Real-time spatiotemporal tracking of infectious outbreaks in confined environments with a host–pathogen agent-based system

Significance

Infection outbreaks in confined environments, such as schools, nursing homes, college dormitories, or cruise ships, can pose substantial medical risks to large populations within short timeframes. Modeling such outbreaks is challenging due to diverse behaviors of host populations and variations in transmission dynamics across different pathogens. Here, we introduce an approach that integrates state-of-the-art AI and geographic information system technologies. Hosts are represented as thousands of agents, intelligent programs running in parallel and sharing information about the infection, while pathogens are specified through mathematical functions capturing their biological properties. We apply our approach to study outbreaks of key human infections on cruise ships, showing its high accuracy on historical data and demonstrating the efficacy of selected protocols to contain infections.

Abstract

Deadly infection outbreaks in confined spaces, whether it is a COVID-19 outbreak on a cruise ship or measles and stomach flu outbreaks in schools, can be characterized by their rapid spread due to the abundance of common spaces, shared airways, and high population density. Preventing future outbreaks and developing efficient mitigation protocols can benefit from advanced computational modeling approaches. Here, we developed an agent-based modeling approach to study the spatiotemporal dynamics of an infection outbreak in a confined environment caused by a specific pathogen, and to determine effective containment protocols. The approach integrates the 3D geographic information system of a confined environment, behavior of the hosts, key biological parameters about the pathogen obtained from the experimental data, and the general mechanics of host–pathogen and pathogen–fomite interactions. To assess our approach, we applied it to the historical data of infectious outbreaks caused by norovirus, H1N1 influenza A, and SARS-CoV-2 viruses. Our AI-GIS Infection Dynamics (AGID) model accurately predicted daily infection numbers, correctly identified the day when the CDC vessel sanitation protocol would be triggered, singled out key biological parameters affecting the infection spread, and propose pathogen-specific changes to existing containment protocols. Our work advances the understanding of infection spread on cruise ships while offering insights applicable to other similar confined settings, such as nursing homes, schools, and hospitals. By providing a robust framework for real-time outbreak modeling, this study proposes more effective containment protocols and enhances our preparedness for managing infectious diseases and emerging pathogens in confined environments.

Infection outbreaks in predominantly confined environments, including schools, nursing homes, college dormitories, large open-plan offices, meat-packing facilities, grocery stores, and cruise ships, represent a persistent and growing public health concern (1–5). These settings present a substantial healthcare challenge due to high population density with prolonged interpersonal contact and limited on-site access to comprehensive medical care, conditions that facilitate pathogen transmission and amplify outbreak severity. The COVID-19 pandemic further emphasized the critical need to understand the dynamics of infectious outbreaks due to devastating outbreaks on the Diamond Princess cruise ship (6), USS Air Career Roosevelt (7), and at Kirkland, WA, and Holyoke, MA, nursing homes (8, 9). Cruise ships have been at the epicenter of main infectious outbreaks, caused primarily by noroviruses (10), influenza (11), and lately SARS-COV2 (12), due to increased frequency of close interactions between a large cohort of individuals, and the presence of high foot traffic areas, such as dining rooms and theaters, thus being one of the best documented sources of historical data on infection dynamics (13). Unfortunately, the current containment protocols developed primarily for norovirus infections proved not to be efficient for SARS-CoV-2, perhaps due to the extended asymptomatic period with viral shedding and a large percentage of asymptomatic carriers infected with COVID-19 (14) and its different primary mode of transmission (airborne for SARS-CoV-2 and surface-based for norovirus) (15, 16).

The ability to track the spatiotemporal dynamics of an infectious outbreak in a confined environment in real-time is critical for determining key factors driving the outbreak and developing optimal protocols for its effective and efficient containment. Conventional mathematical models (17–19), including those recently developed to study transmission dynamics of COVID-19 (20, 21), have been a critical driving force in understanding and ultimately controlling the pandemic. They have significantly contributed to the domain knowledge of the emerging virus, ranging from estimating key epidemiological factors, such as the viral transmission rate and the asymptomatic ratio (22), to offering insights into the role of herd immunity in global infection dynamics (23), and identifying key determinants of the population-level impact of vaccination (24). These methods generally focus on studying large-scale populations and are often unable to integrate complex spatiotemporal details on the individual-level interactions among the environment, host, and pathogen, such as person-to-person transmission, population density variation within confined spaces, and specific pathogen transmission characteristics.

In addition to the conventional compartmental epidemiological models (25), an AI approach, agent-based models (ABMs), has been recently applied in epidemiology and public health settings (26, 27). ABMs can represent the interaction and heterogeneous behavior of individuals (agents) within a system rather than the aggregate behavior of populations in compartmental models. Aggregate behavior then becomes an emergent property of ABM systems, providing increased accuracy as compared to other modeling systems (28, 29). The focus on individual behavior of the agents also allows for the ability to scale ABMs, from focusing on individual transmission dynamics (25) to urban contexts (30, 31), and even country-wide epidemic modeling (32–34). However, such models have not incorporated detailed host behavior in a specific environment (35), and importantly, no epidemic model to date has used a highly detailed three-dimensional environment representation that is traversable by both the host agents and pathogens (36).

Here, we develop an approach to study real-time spatiotemporal dynamics of an infection on cruise ships by utilizing an ABM framework, pathogen modeling, and geographic information system (GIS) representation of the cruise ships. We first assess this approach using historical data from past outbreaks of norovirus, whose economic and health burden is well documented (SI Appendix, Fig. S1). Then, we analyze the dynamics of potential outbreaks for SARS-CoV-2, Ebola virus, and the 2009 H1N1 pandemic influenza virus, identifying the pathogen-specific key contributing factors and suggesting improvements to the current containment protocols.

