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 ${ℛ}_0$ has been calculated and we have shown that if , the whole population will be extinct. For the case of ${ℛ}_0>1$, 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.