Stability analysis of mutualism model with time delay and proportional harvesting

Abstract

This paper studies the effect of time delay and proportional harvesting on stability of mutualism model as well as to establish conditions for sustainable harvesting so that the unique positive equilibrium point is stable. First the stability of the model with harvesting is analyzed. The model is then improved by considering a time delay in the mechanism of the growth rate of the population. The analysis shows that when there is no delay, varying the harvesting rate does not affect the stability of the model if the value of harvesting rate is under control while time delay can cause a stable equilibrium point to become unstable.