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Adversarial Data Modeling in Epidemiology

This paper introduces a signaling game framework to model and mitigate the impact of strategically misreported behavioral data in epidemiology, demonstrating that effective epidemic control can be maintained even under pervasive dishonesty through robust sender-receiver strategies.

Original authors: Yiqi Su, Christo Kurisummoottil Thomas, Walid Saad, Sanmay Das, Bud Mishra, Naren Ramakrishnan

Published 2026-08-19

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Yiqi Su, Christo Kurisummoottil Thomas, Walid Saad, Sanmay Das, Bud Mishra, Naren Ramakrishnan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Public health officials have long relied on a simple, if imperfect, tool to understand how diseases spread: asking people what they are doing. When a new virus emerges, authorities need to know if the population is getting vaccinated, wearing masks, or keeping their distance. They ask, and people answer. But in the real world, these answers are not always honest. People might lie to avoid getting fired, to keep their social standing, or simply because they distrust the people asking the questions. This creates a dangerous gap between what officials think is happening and what is actually happening. If a health agency believes everyone is wearing masks because people say they are, but in reality, few are, the agency might relax its safety rules too soon, allowing the virus to surge. This problem is not just about bad data; it is about a strategic game where the people being studied are actively trying to manage the information they give.

A team of researchers has developed a new way to look at this problem, treating the interaction between the public and health authorities not as a simple survey, but as a complex conversation where both sides are trying to outsmart each other. By building a mathematical model that simulates this game, they discovered that even when people lie frequently, it is possible to design policies that still stop an epidemic. Their work suggests that health officials do not need to catch every liar to succeed; instead, they need to understand the patterns of lying and adjust their strategies accordingly. The study shows that as long as the system can detect when the reported numbers are too good to be true, it can compensate for the deception and keep the disease under control.

The core of this research is a simulation that mimics how a disease moves through a population while simultaneously tracking how people report their behavior. The researchers created a virtual world with ten thousand people and a public health authority. In this world, the authority asks people about their vaccination and mask-wearing habits. The people, acting as rational players in a game, decide whether to tell the truth or lie based on what benefits them most. If lying helps them keep their job or avoid a fine, they might do it. The health authority, knowing that people might lie, does not just take the answers at face value. Instead, it looks at the answers alongside hard data, such as the number of people being hospitalized, to figure out the truth.

The researchers found that the outcome of this interaction depends heavily on how the population behaves as a group. In the worst-case scenario, known as a "pooling" equilibrium, everyone lies and claims to be doing the right thing, regardless of what they are actually doing. In this situation, the health authority receives a flood of identical, false reports. Because the reports all look the same, the authority cannot tell who is lying and who is telling the truth, so it is forced to ignore the reports and rely only on hospitalization numbers. This makes it very difficult to control the disease, as the authority is flying blind regarding the population's actual behavior.

However, the study revealed a more hopeful middle ground. In a "partial pooling" scenario, some people tell the truth while others lie. This mix of honest and dishonest reports creates a signal that the health authority can actually use. Even if a significant portion of the population is dishonest, the authority can detect the inconsistencies between what people say and what is happening in the hospitals. By using a smart, adaptive strategy that weighs the reports based on how likely they are to be true, the authority can still figure out the real level of protection in the community. The simulations showed that even with high levels of deception, this adaptive approach could bring the spread of the disease under control, whereas a system that ignored the reports or treated them all as equally reliable would fail.

One of the most striking findings was how much deception a system can tolerate before it breaks down. The researchers calculated that there is a specific threshold of lying that a health authority can handle. As long as the population's actual vaccination and mask-wearing rates are high enough, the system can absorb a surprising amount of dishonesty. For example, if the initial levels of protection are low, even a small amount of lying can cause the system to fail. But if the population starts with a decent level of compliance, the system becomes much more robust. The study showed that vaccination and masking work together; if one is high, the system can withstand more lying about the other. This means that building a strong foundation of real protection makes the entire system more resilient to the inevitable lies that will occur.

