Discrete and dynamic population models with logistic growth rate
"The Beverton-Holt difference equation defines a discrete relation describing a population model. Considering periodic carrying capacity and periodic inherent growth rate, a population with seasonal changing life cycle and environment is reflected. The so-called periodically forced Beverton-Holt equation is investigated and its unique periodic solution is derived. This provides the first Cushing-Henson conjecture, while a counterexample proves that the classical second Cushing-Henson conjecture is not satisfied. Modifications of the conjecture are formulated. To extend the studies, the Beverton-Holt equation is investigated in the quantum calculus time setting. The existence of the globally attracting periodic solution of the Beverton-Holt q-difference equation is derived and modified versions of the second Cushing-Henson conjecture are presented. To include ecological aims in the population model, the exploitation of a single population is discussed. Instead of the classical approach of variational calculus, a novel technique is applied to obtain the maximum sustainable yield of a harvested single population with logistic growth. This powerful tool serves as a foundation for the analysis of the exploitation of the discrete population model. The Beverton-Holt population model including harvesting is defined and its unique periodic solution derived. The goal is to optimize the annual-sustainable yield with respect to the harvest effort. Logistic differential equations not only appear in context of single population models but also in epidemiology. One of the basic epidemic models introduced by Kermack and McKendrick in 1927 is the SIS model, Susceptible-Infected-Susceptible model. This system of logistic differential equations describes the spread of infectious diseases. In this work, we present the formulation of the epidemic SIS model in the general setting of time scales"--Abstract, page iv.
Criteria, EOR, Polymer, Prediction, Screening, Semantic, Mathematics
Missouri University of Science and Technology
Networked Digital Library of Theses and Dissertations