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
Submission Date: January 13, 2017
Revision Date: November 17, 2017
Accteptance Date: March 27, 2018
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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.
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ISRP Style
Ebrahim As-Shareef, Arif Saif, Cui-Hong Yang, Xin-An Zhang, Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria), Journal of Mathematics and Computer Science, 18 (2018), no. 3, 294--305
AMA Style
As-Shareef Ebrahim, Saif Arif, Yang Cui-Hong, Zhang Xin-An, Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria). J Math Comput SCI-JM. (2018); 18(3):294--305
Chicago/Turabian Style
As-Shareef, Ebrahim, Saif, Arif, Yang, Cui-Hong, Zhang, Xin-An. "Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)." Journal of Mathematics and Computer Science, 18, no. 3 (2018): 294--305
Keywords
- Congenital malaria
- vertical transmission
- basic reproduction number
- stability
MSC
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