# The Impact of Malaria Transmission from Mother to the Newborn on the Spread of Malaria

The Impact of Malaria Transmission from Mother to the Newborn on the Spread of Malaria

Ghoul RafiaJing He Sana Djaidja Ebrahim As-Shareef

Department of Computer Science and Technology, College of Computer Science and Engineering, Hunan University, Changsha 410000, China

Department of Medicine, Faculty of Medicine of Algiers - Mohamed Maherzi (Ex Laperrine), Algiers 16000, Algeria

Department of Mathematics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430000, China

Corresponding Author Email:
Tigre.eco@live.fr
Page:
88-97
|
DOI:
https://doi.org/10.18280/ama_a.550208
12 March 2018
|
Accepted:
17 May 2018
|
Published:
30 June 2018
| Citation

OPEN ACCESS

Abstract:

The main objective of this paper is to develop a mathematical model to study the dynamic of malaria transmission for the human and mosquito populations. In this study we have clarified the significant impact of congenital malaria (vertical transmission of malaria from mother to baby before or during birth). We see the direct effects of congenital malaria on the spread of malaria and impact it on the basic reproduction number. In our model the human population is divided into three classes and the mosquito population is divided into two classes, our appropriate model of 5-dimensional nonlinear system which incorporates and includes the infection newborn shows that the disease-free equilibrium is globally asymptotically stable if 〖R〗_0<1 and if 〖R〗_0>1 the endemic equilibrium is locally asymptotically stable proved by Routh- Hurwitz criterion. Our numerical simulations and graphical results conform the analysis predictions.

Keywords:

congenital malaria, vertical transmission, basic reproduction number, asymptotically stable, numerical simulation

1. Introduction
2. Mathematical Model Description and Analysis
3. Disease-Free Equilibrium Point and Reproduction Number
4. Numerical Simulation
5. Discussion
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