Stochastic games of parental vaccination decision making and bounded rationality

TL;DR

This paper models parental vaccination decisions using stochastic differential equations to account for bounded rationality and social influences, revealing complex dynamics and potential strategies to improve vaccination uptake.

Contribution

It introduces a novel stochastic differential equation framework combining SIR models with bounded rationality in parental decision-making.

Findings

Stochasticity causes new dynamic behaviors in vaccination decisions.

Bounded rationality influences the impact of social norms.

Optimal control strategies can mitigate bounded rationality effects.

Abstract

Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of utility functions of the decisions over time, as well as in the disease transmission rates. This approach leads to a system of stochastic differential equations of a susceptible-infected-recovered (SIR) model coupled with a stochastic replicator equation. We explore the dynamics of these equations and identify new behaviors emerging from stochastic influences. Interestingly, incorporating stochasticity into the utility functions for vaccination and nonvaccination leads to a decision-making model that reflects the bounded rationality of humans. Noise, like social norms, is a two-sided sword that depends on the degree of bounded rationality of each group. We also perform a stochastic optimal control as a discount to the cost of vaccination to counteract bounded rationality.