Abstract
An infectious disease may reduce or even stop the exponential growth of a population. We consider two very simple models for microparasitic and macroparasitic diseases, respectively, and study how the effect depends on a contact parameter K. The results are presented as bifurcation diagrams involving several threshold values of к. The precise form of the bifurcation diagram depends critically on a second parameter ζ, measuring the influence of the disease on the fertility of the hosts. A striking outcome of the analysis is that for certain ranges of parameter values bistable behaviour occurs: either the population grows exponentially or it oscillates periodically with large amplitude.
Original language | English |
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Pages (from-to) | 539-570 |
Number of pages | 32 |
Journal | Journal of Mathematical Biology |
Volume | 29 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Jan 1991 |
Keywords
- Bistable behaviour
- Epidemic
- Oscillations
- Population regulation
- Threshold values for contact parameter