Survival to extinction in a slowly varying harvested logistic population model

This work considers a harvested logistic population for which birth rate, carrying capacity and harvesting rate all vary slowly with time. Asymptotic results from earlier work, obtained using a multiscaling technique, are combined to construct approximate expressions for the evolving population for the situation where the population initially survives to a slowly varying limiting state, but then, due to increasing harvesting, is reduced to extinction in finite time. These results are shown to give very good agreement with those obtained from numerical computation.