App-based epidemic game in a university campus reveals how risk perception and behavioral interventions shape disease transmission dynamics

Abstract

Effective infectious disease control requires understanding transmission dynamics and behavioral factors that influence non-pharmaceutical interventions (NPIs) such as social distancing and quarantining. To investigate these dynamics in a real-life setting, we conducted a two-week gamified epidemic experiment at Wenzhou-Kean University, China, involving nearly 1,000 students. A Bluetooth-enabled app was used to simulate the spread of a virtual pathogen and collect real-time behavioral and epidemiological data. We developed a Susceptible-Exposed-Asymptomatic-Infected-Removed model with time-varying transmission rates to incorporate behavioral feedback and assess the effectiveness of interventions. Our results show that NPIs alone may not be sufficient unless coupled with high compliance driven by elevated risk perception. Participants who adhered strongly to NPIs significantly reduced transmission. Additionally, superspreader statistics and a heavy-tailed transmission tree structure mirroring patterns seen in biological outbreaks provides support for the external validity of the data. This study reveals the importance of integrating adaptive human behavior and heterogeneity into epidemiological models and highlights the potential of our app-based epidemic experiments as tools for studying outbreak dynamics in real-life settings.

Digital technologies have transformed infectious disease research¹, yet a persistent challenge remains: integrating endogenous human behavior into mathematical models. While traditional compartmental models often assume static transmission rates, real-world outbreaks are shaped by feedback loops where individuals adapt their behavior based on perceived risk. This study addresses this critical need by presenting a Susceptible-Exposed-Asymptomatic-Infected-Removed (SEAIR) modeling framework with time-varying transmission, calibrated using high-resolution data from an app-based “experimental epidemic game”. While the comprehensive methodological protocol for the epidemic game approach is detailed elsewhere², this paper focuses on utilizing the resulting multimodal dataset to quantify the efficacy of non-pharmaceutical interventions (NPIs) under varying behavioral patterns. We piloted the protocol during a two-week epidemic game at Wenzhou-Kean University (WKU), an international Chinese-American institution of higher-education in the Zhejiang province of China³, to generate a comprehensive real-world outbreak dataset explicitly including endogenous human behavior. By leveraging this dataset, we move beyond simulations based on theoretical assumptions to evaluate how granular behavioral actions, such as voluntary quarantine and mask-wearing, influence the simulated outbreak’s trajectory in a naturalistic social setting. Our primary objective is to demonstrate how this modeling framework can guide public health policy by accounting for the complex interplay between individual risk perception and pathogen spread.

We created a customized version of the Operation Outbreak (OO) app⁴ to apply the concept of experimental games⁵, which are field experiments where participants’ decisions affect their own and other’s quantifiable outcomes, to epidemiology research using mobile technology. The OO app was originally developed in 2018⁶ for immersive “mock” outbreaks in real-life settings, such as schools and conferences, by spreading a simulated pathogen via Bluetooth. The OO project’s initial motivation was infectious disease education in middle and high schools on public health, outbreak response, and societal roles during health emergencies⁷. Early OO deployments in college campuses suggested that app-enabled, real-world simulated outbreaks could be used to study epidemic dynamics and response strategies thanks to their capacity to incorporate naturalistic human behavior and controlled transmission mechanics⁸. While prior real-life epidemic experiments via proximity-sensing platforms like SocioPatterns ⁹, FluPhone ¹⁰, and SafeBlues ¹¹ have simulated pathogen transmission among human participants, they often lack real-time behavioral feedback in naturalistic settings and configurable transmission parameters. Thanks to the advances in mobile technology in the last decade, we were able to construct a new platform with greater potential for customization and scale than earlier projects, capable to collect multimodal datasets ranging from contact networks to attitudinal preferences and behavioral choices.

Epidemiological modeling, when applied to datasets that incorporate endogenous human behavior such as those from our epidemic games, serves as a foundational tool for studying and evaluating the impact of non-pharmaceutical interventions (NPIs), such as social distancing, mask-wearing, and voluntary quarantine, on disease dynamics^12–22. For instance, SIRS models have demonstrated that the attributes of a pathogen, particularly its basic reproduction number (), significantly influence the long-term epidemiological outcomes of transmission reduction efforts^23,24. Pathogens with high values may exhibit only temporary reductions in transmission rates, with minimal impact on the epidemic’s overall dynamics²⁵. The interaction between NPIs and pathogen characteristics necessitates ongoing evaluation and adjustment of intervention strategies to effectively address unexpected outcomes^24,26–28.

