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

Published online by Cambridge University Press:  17 February 2009

Ravi P. Agarwal ,
Donal O'Regan  and
Patricia J. Y. Wong
Ravi P. Agarwal
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, Florida 32901–6975, USA; e-mail: agarwal@fit.edu.
Donal O'Regan
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland.
Patricia J. Y. Wong
Affiliation:
School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore; e-mail: ejywong@ntu.edu.sg.
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Abstract

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We consider the following model that describes the spread of n types of epidemics which are interdependent on each other:

Our aim is to establish criteria such that the above system has one or multiple constant-sign periodic solutions (u1, u2, …, un), that is, for each 1 ≤ i ≤ n, ui, is periodic and θiui ≥ 0 where θi, ε (1, −1) is fixed. Examples are also included to illustrate the results obtained.

Keywords

periodic solutionsintegral equationsepidemicsfixed point theorems
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 3 , January 2006 , pp. 309 - 332
Copyright
Copyright © Australian Mathematical Society 2006

References

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