Population extinction in an inhomogeneous host-pathogen model

We study inhomogeneous host-pathogen dynamics to model the global amphibian population extinction in a lake basin system. The lake basin system is modeled as quenched disorder. In this model we show that once the pathogen arrives at the lake basin it spreads from one lake to another, eventually spreading to the entire lake basin system in a wave like pattern. The extinction time has been found to depend on the steady state host population and pathogen growth rate. Linear estimate of the extinction time is computed. The steady state host population shows a threshold behavior in the interaction strength for a given growth rate.