A mathematical model of the population dynamics of disease-transmitting vectors with spatial consideration

• Published in: Journal of biological dynamics Vol. 5; no. 4; pp. 335 - 365
• Main Authors: Nourridine, Siewe, Teboh-Ewungkem, Miranda I., Ngwa, Gideon A.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.07.2011
• Subjects: 34A; 34C; 92B; compartmental framework; flight range domain; Hopf bifurcation; population dynamics; vector-breeding sites and human habitat
• ISSN: 1751-3758; 1751-3766
• DOI: 10.1080/17513758.2010.508540

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 steady-state 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, , 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.