MATHEMATICAL MODELS FOR THE TRANSMISSION OF MALARIA WITH SEASONALITY AND IVERMECTIN

Abstract

Ivermectin has shown good effects for malaria control in clinical trial stages because it can kill mosquitoes feeding on recently treated individuals. In this article, we formulate and analyze a novel delay malaria transmission model taking into account seasonality and ivermectin. We show that the dynamics of the model is totally determined by the basic reproduction ratio R0; that is, malaria will gradually die out if R0 < 1 and will persist if R0 > 1. Numerically, we verify the obtained theoretical results and evaluate the effect of ivermectin by related data of Kenya. We find that our simulation of the impact agrees with the prediction of the existing clinical trials in which it takes at least 25 years to eliminate malaria from Kenya with malaria control measures intact.