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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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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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.
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.
Aslan G, Seyrek A. (2007). The diagnosis of malaria and identification of plasmodium species by polymerase chain reaction in turkey. pp:87-102
Deressa, Wakgari, Ali, Ahmed and Berhane, (2000). Yemane Maternal responses to childhood febrile illnesses in an area of seasonal malaria transmission in rural ethiopia. Acta tropica, pp: 134-166
Dietz, Molineaux and Thomas (1974) Development of a new version of the Liverpool malaria model. Oxford University Press, Oxford.
Kakkilaya, B. S. (2003). Rapid diagnosis of malaria, lab medicine, 8(34), 602-608
Nedelman J. (1985) Estimation for a model of multiple malaria infections. Phil. Trans. R. Soc. London. 65(4), 291: 451-524
Perandin F. (2003). Development of a Real-time PCR assay for detection of plasmodium falciparum, plsmodium vivax, and plasmodium ovale for routine clinical diagnosis. Journal of clinical microbiology, 42 (3), 1214-1219, A Moody, Rapid diagnostic tests for malaria parasites, Clin Microbiol Rev 15 (2002), pp. 66–78.
Tumwiine, Mugisha J. Y. T and Lubobi L. S (2007). Applied mathematics and computation. 189(2007) pp1953-1965.
Yang Hyun. M, (2000) Mapping and predicting malaria transmission in the People’s Republic of China, using intergrated biology-driven and statistical models. Phil. Trans. R. Soc. London, pp: 291: 451-524.