The Fixed Points of a Seasonal Model of Population Infectives

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Title: The Fixed Points of a Seasonal Model of Population Infectives
Author: Gaither, Jeffrey Beau Sellers
Advisors: John Franke, Committee Chair
Xiao-Biao Lin, Committee Member
James Selgrade, Committee Member
Abstract: We model the spread of epidemics among insect populations. The mapping Ft = (1−e−INt )(Nt −I) + I iterates on the current number of infectants to produce the number of infectants in the next time-period. The value Nt is the current population, and it is known that population follows a globally attracting cycle N1 . . .Np, which represents the population at various times of the year. Thus, the function F = Fp ο ... οF1 maps infectants to infecants on a month-to-month or seasonto- season basis. We show that for p = 2, F has only one attractor. We also show that for any F there is 0 such that for any > 0, F has only one attractor. We give an example of multiple attractors in the p = 4 case, and provide a means by which the composition F can be represented as a composition of functions which are all scalar multiples of F1.
Date: 2007-04-30
Degree: MS
Discipline: Mathematics

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