The experimental epidemic game conducted during the Fall semester of 2023 at the WKU campus, which we will call the WKU epigame for the reminder of the paper, generated a comprehensive real-world outbreak dataset. This dataset enabled us to combine empirical data with an epidemiological framework to study pathogen spread within a largely closed population. Using this framework, we focused on behavioral responses and the effectiveness of interventions in containing and mitigating disease outbreaks^29–33. Researchers have used online behavioral experiments to measure and model the effect of individuals’ preferences and decisions on adoption of NPIs^34–36; however, such experiments often reduce complex human behavior to simple abstract decisions that may fail to capture social contexts and disease exposure patterns that influence behavior in realistic environments. Our approach has the advantage of providing a reproducible field experimentation framework with high degree of mechanistic realism for the transmission processes and a naturalistic environment able to capture inter-individual variation in real-life social settings. However, one also needs to be aware that these technologies are not perfect; in addition to non-response and attrition from app users, measuring proximal contacts using Bluetooth is affected by signal noise and imperfect implementation of Bluetooth standards across devices. Even with these limitations, the ubiquity of smartphones allows us to conduct these experiments at scales that were simply not possible before, as well as to iterate rapidly to improve the platform based on feedback from users and our own observations.

With the WKU epigame dataset, we were able to generate models that not only capture the immediate impact of NPIs such as social distancing and mask-wearing but also consider the feedback loops between behavioral adaptations and disease dynamics^37,38. This experimental data-driven framework can provide a more realistic and nuanced understanding of pathogen transmission, reflecting the complex interplay between human actions and epidemiological outcomes^14,17,37 in naturalistic settings. By leveraging mobile app technology, our platform allows for a detailed examination of how individual decisions-such as mask-wearing, social distancing, or quarantining when symptomatic-affect transmission dynamics within the controlled environment of the game, which, in turn, is embedded in the real-life setting of a college campus. In this paper, we seek to establish a foundation for comprehensive models that can guide public health policies and strategies to prevent and reduce infectious disease outbreaks by both advancing our theoretical understanding of socio-epidemiological interactions and offering practical guidance for managing infectious diseases across diverse settings.

Results

Evaluating the impact of individual perception and NPIs

We conducted an initial descriptive statistical analysis of the data from the WKU epigame to capture the main time-dependent patterns of the experiment, provided in the supplementary materials. By fitting the unified simplified model given in  (3) to this data, where individual risk perception and NPIs’s strength were modeled with two parameters, and , respectively, we were able to run simulations that probed the dynamics of pathogen transmission under varying levels of risk perception and NPI strength. Fig. 3 (a) illustrates simulated daily new cases across three distinct scenarios: a naive scenario with no interventions ( and ), a scenario driven by individual perception (only ), and a combined scenario incorporating both individual perceptions and NPIs.

Figure 3.

Daily cases and reporting ratios from the intervention simulation scenarios. (A) Daily new cases across three intervention scenarios during the WKU epigame represented by the black shadowed curve. The orange solid curve represents the naive scenario of the simulation with no interventions, showing a rapid increase in new cases. The red curve illustrates the scenario with individual perception based on behavior change, resulting in a significant reduction in new cases. The green solid curve depicts the scenario combining individual reactions with NPIs such as quarantine and isolation, showing the most pronounced decrease in daily new cases. The grey curve with dots represents the simulated reported cases, aligned with official data, validating the accuracy of our model. The effect of interventions takes a couple of days to show up in the data. (B) Reporting ratio between observed cases and model estimates under the combined scenario of individual perception (IP) and non-pharmaceutical interventions (NPIs) and (C) IP only, respectively. The relatively stable ratio indicates that the model accurately captures the dynamics of reporting behavior and intervention efficacy. This stability underscores the effectiveness of coordinated interventions in mitigating the pathogen’s spread and ensuring consistent reporting accuracy.

In the naive scenario, represented by the orange solid curve, we can observe a rapid increase in new cases, highlighting the unmitigated spread of the pathogen in the absence of any intervention. This serves as a baseline, demonstrating the potential severity of an outbreak without any behavioral change or NPIs. The second scenario, depicted by the red dashed curve, we modeled the impact of individual behavioral responses to the perceived risk of infection. Here, susceptibles’ behavior adjusts to response to the evolving outbreak situation, such as by reducing contacts or increasing protective measures like mask-wearing. The substantial reduction in new cases one sees in this scenario underscores the significant role that individual perception plays in controlling disease spread. This finding is consistent with previous research that emphasizes the importance of individual actions in epidemic management^39,40. For the third scenario, represented by the green solid curve, we combined individual perception with structured NPIs, such as quarantine and isolation. This scenario shows the most pronounced decrease in daily new cases, illustrating the enhanced effectiveness of combining adaptive human behavior with coordinated public health interventions. The close alignment between the simulated output for the combined scenario (green solid curve) and the observed data (grey curve with dots) demonstrates the model’s ability to accurately recreate the outbreak’s trajectory and provides strong support for its validity in representing the transmission dynamics of the WKU epigame.