Results

In our agent-based modeling approach, called AI-GIS Infection Dynamics (AGID), a real-world cruise ship (which we refer to as Ship X) was represented as a three-dimensional geographic information system (GIS): each deck was modeled as a two-dimensional GIS and the decks were connected into a spatially ordered network, with connections corresponding to the elevators and stairwells between the decks (Fig. 1 and SI Appendix, section 1). The hosts, i.e., passengers and crew, were modeled as agents, which allowed us to explicitly define complex interactions among hosts, between hosts and pathogens, as well as between hosts and the environment. Each agent class (passengers, crew) had specific parameters defining their behavior in the system, which were integrated with pathogen modeling (Fig. 1A). Pathogen dynamics was modeled by defining, in real-time, the probability of infection and illness for each exposed agent based on the dose–response curve.

Fig. 1.

Overview of the AGID real-time infection modeling system. (A) The core of the system consists of the geographical information system (GIS) based 3D representation of the cruise ship as a traversable network for the agents. Agent modeling consists of a population representation and action modeling, where the crew and passenger agents follow their respective schedules. Pathogen modeling is carried out individually for each viral strain through a set of parameters, such as viral shedding, incubation period, and R₀, among others. CDC vessel sanitation program and other containment protocols are implemented to study their effects in mitigating an outbreak. (B) The graphical user interface (UI) provides a real-time display of agent movement, pathogen transmission, and infection cases. The UI provides functionality to interact with the GIS by zooming in/out to high-density areas. The cruise ship areas and agent states are represented by a colored legend. The infection icon is displayed specific to the location where a previously infected agent successfully passed the infection to a healthy agent.

Assessment of Critical Parameters Affecting Infection Dynamics.

We first assessed the importance of explicitly defining in the AGID model its agent-specific parameters. We compared the performances of three basic (naïve) types of models (Types I, II, and III, Fig. 2A and SI Appendix, Fig. S2 and section 2.2), where the key host and/or pathogen parameters were substituted by simplified values, not reflecting the real-world characteristics. Eight naïve models, which we referred to as Naïve Sim-1 – Naïve Sim-8, were developed to simulate a specific norovirus outbreak that occurred on Ship X in 2006, and assessed by comparing the simulation results against the historical data (Fig. 2A and SI Appendix, Fig. S2). The historically observed cases over the 9-d cruise reached an attack rate (AR) of 6.5%. The models of Type-I (Naïve Sim-1 & 2) were designed to assess the importance of explicitly specifying the daily routines for the host agents. Naïve Sim-1 lacked the information on the daily activities of the host agents: instead, the agents randomly traversed the ship without any breaks, while other parameters, including pathogen-specific characteristics, were accurately defined (SI Appendix, Fig. S2). Since an infectious agent did not spend significant time in any location or interact with another host agent, the infection spread was substantially lower compared to the historical data, with AR of ~1%. Adding the breakfast schedule in Naïve Sim-2 increased agent interaction in dining rooms, causing AR to reach 2.5%. In models of Type-II (Naïve Sim-3, 4 & 5), the agents still performed a randomized traversal of the ship, while being infectious, with modifications designed to enhance infection characteristics and therefore increase the infection rate, such as extending the infectious period of an infected agent and increasing the probability of transmission from infected to susceptible agents. Specifically, in Naïve Sim-3, the agents remained infectious all the time after getting infected; in Naïve Sim-4, an infectious agent transmitted the pathogen to all agents in the vicinity (i.e., within a transmission radius); and in Naïve Sim-5, the agents remained infectious all the time and infected everyone in the vicinity. The transmission radius was defined to be 0.5 feet. Increasing the transmission rate did not increase AR beyond 1% (SI Appendix, Fig. S2), because the agent-to-agent interaction was still minimal. Models of Type-III explored the impact of the parameters defining the infection transmission alone. Specifically, in three models, Naïve Sim-6, 7 & 8, the host agents followed an accurate schedule, while the parameters accounting for pathogen transmission were changed in the same way as in Naïve Sim-3, 4 & 5, respectively. In a stark contrast to the previous five models, for Naïve Sim-6, 7, 8, we observed a substantially higher AR, compared to the historical data, reaching a maximum of 80%. The infection numbers increased sharply due to the higher-than-usual transmission dynamics from Naïve Sims-6 to 8 (Fig. 2A). Overall, none of the eight naïve simulations matched the observed outbreak: they were substantially different at each observed time point, demonstrating the critical need for the parameters describing both host actions and pathogen transmission to accurately model an outbreak.

Fig. 2.

Evaluation of simulated norovirus outbreaks shows a superior performance by AGID models. (A) Simulation of three types of naïve agent models and pathogen modeling (a total of eight different set-ups), and comparison with the observed outbreak on Ship X. The naïve models failed to match the observed outbreak. (B) The detailed agent and pathogen modeling in AGID (green line corresponds to the means of 10 independent simulations, shaded light green region corresponds to their SD) is closely aligned with the observed epidemic curve on Ship X (gray) w.r.t cases and time, including reaching VSP threshold, whereas the conventional SIR (orange) and SEIR (red) model predictions using default parameters extracted from historical data (1/γ = 3 d, ${\mathrm{R}}_0\approx 1.5$) differed substantially from the observations. (C) Comparative assessment of the prediction by the AGID model simulations (green) together with conventional SIR (orange) and SEIR (red) models w.r.t historical observations (gray); both RMSE and MAE were an order of magnitude greater for the two conventional models. (D) Kolmogorov–Smirnov test of the predicted and historically observed cases showed the predictions from AGID simulations (green) were similar to the distribution of the observed cases (gray), with a small D value, while SIR (orange) and SEIR (red) predictions had large D values and did not satisfy the null hypothesis. (E) Evaluation of simulated norovirus outbreaks on Ship X using a stratified SEIR stochastic compartmental model, SEIR-SCM, over an expanded range of parameters (${\mathrm{R}}_0=1.5-3.0, 1/\gamma = 2 \mathrm{days}$), and their comparison to the real outbreak data (gray). For each set of parameters, 50 independent simulations were run and summarized. The lines correspond to the means of 50 independent simulations for each set of parameters, and shaded light regions correspond to their SD. (F) Evaluation of simulated norovirus outbreaks on Ship X using a stratified SEIQR-SCM model over an expanded range of parameters (${\mathrm{R}}_0=1.5-3.5, 1/\gamma =2 \mathrm{days}$) and with a moderate VSP scenario: $q_f=0.25$ and $f_{\mathit{VSP}}=0.5$ and their comparison to the real outbreak data (gray). Similar to (E), lines and shaded regions correspond to the means and SD, respectively, of the 50 simulations run for each parameter set. Average and mean values of the simulations corresponding to the SEIQR-QCM model with R₀ = 3.5 and the self-quarantine parameter $q_f$ = 0.25, but with no VSP protocol were included for comparison (red). (G) 10 AGID simulations for each of the five ships performed to validate the system generalizability by recreating specific outbreaks observed on the five cruise ships showed that most predictions had less than one percent deviation from the observed outbreak. (H) AGID simulations (light green) carried out to validate the system’s variability in predictions by providing only median parameters for the five ships, and comparing against the variation in observed outbreaks (light orange): the mean values are similar and mostly within a percentage point.

