Stochastic games of parental vaccination decision making and bounded rationality

Andras Balogh; Tamer Oraby; Andras Balogh; Tamer Oraby

doi:10.3934/mbe.2025014

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 2: 355-388. doi: 10.3934/mbe.2025014

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Stochastic games of parental vaccination decision making and bounded rationality

Andras Balogh ,
Tamer Oraby ^,

School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Dr., Edinburg, Texas, USA

Received: 21 October 2024 Revised: 01 January 2025 Accepted: 13 January 2025 Published: 07 February 2025

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.
- replicator dynamics,
- stochastic differential equations,
- game theory,
- bounded rationality,
- disease models
Citation: Andras Balogh, Tamer Oraby. Stochastic games of parental vaccination decision making and bounded rationality[J]. Mathematical Biosciences and Engineering, 2025, 22(2): 355-388. doi: 10.3934/mbe.2025014

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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.

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