Stochastic games of parental vaccination decision making and bounded rationality

Authors

Andras Balogh, The University of Texas Rio Grande Valley
Tamer Oraby, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2-7-2025

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 Eqs of a susceptible-infected-recovered (SIR) model coupled with a stochastic replicator Eq. We explore the dynamics of these Eqs 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.

Comments

© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

Recommended Citation

Balogh, Andras, Tamer Oraby, Andras Balogh, and Tamer Oraby. 2025. “Stochastic Games of Parental Vaccination Decision Making and Bounded Rationality.” Mathematical Biosciences and Engineering 22 (2): 355–88. https://doi.org/10.3934/mbe.2025014.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Mathematical Biosciences and Engineering

DOI

10.3934/mbe.2025014