Evaluation of the AGID Model and Comparison with the Conventional Models.

Once all parameters of the AGID model were defined, we compared its simulation accuracy to the accuracies of six conventional compartmental models of infection outbreaks: two standard models, SIR (susceptible, infectious, or recovered) (37) and SEIR (susceptible, exposed, infectious, or recovered) (38), recently used for modeling COVID-19 outbreaks in nursing homes (39) as well as four advanced population-stratified models, which treat the passenger and crew member subpopulations independently: SEIR-DCM (SEIR discrete compartmental model), SEIQR-DCM (susceptible, exposed, infectious, quarantined, or recovered discrete compartmental model) that can model self-quarantine scenario and basic CDC Vessel Sanitation Program (VSP) (40) scenario, SEIR-SCM (SEIR stochastic compartmental model), and SEIQR-SCM (SEIQR stochastic compartmental model) which included two advanced VSP scenarios (SI Appendix, section 2.4).

All models were compared to the real-world data, revealing that the AGID model’s predictions for Ship X closely matched the trends in the observed outbreak with respect to the number of cases per day, while the six conventional mathematical models underperformed with a varied accuracy (Fig. 2 B–D and SI Appendix, Figs. S3–S8). When comparing the performance of the AGID simulations against the six conventional models, we saw trends that were similar across all six models. For instance, we found that the longer infection period (1/γ = 3 d vs. 1/γ = 2 d) resulted in fewer daily infections across all six models for all tested parameters. We also determined that the advanced compartmental models, in particular SEIR-DCM and SEIQR-DCM, were able to achieve better performance when assuming higher values of R₀, compared to R₀ ≈ 1.5 derived from the reported historical data (SI Appendix, Table S5 and section 2.4).

Specifically, we observed that the AGID simulations achieved the lowest RMSE (8.86) and MAE (7.33) values, substantially lower than the corresponding values for the SIR (53.67 and 46.02 for 1/γ = 3 d as well as 31.06 and 24.21 for 1/γ = 2 d, respectively) and SEIR (71.89 and 60.97 for 1/γ = 3 d and 50.31 and 42.95 for 1/γ = 2 d, respectively) models that assumed the same R₀ ≈ 1.5 parameter obtained (Fig. 2 B and C and SI Appendix, Fig. S3). As the real and predicted outbreaks were each representative of the case probability distribution over the 9-d cruise period, we also used the Kolmogorov–Smirnov (K-S) test to quantify the difference in the predictions. The three probability distributions were plotted as a function of the cumulative cases (Fig. 2D), and we found that the AGID simulations were similar to the observed outbreak, while the SIR and SEIR models provided poor prediction forecast. The K-S test statistic on the distance between the distributions was the smallest for the AGID simulations (0.22), but substantially larger for the SIR and SEIR models (1/γ = 3 d), 0.67 and 0.78, respectively, with the statistical significance (P < 0.05).

Interestingly, introducing more advanced population-stratified discrete and stochastic models under the same initial conditions, including the same R₀ (R₀ ≈ 1.5), did not improve the accuracy (Fig. 2 E and F and SI Appendix, Figs. S4–S8): the most accurate models (SEIR-DCM, 1/γ = 2 d and SEIR-DCM with moderate VSP, $f_{\mathit{VSP}}$ = 0.5, 1/γ = 2 d) achieved RMSE and MAE of 62.69 and 53.63 as well as 63.90 and 54.69, respectively (SI Appendix, Figs. S4 and S6). The primary reason for such poor performance was the fact that all advanced models with population stratification consistently underestimated the number of daily infections under the original R₀ value. Moreover, the introduction of self-quarantine and VSP scenarios in both the discrete and stochastic models only reduced the daily infection numbers, further degrading the models’ performances for this R₀ (Fig. 2 E and F and SI Appendix, Figs. S5, S6, and S8).

We next examined the performance of the four advanced compartmental models as a function of R₀. To do so, four additional R₀ values higher than the experimentally derived estimate (R₀ ≈ 1.5) were considered (Fig. 2 E and F and SI Appendix, Figs. S4–S8): R₀ = 2.0, 2.5, 3.0, and 3.5 (the latter applied only to the SEIQR-SCM model). Increasing R₀ generally enhanced model performance under specific parameter configurations, in some cases substantially. The largest improvement was observed for the SEIR-DCM model under the VSP scenario (R₀ = 2.5, 1/γ = 2 d, $f_{\mathit{VSP}}$ = 0.5; RMSE = 19.58, MAE = 15.81). Even under these less realistic R₀ values, the associated errors remained roughly twice those achieved by AGID. We note, however, that further optimization, such as extending the parameter search beyond the current range, could yield a closer fit to historical data, as demonstrated for the SEIR-DCM under the VSP scenario and SEIQR-DCM (SI Appendix, Fig. S8 E and F). Last, although the AGID model does not explicitly rely on R₀, this parameter could be inferred from AGID-predicted daily infections using the same log–linear regression of log-fitted values method applied to CDC-reported caseloads (SI Appendix, section 2.4). This yielded a value of R₀ ≈ 1.4, closely matching the original estimate R₀ ≈ 1.5 derived from the historical data.

