Abstract
A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
Original language | English |
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Pages (from-to) | 661-686 |
Number of pages | 26 |
Journal | Mathematical Biosciences and Engineering |
Volume | 12 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- And stability)
- Basic reproduction number
- Boundedness
- Equilibria (existence
- Extinction
- Lyapunov functions
- Persistence
- Uniqueness
ASJC Scopus subject areas
- General Medicine
- Modelling and Simulation
- General Agricultural and Biological Sciences
- Computational Mathematics
- Applied Mathematics