### A Delayed Mathematical Model to break the life cycle of Anopheles Mosquito

#### Abstract

In this paper, we propose a delayed mathematical model to break the life cycle of anopheles mosquito at the larva stage by incorporating a time delay τ at the larva stage that accounts for the period of growth or development to pupa. We prove local stability of the system’s equilibrium and find the critical values for Hopf bifurcation to occur. Also, we find that the system’s equilibrium undergoes stability switching from stable to periodic to unstable and vice versa when the time delay τ crosses the imaginary axis from the left half plane to the right half plane in the (Re,Im) plane. Finally, we perform some numerical simulations and the results agree well with the analytical analysis. This is the first time such a model is proposed.

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DOI: http://dx.doi.org/10.23755/rm.v31i0.319

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