Malaria is a major public health issue in many parts of the world, and the anopheles mosquitoes which drive
transmission are key targets for interventions. Consequently, a best understanding of mosquito populations
dynamics is necessary in the fight against the disease. Hence, in this paper we propose a delayed mathematical
model of the life cycle of anopheles mosquitoes by using delayed-logistic population growth. The model is
formulated by inserting the time delay into the logistic population growth rate, that accounts for the period of
growth from eggs to the last aquatic stage, which is pupae. Depending on the system parameters, we establish
a threshold for survival and extinction of the anopheles mosquitoes population. Moreover, by choosing the time
delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when
time delay passes through some critical values. Finally, we perform some numerical simulations and the results
are well in keeping with the analytical analysis.

Mosquitoes population delayed-logistic growth malaria transmission mathematical analysis