A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration
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Abstract
- A deterministic model with spatial consideration for a class of human disease-transmitting vectors is
presented and analysed. The model takes the form of a nonlinear system of delayed ordinary differential
equations in a compartmental framework. Using the model, existence conditions of a non-trivial steadystate
vector population are obtained when more than one breeding site and human habitat site are available.
Model analysis confirms the existence of a non-trivial steady state, uniquely determined by a threshold
parameter, Rj0
, whose value depends on the distribution and distance of breeding site j to human habitats.
Results are based on the existence of a globally and asymptotically stable non-trivial steady-state human
population. The explicit form of the Hopf bifurcation, initially reported by Ngwa [On the population
dynamics of the malaria vector, Bull. Math. Biol. 68 (2006), pp. 2161–2189], is also obtained and used
to show that the vector population oscillates with time. The modelling exercise points to the possibility of
spatial–temporal patterns and oscillatory behaviour without external seasonal forcing.
| Title | A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration |
|---|---|
| Creator | Ngwa, G. A. |
| Teboh-Ewungkem, Miranda | |
| Nourridine, S. | |
| Publisher | Journal of Biological Dynamics |
| Academic Department | Mathematics |
| Division | Natural Sciences |
| Organization | Lafayette College |
| Date Issued | 2011 |
| Date Available | 2013-01-23T15:49:45Z |
| Type | Article |
| Language | English |
| Keyword | Hopf bifurcation |
| population dynamics | |
| compartmental framework | |
| vector-breeding sites and human habitat | |
| flight range domain | |
| Bibliographic Citation | Nourridine, S. et al. (2011) "A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration." Journal of Biological Dynamics 5 (4): 335-365. |
| Standard Identifier | Handle 10385/1054 |
| DOI 10.1080/17513758.2010.508540 | |
| Permalink | http://hdl.handle.net/10385/1054 |
| Rights Statement |
In Copyright
|
| Rights Holders | Taylor & Francis |
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