Spatio-temporal games of voluntary vaccination in the absence of the infection: the interplay of local versus non-local information about vaccine adverse events

Antonella Lupica; Piero Manfredi; Vitaly Volpert; Annunziata Palumbo; Alberto d'Onofrio; Antonella Lupica; Piero Manfredi; Vitaly Volpert; Annunziata Palumbo; Alberto d'Onofrio

doi:10.3934/mbe.2020058

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 2: 1090-1131. doi: 10.3934/mbe.2020058

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Research article Special Issues

Spatio-temporal games of voluntary vaccination in the absence of the infection: the interplay of local versus non-local information about vaccine adverse events

1.
Department of Mathematics and Computer Sciences, University of Catania, V.le A. Doria 6, 95125 Catania, Italy
2.
Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, V.le F. D’Alcontres 31, 98166 Messina, Italy
3.
Department of Economics and Management, University of Pisa, Via Ridolfi 10, 5612 Pisa, Italy
4.
Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
5.
INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
6.
Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, Russia
7.
International Prevention Research Institute, 95 Cours Lafayette 69006 Lyon, France

Received: 13 June 2019 Accepted: 05 November 2019 Published: 14 November 2019

Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics, by extending to a continuous spatially structured setting existing behavioral epidemiology models for the impact of vaccine adverse events (VAEs) on vaccination choices. We considered the simplest spatial setting, namely classical 'Fickian' diffusion, and focused on the noteworthy case where the infection is absent. This scenario mimics the important case of a population where a previously endemic vaccine preventable infection was successfully eliminated, but the re-emergence of the disease must be prevented. This is, for example, the case of poliomyelitis in most countries worldwide. In such a situation, the dynamics of VAEs and of the related information arguably become the key determinant of vaccination decision and of collective coverage. In relation to this 'information issue', we compared the effects of three main cases: (ⅰ) purely local information, where agents react only to locally occurred events; (ⅱ) a mix of purely local and global, country-wide, information due e.g., to country-wide media and the internet; (ⅲ) a mix of local and non-local information. By representing these different information options through a range of different spatial information kernels, we investigated: the presence and stability of space-homogeneous, nontrivial, behavior-induced equilibria; the existence of bifurcations; the existence of classical and generalized traveling waves; and the effects of awareness campaigns enacted by the Public Health System to sustain vaccine uptake. Finally, we analyzed some analogies and differences between our models and those of the Theory of Innovation Diffusion.
- human behavior,
- vaccination,
- infectious diseases,
- spatiotemporal,
- nonlocal,
- integrodifferential,
- traveling waves
Citation: Antonella Lupica, Piero Manfredi, Vitaly Volpert, Annunziata Palumbo, Alberto d'Onofrio. Spatio-temporal games of voluntary vaccination in the absence of the infection: the interplay of local versus non-local information about vaccine adverse events[J]. Mathematical Biosciences and Engineering, 2020, 17(2): 1090-1131. doi: 10.3934/mbe.2020058

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Abstract

Under voluntary vaccination, a critical role in shaping the level and trends of vaccine uptake is played by the type and structure of information that is received and used by parents of children eligible for vaccination. In this article we investigate the feedbacks of spatial mobility and the spatial structure of information on vaccination dynamics, by extending to a continuous spatially structured setting existing behavioral epidemiology models for the impact of vaccine adverse events (VAEs) on vaccination choices. We considered the simplest spatial setting, namely classical 'Fickian' diffusion, and focused on the noteworthy case where the infection is absent. This scenario mimics the important case of a population where a previously endemic vaccine preventable infection was successfully eliminated, but the re-emergence of the disease must be prevented. This is, for example, the case of poliomyelitis in most countries worldwide. In such a situation, the dynamics of VAEs and of the related information arguably become the key determinant of vaccination decision and of collective coverage. In relation to this 'information issue', we compared the effects of three main cases: (ⅰ) purely local information, where agents react only to locally occurred events; (ⅱ) a mix of purely local and global, country-wide, information due e.g., to country-wide media and the internet; (ⅲ) a mix of local and non-local information. By representing these different information options through a range of different spatial information kernels, we investigated: the presence and stability of space-homogeneous, nontrivial, behavior-induced equilibria; the existence of bifurcations; the existence of classical and generalized traveling waves; and the effects of awareness campaigns enacted by the Public Health System to sustain vaccine uptake. Finally, we analyzed some analogies and differences between our models and those of the Theory of Innovation Diffusion.

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