The Fixed Points of a Seasonal Model of Population Infectives

insect epidemic infectives

Gaither, Jeffrey Beau Sellers ; John Franke, Committee Chair,Xiao-Biao Lin, Committee Member,James Selgrade, Committee Member,Gaither, Jeffrey Beau Sellers ; John Franke ; Committee Chair ; Xiao-Biao Lin ; Committee Member ; James Selgrade ; Committee Member

University:North Carolina State University

关键词: insect epidemic infectives;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/1040/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

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 = Fpο ... 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.