees bearing figs which are at suitable stage of development for oviposition.
However, the likelihood of successful location and subsequent arrival at a new host tree is dependent on distance and the
effect of environmental factors such as wind and temperature. This study examines the relationship between ambient temperatures
and the timing of fig wasps emergence from their natal figs and the commencement of their dispersal flight. The behaviour
of the wasps arriving at figs which were ready to be pollinated was also examined. The female wasps did not appear to distinguish
between the figs and other parts of the tree when in flight. However, after landing on the tree their search for figs was
more directed as they visited more figs than leaves. Short-range recognition of figs appears to be by contact chemo-reception,
but the wasps showed a preference for entering figs which did not already contain a female wasp. 相似文献
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IUMS NewsInternational Union of Microbiological Societies Newsletter 相似文献
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