Fig. 3 (b) & (c) presents the reporting ratios between observed cases and model estimates under two scenarios: (a) the scenario combining individual perception and NPIs and (b) the scenario with individual perception only. To quantitatively assess the stability of case reporting, we defined the daily reporting ratio as the proportion of the total simulated infections (determined by the app’s “ground-truth” transmission model) that were reported by participants through health status updates. We calculated for each day of the experiment. Analysis of these daily ratios demonstrated a stable reporting process. Under the combined intervention scenario, the mean reporting ratio was with a standard deviation of , resulting in a low coefficient of variation (). A low CV (typically < 0.10) indicates low relative variance and high stability. To formally test for temporal trends, we performed linear regression of against time . The slope was not significantly different from zero (), confirming no significant increase or decrease in reporting efficiency over the two-week period. This quantitative evidence supports the conclusion of a “relatively stable reporting ratio.” This stability indicates consistent participant engagement in reporting their health status, which is critical for ensuring the reliability of the data used to calibrate the SEAIRD model and estimate time-dependent epidemic metrics such as and (Fig. 4).

Figure 4.

Temporal dynamics of key epidemiological metrics during the WKU epigame. (A) Hourly cases showing infection peaks during the outbreak. (B) Effective reproduction number () over time, with a critical threshold at . (C) Susceptible population () illustrating the progressive depletion of susceptibles. (D) Instantaneous reproduction number () with median estimates, 95% confidence intervals, and the critical threshold, highlighting the transition from epidemic growth to control.

The stability of reporting ratios we observe across scenarios demonstrates the model’s ability to accurately reflect real-life reporting dynamics, capturing outbreak progression as depicted in Fig. 3 (b) & (c). Moreover, the alignment between observed and simulated cases highlights the model’s ability to capture the outbreak trends, making it a valuable tool for analyzing outbreak trajectories under varying conditions. The results show that individual behavioral responses, such as increased mask-wearing or self-isolation driven by perceived risk, substantially reduced daily new cases in the individual perception scenario (Fig. 3(a) red dashed curve). In contrast, the combined scenario, which integrates both individual behavioral changes and structured NPIs like isolation and quarantine, achieved the most pronounced reduction in new cases (Fig. 3 (a) green solid curve). The naive scenario without interventions (orange solid curve) exhibited rapid disease spread, highlighting the critical role of both behavioral adaptations and public health interventions in controlling outbreaks. These results quantitatively demonstrate the enhanced effectiveness of combining individual-level responses with system-level NPIs, validating the model’s robustness in capturing pathogen transmission dynamics and intervention outcomes.

Inferring epidemic metrics for the WKU epigame

Fig. 4 (a)-(d) illustrates the temporal dynamics of key epidemic metrics during the progression of the simulated outbreak at WKU. The effective reproduction number () began at 5.59 in the early phase of the experiment, indicating high transmissibility, and steadily declined to 0.22 by the end of the two-weeks period. This decline was primarily driven by the depletion of the susceptible population (S) and adherence to NPIs such as mask-wearing and social distancing. The basic reproduction number () was estimated at 6.6, reflecting the disease’s transmissibility under baseline conditions without interventions. The proportional relationship demonstrated how decreased the fraction of susceptible individuals (S/N) diminished, reducing the spread of the simulated pathogen. Temporal trends in hourly cases (panel a) revealed distinct infection peaks, while the gradual decline in S(t) (panel c) underscored the progressive depletion of susceptibles. Notably, crossing the critical threshold of 1 marked the transition from a growing epidemic to one that was effectively controlled.

Global and local sensitivity analysis

We carried out a global sensitivity analysis that takes into account both individuals’ perception of risk (which is modeled by ) and NPIs’ strength (which is modeled by ), as well as a time-dependent reporting rates. This analysis shows how the parameters and affect the pathogen spread³⁹. Our analysis demonstrates that both and play vital roles in shaping transmission patterns, although shows greater magnitude. Specifically, we found that exerts a more pronounced effect on transmission dynamics compared to . Small increases in or could result in decreased transmission, as shown in Fig. 5 (a) & (b), but the impact is relatively low for compared to , which causes substantial decreases in transmission, indicating a higher sensitivity to changes in this parameter.

Figure 5.

