## Abstract and Applied Analysis

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

#### 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 ${\scr R}_{0}$ has been calculated and we have shown that if ${\scr R}_{0}<1$, the whole population will be extinct. For the case of ${\scr R}_{0}>1$, 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 145398, 13 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412605855

Digital Object Identifier
doi:10.1155/2014/145398

Mathematical Reviews number (MathSciNet)
MR3206767

Zentralblatt MATH identifier
07021806

#### Citation

Dur-e-Ahmad, Muhammad; Imran, Mudassar; Khan, Adnan. Analysis of a Mathematical Model of Emerging Infectious Disease Leading to Amphibian Decline. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 145398, 13 pages. doi:10.1155/2014/145398. https://projecteuclid.org/euclid.aaa/1412605855

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