The Role of Non-Linear Birth Functions on the Dynamics of Malaria Vector Population

Abstract

As mosquito vector plays a significant role in malaria dynamics, a deterministic delay differential equation model 10 for the
population dynamics of the malaria vector is rigorously analyzed for the non-delay part subject to a new form of vector birth
rate function; the Hassell function. For the Hassell function, the model has a non-trivial equilibrium which is locallyasymptotically
stable under certain conditions. It is also shown that the non-trivial equilibrium corresponding to this birth
function bifurcates into a limit cycle via a Hopf bifurcation. The Maynard-Smith-Slatkin function is better than the
Verhulst-Pearl logistic growth function as the former is associated with increased sustained oscillations 9. Again this
Maynard- Smith-Slatkin function is more preferable than the Hassell function as the prior one is pertained to more sustained
oscillations and holds the analyzed properties for the realistic size of the limiting birth rate.