Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective

Jean Claude Kamgang¹, Vivient Corneille Kamla¹, Stéphane Yanick Tchoumi²

¹Department of Mathematics and Computer Sciences, ENSAI, University of N’Gaoundéré, N’Gaoundéré, Cameroon.
²Department of Mathematics and Computer Sciences, Faculty of Science, University of N’Gaoundéré, N’Gaoundéré, Cameroon.

DOI: 10.4236/am.2014.519298                

Abstract

We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas. The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes. This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model. We compute the basic reproduction number, and show that if, the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant. If, the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable. Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature. Finally, we discuss the relative effectiveness of different kinds of bed nets.

Keywords

Epidemiological Model, Malaria, Basic Reproduction Number, Lyapunov Function, Global Asymptotic Stability, Non-Standard Finite Difference Scheme (NFDS), Simulation

Conflicts of Interest

The authors declare no conflicts of interest.

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