Sensitivity analyses assessing the effects of key parameters on the transmission dynamics and control. (A) and (B) depict the global sensitivity analysis with parameters (intervention strength) and (intensity of individual response) on the disease dynamics. The analysis highlights that has a notably stronger impact than , with even slight increases in leading to substantial reductions in transmission rates. (C) and (D) illustrate local sensitivity analysis using and attack rate as response functions, respectively, assessed through partial rank correlation coefficients (PRCCs). The analysis identifies the transition rate from exposed non-isolated individuals to the infected non-isolated class and the probability of transmission per contact as the most influential parameters on both and the attack rate.

To delve deeper into our model’s dynamics and parameter effects, we conducted a local sensitivity analysis using partial rank correlation coefficients (PRCCs) to evaluate the influence of key parameters on transmission dynamics, with and infection attack rate as response functions^41,42. Sampling 5,000 random instances from uniform parameter distributions, we simulated outcomes and calculated PRCCs between parameters and . As shown in Fig. 5(c) and (d), the transition rate of exposed non-isolated individuals to the infected non-isolated class and the probability of transmission per contact emerged as the most influential parameters, highlighting the essential role of minimizing interactions between susceptible and infected individuals and lowering transmission probability per contact.

Superspreader epidemiology of the WKU epigame

To further investigate the transmission dynamics captured during the WKU epigame, we applied the statistical framework introduced by Taube et al. ⁴³, which systematically quantifies superspreading behavior using standardized transmission tree metrics derived from real-world outbreaks caused by biological pathogens. Specifically, we focused on the largest connected component of the WKU transmission tree (Fig. 6) and calculated three key indicators: the temporal shift in the effective reproduction number () across transmission generations, the dispersion parameter () representing individual-level variation in secondary infections, and the superspreader–superspreader (SS) ratio reflecting clustering of high-transmitting individuals.

Figure 6.

Network and superspreader epidemiology analysis of the WKU data. (A) Contact network aggregated over the two weeks of the WKU epigame and colored by final infection status (blue for participants who were never infected, orange for those infected at some point during the game), (B) three largest connected transmission trees connecting infectors with infectees, (C) decrease in R by disease, R was below 1 in the second half of all trees (red line denotes R = 1), and (D) proportion of cases causing super spreading events as function of dispersion parameters, as predicted by theory and measured from the data. (C) and (D) were adapted from⁴³.

These analyses yielded several notable results. First, we identified a marked decline in the effective reproduction number between the first and second halves of the tree, consistent with the deceleration patterns documented in outbreaks of SARS, MERS, and COVID-19. Second, we found that the estimated dispersion parameter for the virtual pathogen used in the WKU epigame was , indicating moderate transmission overdispersion. This value aligns closely with empirical estimates for superspreading-prone diseases such as SARS (), MERS (), and COVID-19 (), further supporting the plausibility of the simulated dynamics. Third, the ratio of observed to expected superspreader-superspreader dyads we calculated for the WKU tree exceeded random expectation, reaching a value of 14 when including all nodes and 19 when restricted to non-terminal nodes-comparable to the elevated ratios observed in COVID-19 trees (often >8). Hence, these findings offer strong evidence that the transmission tree from the WKU epigame closely replicates the superspreading structure observed in biological outbreaks. This complementary network-based validation enhances the credibility of the platform in simulating realistic epidemic processes in naturalistic congregate environments such as university campuses.

Discussion

The pilot implementation at WKU served as a successful validation of our behaviorally-adaptive modeling framework. By integrating high-resolution contact detection with real-time behavioral measurements (Figs. S3 and S2) via a gamified proximity-sensing app, we were able to generate a dataset that allowed for the empirical estimation of transmission parameters that are typically assumed in theoretical models. Our findings demonstrate that a variable transmission rate model effectively describes the dynamics observed in the experiment, emphasizing that the inclusion of self-regulated behaviors modulated by perceived risk reflects real-life adaptive responses to outbreaks. A key insight derived from our model simulations is the critical threshold where individual risk perception becomes a more significant driver of transmission reduction than the interventions themselves. As shown in our sensitivity analysis, minor increases in behavioral intensity () and intervention efficacy () yielded disproportionately large reductions in cases, illustrating that a flattened epidemic curve is most effectively achieved when coordinated NPIs are coupled with high population risk awareness. Furthermore, the model’s ability to recapitulate hallmark features of real-world epidemics, such as nonlinear transmission dynamics and superspreading patterns, consistent with SARS, COVID-19 and other respiratory pathogens, validates the epidemiological realism of the data generated by the epidemic game approach.

