Agent-Based Computational Epidemiological Modeling

Abstract

The study of epidemics is useful for not only understanding outbreaks and trying to limit their adverse effects, but also because epidemics are related to social phenomena such as government instability, crime, poverty, and inequality. One approach for studying epidemics is to simulate their spread through populations. In this work, we describe an integrated multi-dimensional approach to epidemic simulation, which encompasses: (1) a theoretical framework for simulation and analysis; (2) synthetic population (digital twin) generation; (3) (social contact) network construction methods from synthetic populations, (4) stylized network construction methods; and (5) simulation of the evolution of a virus or disease through a social network. We describe these aspects and end with a short discussion on simulation results that inform public policy.

Keywords: Agent-based simulation; Computational epidemiology; Data-driven social network generation; Discrete dynamical systems; High performance computing; Large-scale stylized network construction; Synthetic populations.

Figure 1:

Major components of the agent-based modeling system for computational epidemiology. These boxes are the topics in Sect. 4 below. Feedback loops are not shown. For example, based on the results of system behavior, the population construction methods may be changed, stylized networks with different properties may be generated, or parameters of the dynamics model may be changed.

Figure 2:

State transition diagrams for the susceptible-infected-recovered (SIR) model. The state set $K=\{S,I,R\}$. Vertex functions quantify the conditions under which a vertex changes state.

Figure 3:

Illustrative example of a 4-time step forward trajectory for a synchronous GDS where each vertex function is an SIR model. The dependency graph has 4 vertices and 4 edges. The infectious duration for each vertex (agent) is $t_{\mathit{dI}}=2$, and the probability of infection is p for each vertex. The vertices (agents) are labeled in the graph at the left, corresponding to the initial state x(0). The state corresponding to each time, displayed below the time, is given as $x(t)=(x_1,x_2,x_3,x_4)$. This particular sequence of states is dependent on the random numbers $r_i$, $1\le i\le 5$, and their relation to p.

Figure 4:

Illustrative example of a person-location bipartite graph, where people (1 through 4) are the elements of the left partite set and locations (A through G) are the elements of the right partite set. The edges are labeled with time. When two people are co-located, they form a person-person edge in a social network such as that in Fig. 3. Since these interactions give rise to the same person-person edges as in Fig. 3, and the same SIR model vertex functions are used, this network produces the same forward trajectory as that in in Fig. 3.

Figure 5:

Synthetic individuals (bottom) in a baseline synthetic population (top left) have associated demographics and are located in a specific geographic context (e.g., city, state, country). They are assigned activities to be performed at specific locations and times of day, creating a people-location network (top right). As described in Sects. 4.1.2 and 4.1.3, a person-to-person contact network (top middle) can be constructed from the people-location graph. The person-to-person network is conceptually the same as that in Fig. 3, while the people-location graph is conceptually the same as that in Fig. 4.

Figure 6:

A sequence of all possible potential edges. Each circle represents a potential edge. The white circles are the skipped edges, and the solid black circles are the selected edges in an Erdös–Rényi graph.

Figure 7:

A preferential attachment network with 5 nodes generated using the copy model. Solid lines show final decided edges, and dashed lines denote waiting of processors for node attachment to be resolved—the undecided edges. For node $t=3$, k is chosen to be 2, $F_3$ is chosen to be $k=2$, and thus edge (3, 1) is decided immediately. Similarly, edge (1, 0) is also decided immediately. For node $t=4$, k is 2 and $F_4$ is set to be $F_2$. That is, $F_4$ is dependent on $F_2$. Similarly, $F_2$ is dependent on $F_1$. Finally, we have $F_4=F_2=F_1=0$.

Figure 8:

PTTS for the H5N1 disease model. Ovals represent disease states, while lines represent the transition between states, labeled with the transition probabilities. The line type represents the treatment applied to an individual. The states contain a label and the dwell time within the state, and the infectivity if different from one.

Figure 9:

An example social contact network: (a) the bipartite graph representation showing people visiting locations; (b) the temporal and spatial projection of the network; (c) the person-person graph showing interactions between temporally and spatially co-located people; (d) potential disease transmission between an infectious person 2, and susceptible people 1 and 3.

Figure 10:

The computational structure of the sequential EpiSimdemics algorithm.

Figure 11:

These plots show the performance of EpiSimdemics when run on NCSA’s Blue Waters system using up to 352,000 cores. The spread of Influenza through the population of the United States (on the order of 300 million people) is being simulated for 120 days, with no interventions, in 12 seconds.