The researchers also tested their model against real-world data to see if their assumptions held up. They looked at how misinformation spreads and how people actually report their health behaviors in surveys. They found that lies are not random; they follow specific patterns. People tend to lie in ways that look like they are trying to avoid penalties or gain benefits, rather than just making random mistakes. Because these lies are structured, the health authority's adaptive model, which is designed to spot these specific patterns, performs much better than simpler methods that assume errors are just random noise. This suggests that the key to managing public health data is not to demand perfect honesty, which is impossible, but to build systems that are smart enough to see through the strategic deception.

Ultimately, this work changes how we think about the relationship between the public and health officials. It moves away from the idea that officials must simply trust the data they are given or that they must punish liars to get the truth. Instead, it proposes a dynamic relationship where officials constantly update their understanding based on the signals they receive, knowing that those signals might be distorted. The study demonstrates that with the right tools, a health authority can maintain control over an epidemic even when the population is not fully honest. It offers a path forward for designing policies that are robust enough to handle the messy reality of human behavior, ensuring that public health decisions are based on the best possible understanding of the truth, even when that truth is partially hidden.

Technical Summary: Adversarial Data Modeling in Epidemiology

Problem Statement

Epidemiological modeling increasingly relies on crowdsourced, self-reported behavioral data (e.g., vaccination status, mask usage, social distancing) to forecast disease transmission and guide non-pharmaceutical interventions (NPIs). However, this data is not passively sampled; it is strategically reported. Individuals often misreport behaviors to avoid penalties, access benefits, or due to distrust in public health authorities (PHA). This strategic misreporting introduces systematic biases that traditional models fail to account for, treating reported data as truthful observations rather than adversarial inputs. Consequently, PHAs may underestimate key parameters, leading to ineffective policies and sustained epidemic transmission. Existing approaches largely treat parameter uncertainty as a static estimation problem rather than a dynamic behavioral process driven by incentives.

Methodology

The authors propose a game-theoretic framework that models the interaction between a population and a PHA as a signaling game. This approach integrates rational speech act (RSA) models with stochastic compartmental epidemiological dynamics.

Core Framework

Signaling Game Formulation:
- Senders (Individuals): A population of individuals chooses whether to report their true behavioral type (vaccination and masking status) or to deceive. They act under bounded rationality, weighing individual incentives (e.g., avoiding penalties) against the "semantic loss" (the cost of being misunderstood or the degradation of the collective signal).
- Receiver (PHA): The PHA observes reported messages and aggregate hospitalization data (the only ground-truth proxy available). It updates its beliefs about population behavior using Bayesian inference and adjusts epidemiological parameters (vaccination rate $\psi$ , masking rate $\eta$ ) to maintain the controlled reproduction number ( $R_c$ ) below 1.
- Utility Functions:
  - Sender Utility: Maximizes individual incentives from deception while minimizing semantic loss (inaccuracy in the receiver's interpretation) and accounting for the economic impact of a high $R_c$ (e.g., business closures).
  - Receiver Utility: Minimizes the distortion between predicted and observed hospitalization trajectories while maximizing the information gain from reported messages.
Epidemiological Model:
- The framework utilizes a SVEAIR compartmental model (Susceptible, Vaccinated, Exposed, Asymptomatic, Symptomatic, Recovered).
- The model incorporates vaccination and masking rates as parameters that reduce contact rates.
- The PHA uses an estimated version of these ODEs to predict hospitalization counts ( $H(t)$ ) based on inferred behavioral parameters.
Equilibrium Analysis:
The paper analytically characterizes three distinct equilibrium regimes based on the degree of deception:
- Separating Equilibrium: All individuals report truthfully. The PHA recovers unbiased parameters, enabling effective epidemic control ( $R_c < 1$ ).
- Pooling Equilibrium: All non-compliant individuals lie and report full compliance. The PHA cannot distinguish types, relying solely on priors and hospitalization data, often leading to sustained transmission.
- Partial Pooling Equilibrium: A mixed state where some individuals lie while others tell the truth. The paper derives conditions for the existence of this equilibrium and characterizes the "tolerance frontier"—the maximum level of deception the system can withstand while maintaining epidemic control.
Adaptive Policy:
The PHA employs an adaptive feedback policy. It updates intervention recommendations ( $\psi_r, \eta_r$ ) by minimizing the distortion between observed hospitalizations and model predictions, effectively weighting reported data by inferred credibility.

