Michaelis-Menten Models with Constant Harvesting of Restricted Prey Populations Minimum Place and Amount Capacity

Food chain modeling is currently developing rapidly. The ecosystem is protected from the chain of eating and eating processes. All living things need each other, but if the process of eating them is not balanced, then the extinction of living things will occur. One of them is the prey and predator model that serves as a balancer in the food chain system. The Michaelis-Menten model is a prey-predator model that essentially prevents prey extinction. The problem is how to keep the prey from becoming extinct but with maximum harvesting in one place and the minimum amount of prey at the right time. The method used to overcome this problem is to add two new variables to the Michaelis-Menten model, namely the minimum number of prey and the capacity of the place to be occupied. It is seen that the system will be in equilibrium if the predator mortality rate is large so that the prey is kept from extinction until harvesting. In addition, the right time for good breeding can also be determined. From this model, it is found that the right time for harvesting so that prey extinction does not occur is