The AGID simulations reached the 3% CDC VSP threshold on Day 4 (Fig. 2B), consistent with the observed data, which indicated that 3% threshold was met after ~3.5 d. Furthermore, both observed and AGID-simulated cases plateaued at Days 8 and 9, reaching a total attack rate of 6.25% and 6.5% respectively. Only one of the basic models (SIR, with 1/γ = 2 d) was able to reach the VSP threshold of 3%, and it did so on Day 7—significantly later than during the actual outbreak. The two most accurate advanced models described above both reached the VSP threshold on Day 6.

The evaluation was then expanded to test the ability of the AGID simulations to accurately predict multiple outbreaks across five different cruise ships. The cruise ships differed with respect to the overall layout, which includes the number of floors, staterooms, facilities, and their types, as well as occupants (SI Appendix, Table S1). The cruise ships were selected from CDC data such that 1) each ship was involved in at least five different norovirus outbreaks and 2) their layout can still be modeled using the GIS of Ship X. First, we assessed the accuracy of predicting an outbreak on each of the five ships (Fig. 2G). The respective population sizes and cruise durations were used as initialization parameters from the real-world outbreak reports to create the simulations. The results revealed the accuracy of the AGID model in predicting the attack rates across all five cruise ships. The deviation was less than 1% in the median value for the attack rates predicted by our model versus the observed attack rate (Fig. 2G). Additionally, for Ships 1 to 4, the observed attack rate was within the interquartile range of the simulated attack rate. Next, we further expanded our evaluation to model five independent outbreaks for each of the five cruise ships: we expected to see that each ship had a defined range of attack rates if the GIS, population, and pathogen were maintained as constant variables. For this purpose, we use the mean values for each ship to seed the simulations. We analyzed the distributions of observed and simulated attack rates (Fig. 2H) and found that the median values were highly similar, with a difference of less than 1% for Ships 1 to 4 and ~1.5% for Ship 5.

Application of AGID to Simulate Infectious Outbreaks across Different Pathogens.

We next applied the AGID model to study other types of infectious outbreaks on cruise ships that had previously occurred or were considered a possibility (Fig. 3 and SI Appendix, Figs. S9 and S10). We focused on the infections caused by viruses that recently emerged: H1N1 2009 pandemic influenza A strain (H1N1pdm09) (41), SARS-CoV-2 virus causing the recent COVID-19 pandemic (42, 43), as well as Zaire ebolavirus (EBOV), which was linked to more than two dozen outbreaks in Africa and a recent 2014 spread in US and Europe (44). The viral pathogens were selected such that we could analyze the variation in transmission modes, disease cycles, attack rates, fatality rates, and the impact of novel pathogens. The shedding values for H1N1pdm09 and EBOV were obtained from animal model studies (45, 46), the values for norovirus were obtained from the human challenge studies (47), while the values for SARS-CoV-2 (original strain) were obtained from clinical testing (39) (SI Appendix, Fig. S11 and Table S2). Two different transmission modes were introduced into our model: airborne (direct transmission) and contact or surface-based. The airborne viruses, H1N1pdm09 and SARS-CoV-2, have a significant proportion of asymptomatic cases, 10% and 50%, respectively (15, 48–50), making the containment more challenging (Fig. 3A). On the other hand, norovirus and EBOV have a very low or unlikely chance of asymptomatic carriers (51). In addition to the original strain of SARS-CoV-2, we also simulated the infection dynamics of the Delta variant, which was one of the Variants of Concern being monitored by the CDC, due to its higher transmissibility and decreased neutralization by antibodies (52).

Fig. 3.

Simulation of H1N1 and SARS-CoV-2 outbreaks, including the Delta variant and efficiency of the containment protocols. (A) AGID simulation of H1N1pdm09 virus strain highlights the importance of implementing pathogen-specific protocols, with Isolation (green) being the only effective protocol for that outbreak, while closing the dining areas (orange) and implementing CDC VSP (blue) did not substantially reduce the number of infections. (B) AGID simulation (green, depicted with the SD) of the original strain of SARS-CoV-2 using Ship X GIS representation, with conventional SIR (orange) and SEIR (red) models, and comparison with the historically observed cases (gray) on the Diamond Princess cruise ship. (C) Errors present in the prediction of the AGID simulations (green), SIR (orange), and SEIR (red) models w.r.t Diamond Princess observations; both RMSE and MAE are greater by a factor of two for the SIR and SEIR models. (D) Kolmogorov–Smirnov (KS) test of the predicted and observed cases showed that the AGID’s predictions (green) are more similar to the observed case distribution (gray) than the predictions by the SIR (orange) and SEIR (red) models, with a smaller D value. (E) Simulations show that lowering the VSP threshold from 3% (red) to 2% (purple) and even to 1% (blue) for SARS-CoV-2 (original strain) does not provide better containment, while the Isolation protocol (green) is more effective. (F) AGID simulations show the benefit offered by face masks (green) to reduce the case load, as compared to the “no-mask” infection dynamics (purple).

