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Modeling Epidemiological Dynamics Under Adversarial Data and User Deception

Yiqi Su, Christo Kurisummoottil Thomas, Walid Saad, Bud Mishra, Naren Ramakrishnan

TL;DR

This work addresses how adversarial, self-reported behavioral data (e.g., vaccination and masking) affect epidemic forecasting and control. It couples a SVEAIR-type epidemiological model with a two-player signaling game to capture strategic misreporting and belief updating by a public health authority, enabling adaptive policies that weight data credibility. The main contributions are an equilibrium analysis (separating, pooling, partial pooling), a tractable framework for endogenous deception, and a simulation pipeline showing that signal-informed policy can maintain $R_c\le 1$ even under nontrivial deception; the approach highlights the value of considering strategic data in public-health decision-making. The results demonstrate the potential for robust epidemic control through adaptive feedback that accounts for information distortion, informing better design of surveillance and intervention strategies in real-time.

Abstract

Epidemiological models increasingly rely on self-reported behavioral data such as vaccination status, mask usage, and social distancing adherence to forecast disease transmission and assess the impact of non-pharmaceutical interventions (NPIs). While such data provide valuable real-time insights, they are often subject to strategic misreporting, driven by individual incentives to avoid penalties, access benefits, or express distrust in public health authorities. To account for such human behavior, in this paper, we introduce a game-theoretic framework that models the interaction between the population and a public health authority as a signaling game. Individuals (senders) choose how to report their behaviors, while the public health authority (receiver) updates their epidemiological model(s) based on potentially distorted signals. Focusing on deception around masking and vaccination, we characterize analytically game equilibrium outcomes and evaluate the degree to which deception can be tolerated while maintaining epidemic control through policy interventions. Our results show that separating equilibria-with minimal deception-drive infections to near zero over time. Remarkably, even under pervasive dishonesty in pooling equilibria, well-designed sender and receiver strategies can still maintain effective epidemic control. This work advances the understanding of adversarial data in epidemiology and offers tools for designing more robust public health models in the presence of strategic user behavior.

Modeling Epidemiological Dynamics Under Adversarial Data and User Deception

TL;DR

This work addresses how adversarial, self-reported behavioral data (e.g., vaccination and masking) affect epidemic forecasting and control. It couples a SVEAIR-type epidemiological model with a two-player signaling game to capture strategic misreporting and belief updating by a public health authority, enabling adaptive policies that weight data credibility. The main contributions are an equilibrium analysis (separating, pooling, partial pooling), a tractable framework for endogenous deception, and a simulation pipeline showing that signal-informed policy can maintain even under nontrivial deception; the approach highlights the value of considering strategic data in public-health decision-making. The results demonstrate the potential for robust epidemic control through adaptive feedback that accounts for information distortion, informing better design of surveillance and intervention strategies in real-time.

Abstract

Epidemiological models increasingly rely on self-reported behavioral data such as vaccination status, mask usage, and social distancing adherence to forecast disease transmission and assess the impact of non-pharmaceutical interventions (NPIs). While such data provide valuable real-time insights, they are often subject to strategic misreporting, driven by individual incentives to avoid penalties, access benefits, or express distrust in public health authorities. To account for such human behavior, in this paper, we introduce a game-theoretic framework that models the interaction between the population and a public health authority as a signaling game. Individuals (senders) choose how to report their behaviors, while the public health authority (receiver) updates their epidemiological model(s) based on potentially distorted signals. Focusing on deception around masking and vaccination, we characterize analytically game equilibrium outcomes and evaluate the degree to which deception can be tolerated while maintaining epidemic control through policy interventions. Our results show that separating equilibria-with minimal deception-drive infections to near zero over time. Remarkably, even under pervasive dishonesty in pooling equilibria, well-designed sender and receiver strategies can still maintain effective epidemic control. This work advances the understanding of adversarial data in epidemiology and offers tools for designing more robust public health models in the presence of strategic user behavior.
Paper Structure (41 sections, 4 theorems, 66 equations, 12 figures, 4 tables, 1 algorithm)

This paper contains 41 sections, 4 theorems, 66 equations, 12 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Compartmental epidemiological models.
  4. Measurement error and strategic misreporting.
  5. Signaling games and equilibrium selection.
  6. Framework
  7. Basics.
  8. Epidemiological model.
  9. Realistic assumptions for vaccination and masking.
  10. Signaling game.
  11. Sender utility function.
  12. Receiver utility function.
  13. Game solution.
  14. Equilibrium Analysis
  15. Separating equilibrium.
  16. ...and 26 more sections

Key Result

Theorem 1

Suppose all non-compliant individuals strictly prefer misreporting over truthful reporting for both vaccination and masking, i.e., for all non-compliant types. Then there exists a pooling equilibrium in which all individuals report full compliance, i.e., $m_k = 00$ for all $k\in\mathcal{K}_c$, and the receiver’s posterior beliefs coincide with the prior distribution over types.

Figures (12)

  • Figure 1: Illustration of the signaling game framework.
  • Figure 2: Compartmental SVEAIR epidemiological model with vaccination and masking. The 'H' is not a separate compartment but denotes (observed) hospitalization numbers, typically a fraction of the true numbers from the infected compartment.
  • Figure 3: Controlled reproduction number ($R_c$) across equilibria vs no-interaction baseline with different initial behavioral rates.
  • Figure 4: Sender strategies and receiver beliefs across equilibria.
  • Figure 5: Comparison of adaptive and random policies under partial pooling with low initial behavioral rates, across epidemic dynamics, policy actions, signaling behavior, and utilities.
  • ...and 7 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • proof
  • Theorem 4: Partial Pooling and Tolerable Deception