Our modeling work included detailed model simulations and sensitivity analyses using the data generated from the experiment. Model fitting and parameter estimates (Fig. S7 and Table S1) demonstrated that our variable transmission rate model effectively describes the transmission dynamics observed in the experiment. The inclusion of human behavioral factors, such as individual adherence to preventative actions and the assessment of risk, enhanced the model’s accuracy. The predicted parameters accurately depicted the transmission situations, highlighting the significance of prompt and synchronized interventions^8,40,44. Biologically and ecologically, the inclusion of self-regulated behaviors modulated by perceived risk reflects real-life adaptive responses to outbreaks and supports the growing evidence that endogenous human feedback plays a critical role in influencing propagation of infectious pathogens.

The superspreader analysis (Fig. 6) provides validation for the epidemiological relevance of the WKU’s data, showing parallels with real-life SARS-like infections and emphasizing the disproportionate role of superspreaders in driving outbreaks. This result reflects the biological reality that a small subset of individuals often contributes disproportionately to pathogen spread due to variations in social connectivity or shedding patterns, underscoring the necessity of integrating individual-level transmission heterogeneity in epidemic models. Furthermore, analysis of the WKU transmission tree revealed superspreading patterns consistent with those observed in outbreaks of SARS, MERS, and COVID-19, with a moderate dispersion parameter and elevated superspreader–superspreader ratios. These results corroborate the biological realism of our platform and highlight the importance of accounting for transmission heterogeneity in outbreak preparedness models.

The model simulation results presented in Fig. 3 (a) revealed the profound impact of individual behavior and NPIs on disease transmission dynamics. The naive scenario, which operates under the assumption of no interventions, illustrated a rapid and uncontrolled spread of the pathogen, emphasizing the critical need for timely interventions to prevent widespread transmission. In contrast, scenarios incorporating individual reactions to the outbreak demonstrated a significant reduction in new cases. The red dashed curve in Fig. 3 (a) reflects this impact, where behavioral responses such as social distancing, mask-wearing, and self-isolation markedly decrease transmission rates. Human behavior plays a pivotal role in controlling the spread of infectious diseases, as individuals’ decisions to adopt preventive measures can substantially alter the trajectory of an epidemic^39,40,45. The most pronounced effects were observed when combining behavioral adaptations with structured NPIs, such as quarantine and isolation, resulting in a markedly flattened epidemic curve and aligning closely with observed data, validating the model’s fitting ability.

These results suggest that perception of risk by individuals is critical and perhaps more so than the interventions themselves (i.e.: a highly impactful intervention will not be of much use if risk perception is low). Therefore, this stresses the importance of finding an appropriate balance between risk perception and intervention strength to determine tailored measures that effectively control outbreaks. The analysis of reporting ratios (Fig. 3 (b) &(c)) further supports the model’s robustness, showing stable reporting under both individual and combined intervention scenarios. This stability underscores the effectiveness of coordinated public health measures and their critical role in ensuring reliable data for decision-making and policy formulation.

To further enhance our results, we examined epidemic metrics of the WKU epigame presented in Fig. 4. The decline of below the critical threshold of 1 emphasizes the role of diminishing susceptibility in curbing epidemic spread. A high of 6.6 indicates significant outbreak potential in the absence of interventions, but the proportional decrease in as declined underscores the impact of immunity and NPIs in reducing transmission. This result shows that experimental epidemic games can provide valuable mechanistic insight into how herd effects emerge dynamically as susceptible pools are depleted. These findings align with theoretical models of infectious disease dynamics, illustrating how interventions and population immunity shape epidemic trajectories⁴⁶. The trends in hourly cases and provide a comprehensive view of disease progression, underscoring the importance of maintaining a high fraction of immune or non-susceptible individuals to suppress transmission effectively.

The global sensitivity results presented in Fig. 5 (a) & (b) further emphasized the pivotal role of key metrics like (intervention efficacy) and (behavioral intensity), with minor increases in these parameters yielding significant reductions in transmission, highlighting the importance of robust, targeted interventions. Moreover, the local sensitivity analysis (Fig. 5 (c) & (d)) identifies key parameters, such as the transmission rate () and transition rate of exposed individuals (), as critical drivers of the reproduction number (). These findings guide the optimization of interventions targeting high-risk transmission pathways. In additional simulations of our model (described in the supplementary materials), we varied key epidemiological parameters to evaluate their effect on transmission dynamics. These results further emphasize the important role of targeted interventions aimed at reducing transmission (e.g., social distancing, mask-wearing) in mitigating both asymptomatic and symptomatic spread. For additional simulations on the impact of key parameters, see Supplementary Figs. S8 & S9.

Our model enhances epidemiological modeling by incorporating empirically-determined dynamic behavioral factors, allowing individuals to adapt NPIs such as social distancing and quarantine based on real-time changes in disease severity and perceived risk^15,17. This approach improves predictions of public health intervention impacts and epidemic trajectories^37,38. However, it does not fully capture behavioral heterogeneity shaped by cultural norms, misinformation, and public trust^47,48. Future refinements should integrate granular data and sociopsychological insights to better model diverse human actions and inform effective public health strategies^15,17.