The AGID simulations for SARS-CoV-2 transmission dynamics accurately modeled the infection trajectory relative to the population and number of days (18.6% attack rate), with a similar distribution of the caseloads to that observed on the Diamond Princess cruise ship (Fig. 3B). Our model estimated that the Diamond Princess COVID-19 outbreak had an average incubation period of approximately 5 d, consistent with the previous reports (53). Compared to the compartmental models, the simulations were more accurate as demonstrated by the error metrics, RMSE of 23.73 and MAE of 16.62 for simulations, and the SIR and SEIR predictions have both RMSE and MAE greater than double the error metrics of the simulations (Fig. 3C). Additionally, the K-S test statistic on the distance between the distributions is smallest for the simulations (0.22), but substantially larger for the SIR and SEIR models, 0.62 and 0.69 respectively (Fig. 3D), with the statistical significance (P < 0.05). A possible explanation for the poor performance of SIR and SEIR models could be the fact that we used a value of R₀ = 2.2, previously reported for SARS-CoV-2 in China (54). However, it has been estimated that the R₀ of the COVID-19 outbreak on the Diamond Princess was significantly higher, up to 14.8 (55). To see if the usage of a higher R₀ can improve the mathematical models, we have run exactly the same simulation, but for R₀ = 14.8. The results did not improve: instead of underestimating the number of infections as happened for R₀ = 2.2, the models grossly overestimated them (SI Appendix, Fig. S9 and section 2.4). In addition, we repeated the simulations for both the original population (3,711 agents) and the scale-down version (2,702 agents) to match Ship X GIS settings (SI Appendix, Fig. S9). In both cases, the compartmental models demonstrated similar performance. Last, following the comparative analysis between AGID and mathematical models that was performed for Ship X, we applied three advanced discrete compartmental models (DCM): SEIR-DCM model and SEIQR-DCM model with two VSP scenarios implemented: moderate ($q_f=0.25$ and $f_{\mathit{VSP}}=0.5$), which means that only 25% of symptomatic agents will self-quarantine and the VSP will reduce R₀ by a factor of 2; and strict ($q_f=0.75$ and $f_{\mathit{VSP}}=0.25$), which means that 75% of symptomatic agents will self-quarantine and the VSP will reduce R₀ by a factor of 4 (SI Appendix, Fig. S9). The analysis of the performances of mathematical models showed that the most accurate model was SEIQR-DCM with the moderate VSP scenario and R₀ = 14.8, but with RMSE and MAE (RMSE = 48.58 and MAE = 39.97) still substantially higher than those ones of the AGID model. Last, when we applied the AGID model to simulate the infection dynamics of the Delta variant, the simulation achieved an attack rate of 54.2%, nearly three times as high as the original virus strain (Fig. 3F).

The spatiotemporal analysis of the infection dynamics using the simulation data from the AGID model demonstrated that the high-density and high-foot traffic areas were the infection hubs, where the pathogen transmission occurred most frequently for any virus (Fig. 4 and SI Appendix, Figs. S12 and S13). The comparison of different viral infections in the same confined environments suggested that the mode of transmission of the virus played a key role in determining the rate of infection. In particular, the comparative analysis of infection dynamics for norovirus and the original strain of SARS-CoV-2 revealed an important difference between the transmission hotspots during the outbreaks (Fig. 4). While both outbreaks had a common hotspot—a hallway leading to a theater (SI Appendix, Fig. S14), where the regularly scheduled events were held—the norovirus infection-specific hotspots were the dining areas, where the hosts would be seated at a distance from each other, but would nevertheless interact with the fomites (e.g., tables), possibly contaminating it and ensuring host–fomite–host mode of transmission, which is characteristic for norovirus infections (56). In addition to the transmission mode, by comparing the four viruses, Norovirus, 2009 H1N1 pandemic influenza, SARS-CoV-2, and Ebola, we observed that the incubation period was also a major determinant of the attack rate achieved during the duration of a cruise. EBOV had a long, 8 to 10 d incubation period, resulting in a low number of infection cases during the cruise (SI Appendix, Fig. S10), whereas for norovirus it was a substantially shorter incubation period, 1 to 3 d, which resulted in more cases (Fig. 2B). When studying the COVID-19 outbreaks, characterized by an incubation period of approximately 5 to 7 d, we observed that the initial growth rate for the original strain of SARS-CoV-2 was slower compared to the norovirus. However, it eventually followed an exponential trend, driven by its mode of transmission. Last, the impact of asymptomatic carriers on the spread of infection varied significantly across different viral pathogens: norovirus exhibited negligible asymptomatic transmission, H1N1pdm09 had approximately 10% of cases transmitted asymptomatically, while the original strain of SARS-CoV-2 involved nearly 50% asymptomatic carriers.

Fig. 4.

Spatial distribution of infection hotspots and efficacy of containment protocols. (A) AGID simulation of a Norovirus outbreak on Ship X during a 9-d cruise. The Left panel shows the infection hotspots for a No Containment scenario (AR: 39%) with primary concentration in the dining halls, and the Right panel shows the effectiveness of CDC VSP to reduce transmission (AR: 6%) (color scale shows two-dimensional kernel density estimate for hotspots). (B) AGID simulation of SARS-CoV-2 (wild type) outbreaks on the ship Diamond Princess (Ship DP) by repurposing GIS of Ship X, with the Left panel showing the outbreak based on the documented 2020 outbreak (AR: 19%) and the Right panel showing implementation of Isolation procedures that largely reduces transmission (AR: 4%) (color scale shows two-dimensional kernel density estimate for hotspots). The outbreaks for both viral pathogens create well-defined infection hotspots when no containment protocols are implemented. We note that the distributions of the infection hotspots are different and dependent on the transmission mode: for norovirus, the most prominent hotspots are the restaurants (red squares) and the main crew corridor (blue square), whereas for SARS-CoV-2, it is only the main crew corridor. The restaurants are modeled to have regularly scheduled events for a large number of agents, while the main crew corridor has the highest traffic among the crew members.

Containment Protocols: Rethinking Existing Measures through an AI-Driven Optimization.

