NDLI: Bistability of Evolutionary Stable Vaccination Strategies in the Reinfection SIRI Model

Content Provider	Springer Nature Link
Author	Martins, José Pinto, Alberto
Copyright Year	2017
Abstract	We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model studied by Bauch and Earn (PNAS 101:13391–13394, 2004). The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability. We introduce the evolutionary vaccination dynamics for the SIRI model and we prove that it is bistable. The bistability of the evolutionary dynamics indicates that the damage provoked by false scares on the vaccination perceived morbidity risks can be much higher and much more persistent than in the SIR model. Furthermore, the vaccination education programs to be efficient they need to implement a mechanism to suddenly increase the vaccination coverage level.
Starting Page	853
Ending Page	883
Page Count	31
File Format	PDF
ISSN	00928240
Journal	Bulletin of Mathematical Biology
Volume Number	79
Issue Number	4
e-ISSN	15229602
Language	English
Publisher	Springer US
Publisher Date	2017-02-23
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Vaccination Reinfection SIRI model Nash equilibrium ESS Vaccination dynamics Mathematical and Computational Biology Life Sciences Cell Biology
Content Type	Text
Resource Type	Article
Subject	Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences

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