Two mathematical models for dissolved oxygen in a lake—CMMSE-16

In this paper two mathematical models for handling water pollution are introduced. In the first one we assume that algae and fungi are in competition for resources that come from wastewater, while in the second one we introduce explicitly the equation of nutrients. Both algae and fungi need dissolved oxygen (DO) for their biological process of growth. But there is a difference, indeed algae produce it too and in a higher quantity than the one they use. For the first model it is shown that if the coexistence equilibrium exists, it is stable without additional conditions. If the competition rate between algae and fungi is not high for a chosen set of parameters the stability of the coexistence equilibrium is reached even without an external constant input of DO in the system. For the second model we have found the matching equilibrium points with the ones of the first model, furthermore other two equilibria are found.