IJPAM: Volume 99, No. 4 (2015)

MATHEMATICAL ANALYSIS OF THE DYNAMICS OF
MALARIA DISEASE TRANSMISSION MODEL

E.A. Bakare$^1$, C.R. Nwozo$^2$
$^1$Department of Mathematics
Federal University Oye Ekiti
Ekiti State, NIGERIA
$^2$Department of Mathematics
University of Ibadan
Ibadan, NIGERIA


Abstract. We formulate a deterministic model for the transmission dynamics of malaria parasite in mosquito and human. The model, which allows for the transmission of the parasite, has a global asymptotic stable disease-free if a certain epidemiological threshold called the reproductive number is less than unity. We realized that the model has a unique academic equilibrium whenever this threshold exceeds unit. We proved that, using a Lyapunov function, that this endemic equilibrium is globally asymptotically stable whenever the basic reproduction number is greater than unity. We also carried out numerical simulations to support our analytical results.

Received: May 1, 2014

AMS Subject Classification: 92B05, 92D25, 92D30, 93D05, 34K20, 34K25

Key Words and Phrases: basic reproduction number, global asymptotic stability, disease-free-equilibrium, endemic equilibrium, Lyapunov function

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DOI: 10.12732/ijpam.v99i4.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 4
Pages: 411 - 437


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