Abstract and Applied Analysis
Volume 2013 (2013), Article ID 293293, 12 pages
http://dx.doi.org/10.1155/2013/293293
Research Article

Stability Analysis of a Vector-Borne Disease with Variable Human Population

Muhammad Ozair,1 Abid Ali Lashari,1 Il Hyo Jung,2 Young Il Seo,3 and Byul Nim Kim2

1Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan
2Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea
3National Fisheries Research and Development Institute, Busan 619-705, Republic of Korea

Received 25 November 2012; Revised 1 March 2013; Accepted 2 March 2013

Academic Editor: Ferenc Hartung

Copyright © 2013 Muhammad Ozair et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A mathematical model of a vector-borne disease involving variable human population is analyzed. The varying population size includes a term for disease-related deaths. Equilibria and stability are determined for the system of ordinary differential equations. If , the disease-“free” equilibrium is globally asymptotically stable and the disease always dies out. If , a unique “endemic” equilibrium is globally asymptotically stable in the interior of feasible region and the disease persists at the “endemic” level. Our theoretical results are sustained by numerical simulations.