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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 145398, 13 pages
http://dx.doi.org/10.1155/2014/145398
Research Article

Analysis of a Mathematical Model of Emerging Infectious Disease Leading to Amphibian Decline

Department of Mathematics, Lahore University of Management Sciences, DHA, Lahore Cantt 54792, Pakistan

Received 9 November 2013; Revised 12 February 2014; Accepted 2 March 2014; Published 28 April 2014

Academic Editor: Igor Leite Freire

Copyright © 2014 Muhammad Dur-e-Ahmad 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

We formulate a three-dimensional deterministic model of amphibian larvae population to investigate the cause of extinction due to the infectious disease. The larvae population of the model is subdivided into two classes, exposed and unexposed, depending on their vulnerability to disease. Reproduction ratio has been calculated and we have shown that if , the whole population will be extinct. For the case of , we discussed different scenarios under which an infected population can survive or be eliminated using stability and persistence analysis. Finally, we also used Hopf bifurcation analysis to study the stability of periodic solutions.