Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number
Pure and Applied Mathematics Journal
Volume 2, Issue 1, February 2013, Pages: 42-50
Received: Mar. 6, 2013; Published: Feb. 20, 2013
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Authors
Adamu Abdul Kareem, Mathematical Sciences Department, School of Pure & Applied Sciences, Modibbo Adama University of Technology, Yola, Adamawa State, Nigeria
Anande Richard Kimbir, Department of Mathematics & Computer, University of Agriculture, Markudi, Benue State, Nigeria
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Abstract
Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have shown that the model has a unique disease-free equilibrium state which is locally and globally asymptotically stable, if 1, and that the endemic equilibrium exist provided > 1, where is a parameter which depends on the given model parameters. Numerical simulations of the modified model clearly show that, with a proper combination of treatment and vaccination, offered at about 65% each on the susceptible and infected population, malaria can be eradicated from the community.
Keywords
Malaria, Disease-Free Equilibrium Point, Reproduction Number, Endemic Equilibrium Point, Global Asymp-totical Stability, Lyaponuv Function
To cite this article
Adamu Abdul Kareem, Anande Richard Kimbir, Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number, Pure and Applied Mathematics Journal. Vol. 2, No. 1, 2013, pp. 42-50. doi: 10.11648/j.pamj.20130201.17
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