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An Epidemic Model With Post-Contact Prophylaxisof Distributed Length II. Stability and Oscillations if Treatment is Fully Effective

Published online by Cambridge University Press:  23 October 2008

H. R. Thieme ,
A. Tridane  and
Y. Kuang
H. R. Thieme
Affiliation:
Department of Mathematics and Statistics, Arizona State University Tempe, AZ 85287-1804, U.S.A
A. Tridane
Affiliation:
Department of Mathematics and Statistics, Arizona State University Tempe, AZ 85287-1804, U.S.A
Y. Kuang*
Affiliation:
Department of Mathematics and Statistics, Arizona State University Tempe, AZ 85287-1804, U.S.A
*
h.thieme@asu.edu
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Abstract

A possible control strategy against the spread of an infectious disease is the treatmentwith antimicrobials that are given prophylactically to those that had contact with an infective person.The treatment continues until recovery or until it becomes obvious that there was no infectionin the first place. The model considers susceptible, treated uninfected exposed, treated infected,(untreated) infectious, and recovered individuals. The overly optimistic assumptions are made thattreated uninfected individuals are not susceptible and treated infected individuals are not infectious.Since treatment lengths are considered that have an arbitrary distribution, the model systemconsists of ordinary differential and integral equations. We study the impact of the treatment lengthdistribution on the large-time behavior of the model solutions, namely whether the solutions convergeto an equilibrium or whether they are driven into undamped oscillations.

Keywords

basic reproduction numberstandard incidence(class) age structuredistributed timedelaydisease persistenceglobal stability of endemic equilibriainstabilityperiodic solutionsfrequency domain
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 267 - 293
Copyright
© EDP Sciences, 2008

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