Conclusions We conducted a large-scale experimental epidemic game involving nearly 1,000 students at WKU, using a gamified proximity-based app to simulate pathogen spread and to collect contact and behavioral data in a real-life setting. This empirical data from the WKU epigame allowed us to calibrate an SEAIRD model with a variable transmission rate representing individuals’ risk perception and strength of NPIs. We ran several computational scenarios with this model, which demonstrated that dynamic behavioral responses, particularly adherence to non-pharmaceutical interventions (NPIs) such as quarantine and social distancing, can substantially reduce disease transmission, and that individuals’ risk perception has a significant effect on this reduction, even more so than the strength of the interventions themselves. By focusing on these mechanistic insights, our findings in this study advance the field of behavioral epidemiology, offering a foundation for models that can predict the impact of layered NPIs across diverse and culturally complex settings. More broadly, we show how an app-based epidemic experimentation platform, integrated with behaviorally adaptive modeling, can recapitulate hallmark features of real epidemics-including nonlinear transmission dynamics, superspreading, and the mitigating impact of layered NPIs. We also highligt the potential of our app-based platform for generating highly realistic datasets of disease transmission and informing experimentally grounded computational analyses of epidemic scenarios.

Materials and methods

Experimental design, participants, and data

We designed the WKU epigame to study human behavior and NPIs during a hypothetical infectious disease outbreak in a college campus. Experimental games are a novel approach that has been applied in fields such as public health and climate science and it is gaining recognition as a valuable source of behavioral data for research^49–51. Our app spreads the digital pathogen using an underlying “ground-truth” transmission model that assigns a probability of infection to each contact between a susceptible and an infectious user (refer to the supplementary materials for details) and informs users of their simulated health status (asymptomatic, mild and severely ill, recovered, and dead) via an animated avatar and changes in the color of the app’s user interface (UI). A key difference with prior experimental games is the naturalistic setting of our experiment, which allows for a highly immersive experience and enables participants to adopt behaviors during our experiment such as socially distancing to reduce their chances of infection, very closely mirroring real-life.

The app gamified health-related decision-making by implementing a point-based system where students earned points through daily choices to “quarantine/isolate” via an app button, without physically restricting movement. Points could be used to purchase virtual masks and diagnostic kits through an in-app “shop.” Quarantine and isolation involved making avatars invisible to others, differentiated by symptomatic status. This system encouraged engagement and personal investment, with points contributing to a school-wide leaderboard and prizes for top scorers, balancing participation with students’ regular activities (see Fig. 1 (a) for illustration).

Figure 1.

Mobile app and informational materials used during the WKU epigame. (A) Students engaging with the smartphone app simulating pathogen transmission and disease progression during the epidemic game at Wenzhou-Kean University (WKU) (top, picture by Xiangyuan Yu). Screenshots of the app, showing (from left to right) the home page with healthy and sick avatars, a pop-up message prompting students to choose whether to quarantine/isolate for the day (which did not imply physical isolation but only in-game quarantine), and the home page interface while in quarantine/isolation (bottom). These visuals illustrate the interactive features of the app, which are integral to collecting behavioral and epidemiological data during the WKU epigame. (B) Materials used to promote the experimental epidemic game at WKU and facilitate student enrollment in the activity. Section of an informational micro-site about WKU epigame with links to the registration form and WeChat group (left). Manual page detailing the use of the app and the features specific to the WKU epigame (center), and flier describing the final prizes to be awarded to top-scoring students (right).

We implemented a comprehensive pre-experiment strategy to engage WKU students, employing a multifaceted strategy across various communication platforms, including a dedicated informational website, WeChat groups, and the distribution of digital and physical fliers (see Fig. 1 (b)), all of this managed by an organizing team of WKU students. An anonymous pre-registration form enabled us gauging interest in the experiment, while WeChat facilitated efficient communication, a proven approach in similar studies^44,45,52. Researchers did not have access to any of the WeChat groups, to avoid interaction with potential study participants. To encourage sustained participation, we offered incentives such as extra-curricular credits, a point-based system, a school-wide leaderboard, and post-game rewards. This strategy garnered interest from over 1,000 students, with 794 ultimately participating in the WKU epigame. The full research protocol of the WKU epigame is available in a separate manuscript².

