IJPAM: Volume 76, No. 3 (2012)

DYNAMICAL FEATURES OF DENGUE DISEASE
WITH SATURATING INCIDENCE RATE

Gul Zaman$^1$, Abid Ali Lashari$^2$, M. Ikhlaq Chohan$^3$
$^1$Department of Mathematics
University of Malakand
Chakdara Dir (Lower), Khyber Pakhtunkhwa, PAKISTAN
$^2$Centre for Advanced Mathematics and Physics
National University of Sciences and Technology
H-12, Islamabad, PAKISTAN
$^3$Business and Accounting Department Al Buraimi
University College
Al Buraimi, OMAN


Abstract. In this paper we present the dynamical feature of dengue disease which is now endemic in more than 100 countries in the world. We develop a mathematical model taking into account the hospitalized compartment to present transmission of mosquitoes (Aedes aegypti) virus and its existence in human population. It is shown that the stability of the equilibria in the proposed model can be controlled by the basic reproduction number of the disease transmission. We use Lyapunove function theory to present global asymptotical stability. Finally, we show parameter estimation that characterize the natural history of this disease with numerical simulations.

Received: December 1, 2011

AMS Subject Classification: 92D25, 49J15, 93D20

Key Words and Phrases: stability, dengue fever, population dynamics, numerical simulation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 3