One of the main utilities of the developed AGID approach lies in its potential to optimize the existing and propose new pathogen-specific containment protocols. The obtained AGID model has shown the effectiveness of the CDC-defined outbreak containment measures for norovirus (Fig. 4A), which are currently triggered when the attack rate reaches 3% (57). It also showed that another containment protocol, i.e., closing all dining areas (Dining Closed) was nearly as effective in controlling the norovirus outbreak: the attack rates for CDC VSP and for the Dining Closed protocol were ~6.5% and ~7%, respectively (SI Appendix, Fig. S15). The GIS framework enabled the spatial analysis of hotspots and helped understand a striking phenomenon—a rapid increase in the number of infection cases during the gradual closure of the dining areas. For instance, when only a single dining area was closed, the outbreak size (SI Appendix, Fig. S15, Dining Restricted) surpassed that one for the no containment scenario (SI Appendix, Fig. S15, No Containment). Indeed, the partial restriction of the dining areas worsens the overcrowding effect in the remaining dining rooms (SI Appendix, Fig. S16), thus leading to the increased infection rate.

Furthermore, for the SARS-CoV-2 virus (original strain), lowering the VSP threshold from 3 to 2%, and even to 1% was not sufficient to mitigate the outbreak (AR were 53.7%, 45.7%, and 42% respectively). Additional restrictions on activities or the use of face masks were determined to be necessary to reduce the case load. While the lowered thresholds for VSP were not efficient, we found that the passenger isolation on presentation of symptoms for the original strain (AR: 5.7%) and face masks on symptom presentation for the delta variant (AR: 6.7%) were able to substantially reduce the case load (Fig. 3 E and F). We also found that the Isolation protocol was efficient when simulating an Ebola outbreak, due to the long and varying incubation periods, differing symptoms, and initial small case load, all of which would not meet the criteria for VSP (SI Appendix, Fig. S10). Overall, the spatiotemporal analysis identified common shifts in the patterns of pathogen transmission: from the explosive nature of infection in the high-traffic areas, such as the main crew corridor, when no containment protocol was implemented, to the localized infections in the staterooms with the Isolation protocol implemented, where only individuals in close physical proximity were infected (Fig. 4B).

Materials and methods

AI-GIS Infection Dynamics (AGID) Model of a Cruise Ship: Environment, Hosts, Pathogens.

The AGID-based model for a specific pathogen in a confined space is dependent on the space’s environment. For a cruise ship, the environment is characterized by the number of decks and their dimensions, the number and spatial distribution of staterooms, dining rooms, other recreational facilities, hallways, stairs, and elevators (Fig. 1B and SI Appendix, Fig. S14 and section 1.1). The AGID model is also dependent on the number of index cases.

The agents (hosts) include passengers and crew members; these two groups are primarily distinguished by their daily schedules (SI Appendix, Figs. S17–S20 and section 1.2). A host agent is also characterized by several time-dependent parameters, such as the current health state, daily activity status, and viral load. In the AGID model, we distinguish five health states for a host agent: healthy, infected asymptomatic, infected symptomatic, recovered, and perished (SI Appendix, section 1.3). The transitions between the states are intrinsically related to the phases of infection (SI Appendix, Fig. S21) and are determined based on the average timeline of the disease life cycle extracted from literature (SI Appendix, Table S2).

A pathogen model is defined for a specific infection and is characterized in the AGID model by quantified transmission modes, incubation period, viral shedding curve, and fatality rate (see SI Appendix, section 1.3 for more details). The viral exposure by a susceptible host is determined by the number of viral particles from another infected host that is in proximity to the susceptible host, and calculating the probability of being infected when exposed to the virus (58, 59):

$$P_{\inf }\left(D;a_I, b_I\right)=1-{\left(1+\frac{D}{b_I}\right)}^{-a_I},$$

where D is the dose of viral particles, which is dependent on the number of shed viral particles by another, already infected, agent; $a_I$ and $b_I$ are the infectivity parameters. The probability of the infected host to progress from the incubation period to illness stage is then estimated as $h\left(D|\eta ,r\right)=1-{(1+\eta D)}^{-r}$, where $\eta$ and r are the maximum-likelihood estimates obtained from literature (60).

The simulation of a viral outbreak is performed by first setting the initial number of infected passengers and the maximum allowed onboard population, and then running the simulation for a specified duration defined by the length of the cruise. During the simulation, the host agents perform a sequence of daily routines, with starting times of recreational activities having variation based on occupancy of common areas on the ship (SI Appendix, Figs. S17 and S19). For the infected and symptomatic crew members, we also implement a commonly used crew containment protocol (SI Appendix, Fig. S20). When a self-isolation protocol (SI Appendix, Table S3) is implemented, passengers follow a similar daily routine (SI Appendix, Fig. S18). In the simulation, we explicitly model interactions between pairs of host agents, one of which may be infected, by defining the agent–agent contacts based on their spatial proximity and interaction duration, specifying the number of particles transmitted through air or surface, and determining the probabilities of infection and subsequent illness for the exposed host agent. Both proximity and interaction duration play critical roles in infection transmission: exposure of a susceptible agent is initiated only if the agent and another, infected, agent are within a transmission radius (SI Appendix, section 1.3). Furthermore, if the agents remain in close proximity over multiple time steps, infection risk increases, as infection probabilities are evaluated cumulatively at each time step.

We used the simulation framework MASON to implement our agent-based model and perform the simulations (61), and the GIS was constructed using ArcGIS (62). The graphical user interface (GUI) (Fig. 1B and SI Appendix, section 1.1) was developed using Java Swing (63). We note that in the current implementation of AGID, all agents operate in a “pseudo-parallel” fashion as determined by MASON framework: for each step of the simulation, the system sequentially carries out the actions of all agents, with the order randomly assigned; the actions of any agent at the next step of the simulation is not initiated until actions by all agents at the previous step are completed.

Evaluation Protocols.

