Model Case Studies About

A Multi-Region SEIR Model with Mobility

Epidemiological models, such as the susceptible exposed infectious recovered (SEIR) model, are essential to understand how infectious diseases spread throughout a population. While impacts of travel are indirectly accounted for within the parameters that describe the overall disease transmission rate, commonly used (single-region) models do not explicitly model mobility at a local scale when considering the disease dynamics. As a consequence, mobility-restricting policies can only be coarsely understood by changing parameters that control the overall transmission rate. Meta-population (or multi-group) SEIR models provide a framework for explicitly modeling the spatial dynamics of the disease spread. This project aims to build a general tool for modeling complex human mobility patterns at local scale and simulate the corresponsing disease dynamics.

Potential Impact

Meta-population compartmental models explicitly account for local-scale mobility patterns and can help support the design of more effective disease containment, mitigation, and recovery strategies. This is especially important for the goal of minimizing travel disruptions and reactivating the economy. It can help answer questions like:

  • Which neighborhoods are most likely to accelerate disease propagation throughout the network?
  • Which travel patterns are most likely to become disease vectors?
  • What combination of social-distancing and travel restriction measures are needed to safely reactivate a region?
  • Where should preventive screening be administered to minimize contagion throughout the network?

  • Simulation Tool (click here for visualization)

    Our goal is to develop simulation tool that can be used to assess the impacts of different social distancing levels and travel restrictions at the state, county and census tract levels across the United States. The tool will utilize publicly available datasets to provide baseline scenarios and allow users to modify these scenarios to reflect specific control measures. The case studies page will list some examples that we hope to put together in collaboration with local public health experts.

    Figure 1 - Preview of the simulation tool.

    Model Overview

    One key parameter in compartment models is the basic reproduction number, denoted Ro, which is the expected number of new infections caused by a single individual. This parameter is not a constant for each individual in the population. Rather, it is a function of both the contagiousness of the disease and the network structure characterizing the affected population [1]. Intuitively, an epidemic is on track to be suppressed if Ro < 1.

    Formally, Ro = β/γ, where β is the expected rate of new infections caused by an infected individual and γ is the rate of disease recovery. In practice, R0 can be controlled through β by, for example, imposing social-distancing measures. Recent research on COVID-19 suggest Ro may range between 5.7 in an uncontrolled epidemic and 1.4 just a few weeks after a population starts practicing social-distancing [2]. However, these numbers reflect the effects of such measures at a very coarse level.

    In particular, the experiences with COVID-19 suggest a strong link between local-scale mobility patterns and disease propagation. Consider the setting depicted in Figure 1. In this motivating example, there are three regions A, B, and C. In the morning, commuters living in A and C travel to their workplace in B. They return home in the afternoon. Therefore, the effective daytime population at B is the population of B plus the commuter population from A and C.

    commuting patterns
    Figure 2 - Commuting patterns between regions A, B, and C.

    We argue that mobility patterns need to be explicitly modeled to better understand the implications of pandemic response measures. In our example, if region B were to lift social distancing measures while hosting commuters, disease would propagate to regions A and C even if these maintained social-distancing within their own jurisdictions. A fixed Ro for the entire network would fail to capture this heterogeneity because it would assume uniform contagion and response. In short, mobility patterns may induce unanticipated network effects that stem from localized decision-making.


    [1] David Easley and Jon Kleinberg. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, 2010.

    [2] S Sanche, YT Lin, C Xu, E Romero-Severson, N Hengartner, and R Ke. High contagiousness and rapid spread of severe acute respiratory syndrome coronavirus 2. Emerging Infectious Diseases, 26(7), 2020.