Abstract:
The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading
insects that transmit disease. The method relies on the release of sterile or treated males in
order to reduce the wild population of anopheles mosquito. We propose two mathematical
models. The first model governs the dynamics of the anopheles mosquito. The second
model, the SIT model, deals with the interaction between treated males and wild female
anopheles. Using the theory of monotone operators, we obtain dynamical properties of a
global nature that can be summarized as follows. Both models are dissipative dynamical
systems on the positive cone R4
+. The value R = 1 of the basic offspring number R is a
forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium
0 being globally asymptotically stable (GAS) when R ≤ 1, whereas 0 becomes unstable and
one stable equilibrium is born with well determined basins of attraction when R > 1. For
the SIT model, we obtain a threshold number ˆλ of treated male mosquitoes above which
the control of wild female mosquitoes is effective. That is, for λ > ˆλ the equilibrium 0 is
GAS. When 0 < λ ≤ ˆλ, the number of equilibria and their stability are described together
with their precise basins of attraction. These theoretical results are rephrased in terms of
possible strategies for the control of the anopheles mosquito and they are illustrated by
numerical simulations.