The accuracy of our model is assessed using historical cruise ship outbreak data available from the Centers for Disease Control and Prevention (CDC), as well as by comparing the model against several naïve, random simulation models and against conventional compartmental models of infections (SI Appendix, section 2). First, we evaluate whether the proposed system can accurately simulate a norovirus outbreak on a particular cruise ship. For Ship X, we collect detailed daily infection data for an outbreak that happened over a 9-d period in 2006 (SI Appendix, Tables S5 and S6). Second, we evaluate the generalizability of the system for the same pathogen (norovirus) in five additional cruise ships of various physical sizes and population sizes by following a rigorous protocol consisting of two steps: i) modeling a specific recorded norovirus outbreak on each ship, and ii) modeling a typical or averaged norovirus spread by aggregating five recorded outbreaks on each ship (SI Appendix, Table S1 and section 2). The CDC Vessel Sanitation Program (VSP) (40) is implemented for each ship using standard guidelines, i.e., when the number of infected individuals reaches 3% of the cruise ship population. The CDC reports provide the total number of passengers and crew, the total number of infections reported for the duration of the outbreak, and the statistics on the duration of the symptomatic stage. Some of the CDC reports also include the daily caseload data, which can be used to obtain an approximate value of the basic reproduction number (R₀) to use in the compartmental models.

Next, we further evaluated the generalizability of the system to model an infection outbreak on a different cruise ship by a recently emerged pathogen—SARS-CoV-2 virus, causing COVID-19. To date, a single well-documented case of a COVID-19 outbreak is the one that occurred on the Diamond Princess cruise ship in February 2020 off the coast of Japan, caused by the original strain of SARS-CoV-2 (64). The outbreak presents a unique opportunity to test the generalizability of our AGID system for an infection outbreak caused by a different (in terms of transmission, incubation period, and infectivity) viral pathogen, but on a cruise ship whose size and shape are comparable. While Diamond Princess is indeed comparable to Ship X, the combined population size of Diamond Princess during the outbreak (N = 3,711) was greater than that of Ship X (N = 2,702). Therefore, in our simulation assessment, we used a scaled model of Diamond Princess by scaling down the population from 3,711 to 2,702, applying the same scaling factor to the number of initial and daily infections (SI Appendix, Table S7), and repurposing the previously developed GIS of Ship X (SI Appendix, section 1.3). We hypothesize that while the absolute numbers of daily infections, and therefore caseloads, in the scale-down version of Diamond Princess are different from the original outbreak, the relative numbers, in terms of population percentage, are preserved and therefore expected to be accurately predicted by the AGID model.

We also assessed the accuracy of the approach’s agent and pathogen modeling by creating three types of indiscriminate/naïve models as well as developing six different kinds of compartmental mathematical models to predict the outbreak on Ship X (SI Appendix, section 2.3). The compartmental models included 1) SIR model, 2) SEIR model, 3) two population-stratified (passengers vs. crew members) SEIR discrete compartmental models, including a basic model (SEIR-DCM) and a more advanced model (SEIQR-DCM) that considers two scenarios: a self-quarantine scenario that enables a fraction of symptomatic hosts to quarantine themselves and VSP scenario, and 4) two population-stratified stochastic SEIR compartmental models including a basic model (SEIR-SCM) and advanced model (SEIQR-SCM) that considers two VSP scenarios, moderate and strict (SI Appendix, section 2.3). Four of the compartmental models, SIR, SEIR, SEIR-DCM, and SEIR-SCM, were also applied to model the COVID-19 outbreak on the Diamond Princess ship.

To systematically compare predictions of the models with the real outbreaks, we use three metrics (SI Appendix, section 2.2): rms error (RMSE) (65), mean absolute error (MAE) (65), and Kolmogorov–Smirnov (K-S) test (66). Furthermore, because of its stochastic nature, our model was evaluated for its consistency to produce robust predictions across multiple runs with the same model parameters. To ensure the computational feasibility of the above assessments, we performed 10 simulations for each combination of GIS, agent, and pathogen parameters, resulting in a total of 190 simulations.

Description of Containment Protocols.

We next implemented and simulated four containment strategies to determine their efficiency in limiting the spread of an infection (SI Appendix, Table S3 and section 1.4). Containment strategies (protocols) are necessary to modify the behavior of individuals in a population to reduce the spread of an infectious outbreak to ultimately “flatten the curve” (67). The protocols are designed based on the environment where an outbreak occurs and are often formulated by a governing agency, such as the CDC. The implemented containment protocols included: 1) closure for cleaning of a dining area where the infection was initially detected; 2) closure of all dining areas, with individual meals delivered to staterooms; 3) CDC vessel sanitation program (VSP), a protocol developed for infections with gastrointestinal illness symptoms, initiated when 3% of passengers or crew report the symptoms; and 4) isolation, where passengers voluntarily isolate themselves when symptoms appear and continue the isolation until symptom free. Additionally, for the evolving dynamics of COVID-19, we implemented two other containment protocols, including the lower VSP thresholds (2% and 1%, respectively) and mandatory wearing of face masks (SI Appendix, section 1.4).

Conclusions

In summary, our study demonstrates that an agent-based modeling approach that integrates both host and pathogen functionalities, along with the detailed GIS-based representation of the environment, can provide unique spatiotemporal insights into the infection dynamics, as well as determine important dos and don’ts during an outbreak. The real-time AGID models developed in this work offer live visualization of the outbreak and allow studying the infection dynamics at the individual host resolution, tracking the health status and changes of each individual. These models accurately predict the impact of epidemics, measured as a function of the daily number of infected agents, for different viruses with distinct virulence and infectivity rates. Notably, the AGID models predicted the attack rates with lower error at each time point, outperforming the basic conventional epidemiological models implemented in this work. The high-resolution GIS presentation reveals infection hotspots on the cruise ship, which traditional ODE-based models cannot capture. Additionally, the GIS representation facilitates the development and simulation of new containment protocols, such as closing all dining areas, to better control the viral outbreak. Our models allow for a better understanding of the pathogenicity of novel viruses, including likely incubation periods, the rate and impact of asymptomatic carriers, and the effectiveness of current containment protocols against emerging pathogens and their variants.