The app collected the following data from participating students: contact events (defined as instances when two participants came within approximately 2 meters of each other, as inferred from Bluetooth signal strength); simulated transmissions and health status (note that no real health data were collected); in-app behavioral choices such as quarantining or mask-wearing; point scores resulting from these choices; and responses to anonymous surveys (including basic demographics and perceptions about quarantine-see supplementary materials for details). None of the collected data included personally identifiable information. Participants joined the game using a preset code specific to this experiment, and the app automatically generated a 128-bit Universally Unique Identifier (UUID) for each participant. This UUID enabled us to distinguish data from different participants without linking it to their personal identities.

Conceptual model framework

We adopted an Susceptible-Exposed-Asymptomatic (infectious)-(symptomatic) Infectious-Removed (SEAIR) conceptual model framework^53,54 to analyze pathogen transmission dynamics during the WKU epigame, incorporating asymptomatic and symptomatic exposures and accounting for quarantine and isolation statuses (Fig. 2). This model assumes a constant population size and homogeneous structure, justified by the two-week experimental period in a residential campus setting while allowing variations in susceptibility and transmissibility to reflect real-life complexities.

Figure 2.

Full conceptual epidemiological model in the WKU epigame. Flow chart for the model defined by equation (1) for pathogen transmission dynamics within the WKU setting. Solid arrows indicate the transitions between compartments, with the associated per capita flow rates shown next to each arrow. The model partitions the total population into ten compartments: non-quarantine susceptible (), quarantine susceptible (), non-quarantine exposed (), isolated exposed (), non-isolated asymptomatically infected (), isolated asymptomatically infected (), non-isolated symptomatically infected (), isolated symptomatically infected (), recovered (R), and dead (D) individuals (all these states represent in-game conditions, not real-life health outcomes).

A key feature in our conceptual model is the integration of human behavior as a dynamic factor influencing transmission rates, where participants’ adherence to NPIs-such as mask-wearing, social distancing, and isolation-evolves with perceived infection risks. The SEAIR model is described in the section below, which includes the model’s ODEs in equation (1).

Mathematical formulation of the conceptual SEAIR model

The full conceptual SEAIR model partitions the total population at any time into nine distinct sub-populations: non-quarantine susceptible (), quarantine susceptible (), non-isolated exposed (), isolated exposed (), non-isolated asymptomatically infected (), isolated asymptomatically infected (), non-isolated symptomatically infected (), isolated symptomatically infected (), recovered (), and deceased () individuals. The model tracks the movement of individuals between these compartments using a system of non-linear ordinary differential equations (ODEs), so that the following condition is satisfied:

In this model, the rate at which individuals move between compartments is determined by various parameters, including the infection rate , transition rates between different states (, , ), and quarantine/isolation dynamics (, ). The model also includes parameters for recovery (), immunity waning (), and disease-induced mortality () (keep in mind that all these parameters represent simulated, not actual, health statuses of participating individuals during the epidemic game). Individuals may leave the susceptible compartment () to become exposed () due to infection, or they may transition into or out of quarantine () based on the rates and . Once exposed, individuals may progress to either asymptomatic () or symptomatic infection (), with similar transitions for their isolated counterparts (, ). Recovered individuals can lose immunity and re-enter the susceptible class. The model further accounts for simulated “deaths” due to the disease, captured by the compartment .

The proposed model is depicted in Fig. 2; the state variables and model parameters (Table S1) fulfill the following system of non-linear ordinary differential equations (ODEs):

1

From model (1), the incidence function or force of infection is given by the following equation:

2

It is worth mentioning that the parameter represents the adjustment factor for reduced infectiousness in infectious individuals, indicating that is more prone to transmitting the disease at a higher rate than . This is meant to represent the silent nature of asymptomatic cases and the reduced activity of severely infected individuals, who are less mobile within the community compared to asymptomatic cases^55,56.

We set the state variable D(t) to measure the number of disease-deceased individuals to keep track of disease-related “deaths” (for calibration and quantification of model parameters).

Unified SEAIRD model with variable transmission rate

The full conceptual SEAIR model is reformulated by aggregating quarantine and non-quarantine (as well as isolated and non-isolated) compartments into a unified SEAIR framework with a variable transmission rate, preserving key dynamics and improving tractability. We then fit the model to the experimental data using a simulation-based inference framework, as proposed by⁵⁷.

The risk perception parameters and were estimated by minimizing the mean squared error between the observed infection curves and model output across the 14-day simulation. This calibration ensured the behavioral component in the model remained aligned with empirical dynamics observed during the WKU epidemic game.

