Dynamic Modeling of Vaccinating Behavior as a Function of Individual Beliefs

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Abstract
Individual perception of vaccine safety is an important factor in determining a person's adherence to a vaccination program and its consequences for disease control. This perception, or belief, about the safety of a given vaccine is not a static parameter but a variable subject to environmental influence. To complicate matters, perception of risk (or safety) does not correspond to actual risk. In this paper we propose a way to include the dynamics of such beliefs into a realistic epidemiological model, yielding a more complete depiction of the mechanisms underlying the unraveling of vaccination campaigns. The methodology proposed is based on Bayesian inference and can be extended to model more complex belief systems associated with decision models. We found the method is able to produce behaviors which approximate what has been observed in real vaccine and disease scare situations. The framework presented comprises a set of useful tools for an adequate quantitative representation of a common yet complex public-health issue. These tools include representation of beliefs as Bayesian probabilities, usage of logarithmic pooling to combine probability distributions representing opinions, and usage of natural conjugate priors to efficiently compute the Bayesian posterior. This approach allowed a comprehensive treatment of the uncertainty regarding vaccination behavior in a realistic epidemiological model. A frequently made assumption in population models is that individuals make decisions in a standard way, which tends to be fixed and set according to the modeler's view on what is the most likely way individuals should behave. In this paper we acknowledge the importance of modeling behavioral changes (in the form of beliefs/opinions) as a dynamic variable in the model. We also propose a way of mathematically modeling dynamic belief updates which is based on the very well established concept of a belief as a probability distribution and its temporal evolution as a direct application of the Bayes theorem. We also propose the use of logarithmic pooling as an optimal way of combining different opinions which must be considered when making a decision. To argue for the relevance of this issue, we present a model of vaccinating behaviour with dynamic belief updates, modeled after real scenarios of vaccine and disease scare recorded in the recent literature.