The Mathematica Journal
Volume 10, Issue 2


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Individual-Based Models of the Spread of Disease, Weeds, and Insects
Art Diggle
Moin Salam
Marta Monjardino


We have constructed a number of simulation models of the spread of organisms across a landscape. These models are based on the spread of representative individual organisms. The models are quite simple but they are typically evaluated thousands or millions of times in a series of time-steps, often resulting in complex emergent behaviour. The models generally represent key features of the life cycle of the organism in question and one or more movement processes such as rain splash, dispersal by wind, human-mediated dispersal, or insect flight. In each spread event an individual moves along a path a distance that is chosen from a probability distribution. Both the path and the distribution of distances are functions of environmental or other parameters.

Mathematica is well suited to the development of this type of model because of its extensive function set, flexible programming style, and graphic capabilities. Generating complex probability surfaces or customised data structures is quite straightforward in Mathematica. It is often possible using functional programming approaches to produce elegant and efficient routines, but dyed-in-the-wool procedural programmers, such as ourselves, can always fall back on a procedural style when necessary.

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