Spatially extended host-parasite interactions: the role of recovery and immunity. (English) Zbl 1118.92066
Summary: Techniques for determining the long-term dynamics of host-parasite systems are well established for mixed populations. The field of spatial modelling in ecology is more recent but a number of key advances have been made. We use state-of-the-art approximation techniques, supported by simulations, in order to investigate the role of recovery and immunity in spatially structured populations. Our approach is to use correlation models, namely pair-wise models, to capture the spatial relationships of contacts and interactions between individuals. We use the pair-wise framework to address a number of key ecological questions; including, the persistence of endemic limit cycles and regions of parasite-driven extinction – features which differentiate spatial from non-spatial models – and the effects on invasion fitness. We demonstrate a loss of limit cycle behaviour, in addition to an increase in the critical transmissibility and extinction thresholds, when recovery is included. This approach allows for a better analytical understanding of the dynamics of host-parasite interactions and demonstrates the importance of recovery and immunity in local interactions.
MSC:
| 92D40 | Ecology |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 65C05 | Monte Carlo methods |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
Keywords:
Spatial structure; Pair-wise approximation; Limit cycles; Host extinction; Invasion fitnessSoftware:
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