Epidemic

SEIR Model

Figure 1. SEIR Model [3]

Using the geo-social agent-based model as a basis [1,2], we have designed a SEIR compartmental disease representation. The SEIR acronym refers a "Susceptible" individual who has the potential to be "Exposed" to a disease. Once exposed, people are potentially "Infected". Finally, infected individuals transition to a "Recovered" state. For each unique disease, the entire population is initially assumed susceptible. To test different characteristics of diseases, we not only vary exposure and infection times but also person-to-person transmission rates. By doing this, it becomes possible to study many diseases ranging from those that quickly disappear to those that infect a large part of the population. We introduce restaurants as a place where new diseases are initiated and susceptible individuals are exposed based on an environmental spread probability. This spread probability decays daily assuming that the disease pathogen weakens and disappears over time. After being exposed, individuals do not immediately spread the disease but they have to become infectious first.

The video above provides a disease simulation using the geo-social agent-based model [1]. The simulation covers the French Quarter, New Orleans, LA (spatial network) and agent locations are shown on the left in the figure. The current social network is depicted on the right, where nodes correspond to agents and links correspond to friendship. In both networks, the color of an agent corresponds to their disease status. The time series of the number of infections in the center of the video shows that we have just passed the epidemic peak-similar to the COVID-19 situation now. This simulation also generates a large data set (several GBs) that captures simulation parameters and results with a 5 min temporal resolution.

Different Diseases

Depending on types of diseases, epidemic dynamics such as epidemic peak vary. To see how epidemiological parameters (e.g., reproduction number) influence disease dynamics, we ran a simulation of two years with randomized epidemiological parameters. Figure 2 shows the number of infectious agents and recovered agents with each disease over time. All diseases are identified as d-ID (e.g., d-12), and the smaller ID number outbreaks earlier than the larger ID number. Only 36 out of 52 diseases outbreak due to epidemiological parameters and diverse environmental aspects. For instance, a disease source might have a very low chance to transmit a disease from environments. It is plausible that some areas that are a potential source of a disease (e.g., d-11) are not well visited. Some diseases (e.g., d-10, d-39) are very contagious and spread quickly during a short period. They have high epidemic peaks. We notice that the numbers of recovered agents with most diseases nearly reach the population, i.e., 5,000 agents. This is because in this scenario no policies are prescribed to mitigate epidemics. Thus, the population tends to carry infections unless the disease has a low transmission rate such as in the case of d-6. Data for this simulation, including temporal social network data, agent check-in data, and disease data (including exposure, infection, and recovery times for each agent) is available at OSF (https://osf.io/k8qjb/).

Figure 2. Disease dynamics varying epidemiological parameters

Prescriptive Analysis of Disease Spread

A geo-social simulation is a powerful tool to explore "what if" scenarios such as in the case of assessing different mitigation measures to limit disease spread. Using agent-based modeling as part of a predictive analytics approach allows us to explore how a change to the simulation (often called an intervention or prescription) will affect the system. Beyond purely predictive analytics, geosimulation allows to explore the parameter space of possible prescriptions to find optimal strategies (or policies) to achieve a desired system state and outcome. We can refer to such a search for optimal policies as prescriptive analytics.

We showcase how to leverage our geo-social simulation for prescriptive analytics using two prescribed policies to mitigate the result of a disease. The first policy requires all agents to wear simulated Personal Protective Equipment (PPE) that reduce the chance of infection by 50%. The second policy enforces strict social distancing measures onto a fixed proportion of 50% of the population. Those who follow the social distancing order avoid recreational site visits from meeting people although they still go to restaurants. As a baseline, we also ran a "null-prescription" in which no intervention was prescribed. Figure 3(a) shows the number of new disease cases immediately after the prescription at a simulation date of 2020-01-01 in all three cases. To quantify the uncertainty of the simulation results, we repeated each of the three scenarios 30 times (differing only in random seeds) and charted the resulting confidence intervals (standard deviation) of new cases. First, we observe that the social distancing prescription was extremely effective. The peak of the curve has been flattened from close to 350 new daily cases to less than 200. However, our simulation shows that merely wearing protective gear without any change in behavior has no significant effect (for the case of this disease). The number of new infections when using protective gear is nearly the same in the case of the null prescription (i.e., take no action). Figure 3(a) shows a weekly periodicity. This is due to most of our agents not working during the weekend, thus having more time to mingle with others at recreational sites.

