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