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Mathematical Medicine and Biology Advance Access originally published online on October 6, 2008
Mathematical Medicine and Biology 2008 25(4):337-357; doi:10.1093/imammb/dqn019
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Fatal SIR diseases and rational exemption to vaccination

Alberto d'Onofrio{dagger}

Division of Epidemiology and Biostatistics, European Institute of Oncology, Via Ripamonti 435, 20141 Milano, Italy

Piero Manfredi

Dipartimento di Statistica e Matematica Applicata all'Economia, Università di Pisa, Via Ridolfi 10, 56124 Pisa, Italy

Ernesto Salinelli

Dipartimento di Scienze Economiche e Metodi Quantitativi, Università del Piemonte Orientale, Via Perrone 18, 28100 Novara, Italy

{dagger} Email: alberto.donofrio{at}ieo.it

Received on March 7, 2008. Revised on June 16, 2008. Accepted on July 29, 2008.

A challenge to disease control in modern societies is the spread of rational exemption to vaccination as a consequence of the rational comparison between the steadily declining risk of infection and the risk of side effects from the vaccine. Here, we consider rational exemption in an susceptible-infectious-removed (SIR) model with information-dependent vaccination where individuals use information on the disease's mortality as their information set. Using suitable assumptions on the dynamics of the population, we show the dynamic implications of the interaction between rational exemption, current and delayed information and the risk of death by the disease. In particular, we illustrate the onset of the long cycles caused by rational exemption when vaccination decisions are based on delayed informations.

Keywords: information; oscillations; rational exemption; SIR models; vaccination


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