(a) New infectious cases

(b) No Action

(d) Social Distancing Order

Figure 3. Experiment

Figures 3(b), (c) and (d) show the time series of different disease states of agents for different policies ranging from the null prescription (No Action), the use of protective gear (PPE), and social distancing (Social Distancing Order), respectively. Initially almost all of the 5000 agents are susceptible. As time passes, agents become exposed, with exposure peaks on weekends. Exposed agents become infectious after a while, and thus are able to expose other agents. In the case of No Action and PPE, we see that the number of recovered agents approaches 5000, implying that almost all agents had the disease at one point during these two months of simulation time. In contrast, Figure 3(d) shows that more than 1000 agents remain susceptible by enforcing social distancing, thus have never been infected even after the disease has disappeared (once all agents are either susceptible or recovered).

Figure 4 compares the epidemic dynamics of different policies. Figure 4(a) shows time series of the numbers of infectious agents for all 90 simulation runs. We observe three distinctive clusters for each scenario. Unlike mathematical models, the figure illustrates the richness of agent-based modeling when it comes to social interactions. Here a small change in one's behavior caused by randomness produces diverging epidemic progressions ("butterfly effect"). Yet the patterns are consistent. For instance, the mitigation effects of two experimental prescriptions can be validated in different possible worlds with three different epidemic peaks around "2020-01-06", "2020-01-15" and "2020-01-20", respectively. For each prescription, Figure 4(b) shows the mean and standard deviation of values represented as a solid line and confidence bands, respectively.

(a) Infectious cases

(b) Mean and confidence interval of infectious cases

(d) Mean and confidence interval of recovered cases

Figure 4. Comparison of epidemic dynamics between policies

Building on these policies, an open question is how to find a policy that minimizes new infections but also minimizes the socio-economic cost of interventions. Not only how many, but which agents should be forced to carry out social distancing? How many, and which agents should be quarantined, and when? Should recreational sites, restaurants and other sites be closed? Which ones and for how long? Answering these questions and finding optimal prescriptions among the combinatorial parameter space is the major challenge of prescriptive analytics.

It is worth noting that we captured four diseases moving through our simulated world in these experiments. Each disease was in a unique phase of its temporal and inter-personal transition across our synthetic, social population and a dynamically emerging social network. Those phases were: 1) a totally new and initial presentation instance, 2) a young (two-week old) instance, 3) a mature disease in full spread, and 4) a near-to-wane disease about to disappear in the population. We expect such a feature will be capable of simulating a simultaneous flu and second-wave COVID-19 epidemic outbreaks recently mentioned as a potential scenario by the CDC director [4].

Our simulation uniquely captures locations and temporal social networks using realistic rules of social behavior based on PoL. As such, we hope that the data sets that we generated, including check-in data, temporal social networks and disease information will help researchers to investigate to what degree it is possible to predict the effect of diseases and social distancing measures on social networks and social needs. With our data providing ground truth data on disease cases, the data also helps investigate the possibility of detecting disease cases and their stages by leveraging both temporal social network and check-in data [5].

Reference

[1] H. Kavak, J.-S. Kim, A. Crooks, D. Pfoser, C. Wenk, and A. Züfle. Location-Based Social Simulation. In SSTD, pages 218–221, 2019.
[2] J.-S. Kim, H. Kavak, U. Manzoor, A. Crooks, D. Pfoser, C. Wenk, and A. Züfle. Simulating urban patterns of life: A geo-social data generation framework. In SIGSPATIAL, pages 576–579, 2019.
[3] J.-S. Kim, H. Kavak, U. Manzoor, and A. Züfle. Advancing simulation experimentation capabilities with runtime interventions. In 2019 Spring Simulation Conference (SpringSim), pages 1–11. IEEE, 2019.
[4] L. H. Sun. CDC Director Warns Second Wave of Coronavirus is Likely to be Even More Devastating, Washington Post, https://www.washingtonpost.com/health/2020/04/21/coronavirus-secondwave-cdcdirector/ (accessed 2020-05-21).
[5] J.-S. Kim, H. Kavak, O. C. Rouly, H. Jin, A. Crooks, D. Pfoser, C. Wenk, and A. Züfle. LBSN-disease-data. https://osf.io/k8qjb/ (accessed 2020-05-21)