The analysis focuses on a specific scenario based on the full conceptual model. We simplified the full model by introducing a modified flexible transmission rate to capture human behavior (perception of individuals). The simplified model with variable transmission rate is given by (3) within a closed domain (WKU campus). To simplify the full model (1), we used coupling dynamics by combining quarantine/isolation and non-quarantine/non-isolation compartments due to their similar dynamic nature (except for the constant and variable transmission rate)⁵⁸. The simplified model is depicted in Fig. S1 (see also Supplementary Fig. S6 for the model implemented in the app). Its dynamics are consistent with that of the full conceptual model and capture human behavior and NPIs through a variable transmission rate, incorporating the time-dependent variable P to represent individuals’ risk perception-a key determinant of transmission behavior. The equations are given by:

3

The model is augmented with an additional equation for P, which we define to increase with the number of infections and decrease over time as follows:

4

where m represents the mean duration of participants’ reaction to the number of infections.

We assumed that the perceived risk increases proportionally with the number of symptomatic individuals and saturates as becomes large. This formulation is supported by prior behavioral epidemic modeling studies^59–61, where awareness rises in response to observable disease prevalence. The linear decay term captures the natural fading of risk perception over time due to habituation or desensitization. Together, these dynamics ensure that remains biologically and behaviorally realistic throughout the simulation.

Building upon this behavioral feedback, we adopted a time-varying transmission rate as proposed in⁴⁰, often referred to as the effective or flexible transmission rate, denoted by . This formulation captures the impact of interventions (modeled, for instance, as a step function) and changes in contact patterns arising from increased public awareness or perceived risk. The resulting transmission rate is defined below in equation (5):

5

Here, the parameter represents interventions’ strength and aims to capture individuals’ response intensity. The parameters and are stepwise functions of time. The dynamics between intervention strength (), response intensity (), and risk perception (P) (with N greater than P(t)) are critical for understanding and predicting disease spread. Adaptive behavioral responses, influenced by real-time changes in perceived risk, significantly shape epidemic trajectories, and our parameter choices can be justified as follows:

• Intervention Strength  (): Represents the impact of public health measures, as the result of their intrinsic effectivity but modulated by disease severity and compliance. Higher perceived severity typically increases , as it induces compliance with preventive actions.

• Response Intensity  (): Measures variability in individual responses to perceived infection risk, often influenced by cultural and personal factors. As increases with social awareness and effective communication, disease transmission would decrease from a baseline given by the level of risk perception in the population.

• Risk Perception  (P): Individuals’ perception of risk can respond to many factors, from pathogen infectivity, information access, and pre-existing attitudes. Heightened P can boost preventive adherence but may also lead to panic or misinformation, complicating control efforts.

The relationship between these three parameters and their effect of disease transmission is potentially very complex. We reached a tractable model by adopting equations (4) and  (5), making the variable transmission rate dependent on , , and P. In turn, P, with its dependence on the number of infections, I, and a built-in progressive decrease reflecting peoples’ physiological traits such as forgetfulness and normalization, introduces these additional important elements into the transmission dynamics. Although simple, this framework has been applied extensively to model real outbreaks with satisfactory results^{39,40,47,62,63}.

Note that individuals in quarantine and isolation are restricted from further spreading the disease. As such, they do not contribute to transmission, and therefore, in this case is defined as , where serves as the modification parameter representing the reduced infectiousness.

Also, our model assumes a Poisson process due to the low frequency of (simulated) fatal cases, which aligns well with the Poisson distribution’s suitability for rare events. This approach is standard in epidemiological modeling for low-frequency events (see references^64,65 for similar applications).

Author contributions

SSM, WM: conceptualization, data analysis, results, figures, manuscript writing; TI: figures, manuscript editing; YD, MK: user interface and graphic design; AG, HH: software development; AW, DK: planning, manuscript revision; SAN, JGY: conceptualization; AC: conceptualization, planning, manuscript writing, project lead, and funding acquisition.

Funding

The development of the original Operation Outbreak app and backend infrastructure has been supported by the Gordon and Betty Moore Foundation (grants GBMF9125, GBMF9125.01, and GBMF11392). The customizations of the app and backend required for the WKU epigame were funded by a startup grant awarded by UMass Chan Medical School to AC.

Data Availability

The data from the WKU epigame can be retrieved from this Zenodo repository: https://zenodo.org/records/10674401.

Declarations

Ethics approval

We followed a study protocol that the UMass Chan Medical School Institutional Review Board (IRB) determined to be non-human subjects research, as defined by U.S. Department of Health and Human Services and Food and Drug Administration regulations (UMass Chan IRB ID: STUDY00000039). Therefore, informed consent was not required from participants in the experimental epidemic game conducted at WKU. The protocol was also approved by the WKU Ethics Committee. All methods were performed in accordance with the relevant guidelines and regulations.

Competing interests

The authors declare no competing interests.

Source code availability

The analysis scripts, written in the R and Python programming languages, are available together with usage documentation at GitHub this repository:https://github.com/colabobio/wku-epigame-modeling.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-49530-y.