Open Conference Systems, StatPhys 27 Main Conference

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The Vaccination Dilemma - A Mean Field Analysis
Benjamin Steinegger, Alessio Cardillo, Paolo De Los Rios, Jesús Gómez-Gardeñes, Alex Arenas

##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-08 11:45 AM – 03:30 PM
Last modified: 2019-06-15

Abstract


Vaccination, whenever possible, is the most effective way to harness and prevent the spreading of a disease. Besides the protection bestowed at individual level, vaccination hinders as well the spreading at whole population level. Therefore, instead of taking the vaccine, free riders can rely on the others’ will to vaccinate, which hinders the population to reach herd immunity. This social dilemma characterizes the voluntary vaccination problem.

Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenza-like diseases, and the expected epidemic incidence (B. Steinegger et al., Physical Review E 97, 032308 (2018)). We model the vaccination uptake through an evolutionary game, in which individuals have only partial information. We then describe the subsequent outbreak of the disease by an SIR model. We obtain analytical expressions for the vaccine coverage and the epidemic thresholds.

A crucial property of vaccines against the seasonal influenza is their effectiveness, which is usually only between 30% and 60%. Interestingly, the system shows a big tolerance regarding the vaccine quality. More precisely, a decrease in the effectiveness of the vaccine can even promote vaccination. At first glance, it may seem counterintuitive. However, this phenomena stems from the competition between the increasing risk of getting infected and the reduced protection bestowed by the vaccine itself. Hence, what may look as an irrational act at first sight is - instead - a rational individual decision of agents striving to mitigate the infection pressure.

Additionally to the high relevance of vaccine effectiveness in the voluntary vaccine uptake, we are recently witnessing the emergence of widespread anti-vaccine movements, which are mainly fueled by misconceptions and mischievous news about vaccines. A way for incorporating these movements in the model is the introduction of zealots; agents who unconditionally do not take the vaccine. Interestingly, the presence of the zealots has a non trivial detrimental effect on the aforementioned tolerance to decreasing vaccine quality.