A novel droop-logistic model for microorganism population studies

Abstract

© 2018, UK Simulation Society. All rights reserved. In this work the Droop model and logistic model are combined to form another mathematical model for a microorganism population that is named the Droop-Logistic model. The equation of the organism growth of this model is from the logistic model, and the growth rate is from the Droop model. Our new model is shown to have a unique solution on an open set by the Lipschitz condition. By analyzing local stability, the condition for having maximum cell numbers and the condition for being stable from the balancing of the surrounding nutrient and the intracellular quota are determined. Numerical examples are given three values of dilution rate. It was found that when the dilution rate satisfies the condition of maximum growth, i.e. it is less than the maximum growth rate, then the cell number will reach its maximum at the stationary time. If the dilution rate is greater than the maximum growth rate, then the cell number will decrease to zero. Lastly, if the dilution rate is zero and the maximum growth condition is satisfied, then the cell number will tend to the maximum value as well.