Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2017 (2017), Article ID 6754097, 15 pages
https://doi.org/10.1155/2017/6754097
Research Article

A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality

Department of Mathematics, Polytechnic University of Bobo Dioulasso, 01 BP 1091, Bobo-Dioulasso 01, Burkina Faso

Correspondence should be addressed to Boureima Sangaré

Received 22 January 2017; Accepted 26 April 2017; Published 4 June 2017

Academic Editor: Sabri Arik

Copyright © 2017 Bakary Traoré et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than , then the disease-free equilibrium is globally asymptotically stable and if it is greater than , then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.