Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 28, pp. 1-22.

Title: Mathematical models for the transmission of malaria with seasonality and ivermectin
       
Authors: Zhihong Zhao (Univ. of Science and Tech., Beijing, China)
         Shaochun Li  (Univ. of Science and Tech., Beijing, China)
         Yulan Lu     (Univ. of Science and Tech., Beijing, China)

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 
R<sub>0</sub>; that is, malaria will gradually die out if R<sub>0</sub>&lt;1 
and will persist if R<sub>0</sub>&gt;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.

Submitted November 16, 2021. Published April 07, 2022.
Math Subject Classifications: 92B05, 37N25.
Key Words: Malaria model; ivermectin; time delay; basic reproduction ratio; sensitivity analysis.