TITLE:
Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective
AUTHORS:
Jean Claude Kamgang, Vivient Corneille Kamla, Stéphane Yanick Tchoumi
KEYWORDS:
Epidemiological Model, Malaria, Basic Reproduction Number, Lyapunov Function, Global Asymptotic Stability, Non-Standard Finite Difference Scheme (NFDS), Simulation
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.19,
November
12,
2014
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.