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On constant-sign periodic solutions in modelling the spread of interdependent epidemics

Agarwal, Ravi P.
; 
O'Regan, Donal
; 
Wong, Patricia J. Y.
Repository DOI
Publication Date
2006-01-01
Keywords
periodic solutions, integral equations, epidemics, fixed point theorems, fredholm integral-equations, positive solutions, differential-equations, infectious-disease, threshold theorem, system, existence
Type
Article
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Citation
Agarwal, Ravi P. O'Regan, Donal; Wong, Patricia J. Y. (2006). On constant-sign periodic solutions in modelling the spread of interdependent epidemics. The ANZIAM Journal 47 , 309-332
Abstract
We consider the following model that describes the spread of n types of epidemics which are interdependent on each other: u(i)(t) = integral(t)(t-r) g(i)(t, s) f(i) (s, u(1)(s), u(2)(s),..., u(n)(s))ds, t is an element of R, 1 <= i <= n. Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions (u(1), u(2),..., u(n)), that is, for each 1 <= i <= n, u(i) is periodic and theta(i)u(i) >= 0 where theta(i) is an element of {1, -1} is fixed. Examples are also included to illustrate the results obtained.
Funder
Publisher
Cambridge University Press (CUP)
Publisher DOI
10.1017/s144618110000986x
Rights
Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (1)