Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)

Volume 18, Issue 3, pp 294--305 http://dx.doi.org/10.22436/jmcs.018.03.05 Publication Date: April 27, 2018       Article History

Authors

Ebrahim As-Shareef - School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China Arif Saif - School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China Cui-Hong Yang - School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China Xin-An Zhang - School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China


Abstract

The main goal of this paper is to develop a mathematical model to study the dynamic of malaria transmission, and the direct effects of congenital malaria on the spread of malaria. In this study, we have clarified the significant impact of malaria on the human community through their impact on the newborn, and that directly increases spread of the malaria in the human community, especially in the newborns with the lower and inexperienced immunity systems. The existence and stability of the disease-free points of the system is analyzed. We established that the disease-free equilibrium point is locally asymptotically stable when the reproduction number \(R_{0}<1\) and the disease always dies out. For \(R_{0}>1\) the disease-free equilibrium becomes unstable and there exists a unique endemic equilibrium.


Keywords


MSC


References