Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 652562, 11 pages
Research Article

Outcome Inelasticity and Outcome Variability in Behaviour-Incidence Models: An Example from an SEIR Infection on a Dynamic Network

Department of Mathematics and Statistics, Room 437 MacNaughton Building, University of Guelph, 50 Stone Road East, Guelph, ON, Canada N1G 2W1

Received 18 July 2012; Revised 6 October 2012; Accepted 6 November 2012

Academic Editor: Alex Welte

Copyright © 2012 Bryce Morsky and Chris T. Bauch. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Behavior-incidence models have been used to model phenomena such as free-riding vaccinating behavior, where nonvaccinators free ride on herd immunity generated by vaccinators. Here, we develop and analyze a simulation model of voluntary ring vaccination on an evolving social contact network. Individuals make vaccination decisions by examining their expected payoffs, which are influenced by the infection status of their neighbors. We find that stochasticity can make outcomes extremely variable (near critical thresholds) and thus unpredictable: some stochastic realizations result in rapid control through ring vaccination while others result in widespread transmission. We also explore the phenomenon of outcome inelasticity, wherein behavioral responses result in certain outcome measures remaining relatively unchanged. Finally, we explore examples where ineffective or risky vaccines are more widely adopted than safe, effective vaccines. This occurs when such a vaccine is unattractive to a sufficient number of contacts of an index case to cause failure of ring vaccination. As a result, the infection percolates through the entire network, causing the final epidemic size and vaccine coverage to be higher than would otherwise occur. Effects such as extreme outcome variability and outcome inelasticity have implications for vaccination policies that depend on individual choice for their success and predictability.