To switch or taper off: the dynamics of saturation.
Many situations in population biology involve a rate--typically a contact or recruitment rate--which increases linearly for small populations but reaches a maximum value (saturates) for large populations. Models for populations of variable size need to incorporate both characteristics to predict behavior accurately. This can be done by defining the rate as a continuous, piecewise linear function with a switch point, or via a Verhulst-type (smooth) saturation function. This paper presents several examples of both approaches and draws some conclusions about the differences from a modeling perspective.
Kribs-Zaleta
Christopher M
CM
Department of UTA Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019-0408, USA. kribs@uta.edu
D000163:Acquired Immunodeficiency Syndrome / Q000453:epidemiology / Q000635:transmission; D004196:Disease Outbreaks / Q000706:statistics & numerical data; D015991:Epidemiologic Measurements; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D008954:Models, Biological; D011157:Population Dynamics