It is possible for conventional ODE-based models to achieve a comparable fit by interpolating historical data, if such data are available. In this study, for example, more complex SEIR and SEIQR models substantially reduced error rates, approaching those achieved by AGID, by optimizing multiple parameters (e.g., R₀, 1/$\gamma ,$ Q_f, or $f_{\mathit{VSP}}$) against historical data. Even a basic SIR model can yield drastically improved fits when implemented in a piecewise fashion, i.e., as a sequence of SIR-based curves each fitted to smaller consecutive time windows. However, such an approach intrinsically depends on the historical data of the specific outbreak and may not generalize well across different outbreaks, confined environment settings, containment protocols, or pathogens if the historical data are absent or incomplete. Metapopulation models (68, 69) also provide a viable alternative to agent-based approaches, particularly for large-scale simulations spanning broad geographic areas and population sizes. Such models are well suited for investigating general principles of disease dynamics, including herd immunity thresholds.

By contrast, our AGID framework, though more complex, offers advantages in confined scenarios with heterogeneous environments, where spatiotemporal analysis is critical, and agent behavior varies by type and health status. First, because it explicitly models biological transmission and host behavior, AGID does not require prefitting to historical data, enabling exploration of novel pathogens, environments, and containment protocols. Second, AGID captures heterogeneous host behavior as a spatiotemporal function; for example, we have shown that simulations based on realistic daily schedules produce more accurate infection dynamics than those based on the random walks. Third, integrating agent-based modeling with GIS enables representation of environmental heterogeneity. For instance, the AGID approach allows for the simulation of high-traffic zones or uneven spatial agent distributions, e.g., individuals seated around a table while dining. The fine-grained spatial-temporal resolution is used for the identification of infection hotspots within specific rooms or areas at precise times, which is critical when developing efficient scenarios for preventing and containing various infectious outbreaks. Fourth, GIS integration supports the design and testing of spatially targeted interventions, such as closing specific corridors, isolating cabins, or rerouting traffic flow, thereby facilitating more efficient layout-specific containment strategies. Last, the AGID approach can incorporate diverse containment protocols.

Indeed, one of the most significant advantages of the AGID models is their ability to systematically assess and compare the effectiveness of various containment protocols, including those that have not been previously implemented by the CDC. Our model demonstrated that in the case of norovirus outbreaks on cruise ships, closing all dining areas while leaving other spaces open could significantly reduce transmission. At the same time, the model revealed that closing only one or a few main dining areas would surprisingly have the opposite effect, creating tighter population bottlenecks in the remaining open dining rooms and thereby increasing infection rates. Furthermore, we found that airborne, influenza-like illnesses require a substantially lower threshold for triggering virtually any type of containment measures, ranging from the closure of dining and recreational areas to the isolation of all passengers. This finding underscores the need for pathogen-specific containment strategies and highlights the importance of rapid, onboard pathogen identification as a critical component of outbreak prevention. AGID approach also demonstrated that containment protocols restricting the movement of symptomatic individuals were highly effective—particularly when individuals self-isolated at the first sign of symptoms or when ship-wide quarantine measures were implemented, as observed during the real-world events on Diamond Princess.

The agent-based modeling approach, while powerful, is not without its limitations. AGID simulations require significantly longer runtimes compared to conventional mathematical modeling. In this light, mathematical models with advanced features described above, such as parameterized stochastic compartmental models (70), a recently developed Markov model-based framework (71), and others (72–75) may offer a useful alternative for capturing infection dynamics. In addition, some epidemiological features, such as the viral shedding curves for specific subpopulations, are often difficult to obtain from the literature. There is significant potential in exploring the AGID model’s capacity to represent complex behavior and diverse populations of host agents. For instance, modeling passenger agents of different ages could be important when considering infection outbreaks that exhibit varying transmission and infection dynamics across age groups, e.g., children vs. adults or adults vs. elderly. While incorporating these and other relevant factors into the model would inevitably increase its complexity, we do not expect a substantial rise in simulation runtime, due to the explicit integration of these factors into infection and transmission probabilities calculations, transmission logic, agent policies, containment protocols, and other model components. Nevertheless, introducing a systematic protocol to evaluate the significance of each factor will help minimize the number of such factors, reducing the model’s complexity without compromising its accuracy or fidelity.

Another important future advancement toward a more scalable AGID approach would be the development of a systematic method to convert an individual cruise ship’s layout into a GIS representation. This challenge could be addressed in the future by creating a library of generic modular GIS templates that can be scaled and adapted to represent key geographic features. Any specific cruise ship could then be mapped to the closest-fitting GIS model. Last, the model’s predictive power could be further enhanced by enabling agents to exhibit adaptive and intelligent behaviors through the use of advanced machine learning techniques, such as reinforcement learning (76), and by incorporating more complex models of the environment (77), such as using computational fluid dynamics to accurately model air conditioning systems (78).

As the world recovers from the COVID-19 pandemic, it is not a question of if, but when the next global pandemic will occur (79). The confined environments we encounter in our everyday lives pose heightened risks for infection spread due to the proximity of healthy and infected individuals. Computational approaches are among the most effective tools not only for forecasting the impact of such outbreaks in various social settings but also for proposing efficient strategies to mitigate them. While the AGID approach was initially applied to study infection outbreaks on cruise ships as one of the most well-documented types of confined environments, it can be adapted to virtually any other setting, including schools, grocery stores, nursing homes, or movie theaters. In the future, the model can be further enhanced to incorporate additional factors, such as vaccination status and innate immunity within the population, the implementation of hygiene measures like hand washing and mask-wearing, and the consideration of infection-specific age and gender groups.

Supplementary Material

Appendix 01 (PDF)

Movie S1.

AGID dashboard showing a part of the simulation run for a Norovirus outbreak on Ship X.

Data, Materials, and Software Availability

The simulation source code is freely available at https://github.com/KorkinLab/infection-dynamics (80).