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MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY

Part of: General theory in ordinary differential equations Mathematical biology in general Integral equations, integral transforms

Published online by Cambridge University Press:  18 December 2020

DINY ZULKARNAEN Open the ORCID record for DINY ZULKARNAEN [Opens in a new window]  and
MARIANITO R. RODRIGO
DINY ZULKARNAEN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: [email protected]. Department of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, West Java, Indonesia; e-mail: [email protected].
MARIANITO R. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: [email protected].
*
e-mail: [email protected]
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Abstract

We assume that human carrying capacity is determined by food availability. We propose three classes of human population dynamical models of logistic type, where the carrying capacity is a function of the food production index. We also employ an integration-based parameter estimation technique to derive explicit formulas for the model parameters. Using actual population and food production index data, numerical simulations of our models suggest that an increase in food availability implies an increase in carrying capacity, but the carrying capacity is “self-limiting” and does not increase indefinitely.

Keywords

logistic modelvariable carrying capacityfood production indexmathematical modelling

MSC classification

Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
Secondary: 65R32: Inverse problems 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 3 , July 2020 , pp. 318 - 333
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Copyright
© Australian Mathematical Society 2020

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