Key Contributions

Game-Theoretic Epidemic Model: The authors couple a stochastic compartmental model with a two-player signaling game. This allows the PHA to infer credibility and account for strategic misreporting rather than assuming truthfulness, designing policies robust to adversarial data.
Equilibrium Characterization and Policy Design: The paper analytically identifies when truthful reporting emerges and how policy levers can be tuned to deter deception. It proposes an adaptive feedback policy that weights data by inferred credibility to maintain $R_c \leq 1$ .
Generalizable Simulation Pipeline: A framework integrating signaling-game equilibria with epidemiological dynamics is developed to study the interaction between behavioral deception, policy adaptation, and epidemic control. This enables systematic evaluation of interventions under varying behavioral assumptions.

Experimental Results

The framework was evaluated using Monte Carlo simulations of a 10,000-person population over 26 weeks, alongside validation on real-world datasets (CHECKED, CoAID, CDC/HHS data).

Interactive Feedback Efficacy: Adaptive, signal-informed feedback between the population and PHA is essential for epidemic control. In simulations, separating and partial pooling equilibria successfully reduced $R_c$ below 1, whereas pooling equilibria and non-interactive baselines failed to control transmission under low baseline behavioral rates.
Information Value of Imperfect Data: Even in partial pooling equilibria with significant deception, the PHA could extract actionable signals. The receiver's posterior beliefs remained non-trivial, allowing for effective policy adjustments compared to random policies.
Deception Patterns: Equilibrium structure dominates the level of dishonesty. Pooling equilibria exhibited the highest deception rates (starting >0.8), while separating equilibria maintained the lowest (~0.3).
Tolerance Frontiers: The study quantified the "tolerance frontier," showing that as vaccination and masking coverage accumulate, the system becomes more robust to active deception. There is a complementarity between interventions; higher adoption of one can partially compensate for lower adoption of the other regarding robustness to misreporting.
Real-World Validation: Analysis of real-world misinformation data revealed that behavioral distortions exhibit structured patterns (high Gini coefficients) rather than arbitrary noise. The proposed framework outperformed simpler approaches in scenarios with structured, risk-dependent distortions, reducing vaccination-state errors by up to 72%.
Robustness: Stress tests indicated that while increasing vaccine efficacy significantly improved control, moderate variations in behavioral incentives had limited effects on long-term dynamics. However, a high non-responsive share (NRS) negatively impacted disease control scores, highlighting the need for sufficient participation.

Significance and Claims

The paper claims to advance the understanding of adversarial data in epidemiology by shifting the perspective from static estimation errors to dynamic, strategic behavioral processes. It argues that:

Strategic Misreporting is a Canonical Adversarial Input: Self-reported data must be modeled as strategic signals rather than passive observations.
Equilibrium Structure Determines Control Quality: The informational content of self-reported behaviors and the achievable quality of epidemic control are directly determined by the equilibrium regime (Separating > Partial Pooling > Pooling).
Robustness is Possible: Even under pervasive dishonesty in partial pooling equilibria, well-designed sender and receiver strategies can maintain effective epidemic control. (Note: The paper indicates that pooling equilibria fail to reach the epidemic threshold within the simulation horizon due to severely degraded information quality).
Structured Patterns Matter: Real-world behavioral distortions are structured, and frameworks that account for this structure offer conditional advantages over methods assuming arbitrary noise.

The authors conclude that their framework offers tools for designing more robust public health models in the presence of strategic user behavior, though they acknowledge limitations regarding individual heterogeneity and the complexity of multi-agent policy settings.