## The Spread of Epidemics and the GLEaM Model

As technology has advanced, so have systems of transportation. The movement of people is an important consideration in how a disease spreads. The GLEaM (Global Epidemic and Mobility) model was developed in response to mass population movement among geographic areas. It is considered a large-scale spatial meta-population model. This means the GLEaM model tracks changes in the movement of people among sub-populations. Here we will describe the features of the GLEaM model and discuss some of its developments.

The smallest unit that the GLEaM model tracks is the sub-culture, which is a subset of the population in a particular geographic area. Transportation and mobility data are used to simulate the movement of people into and out of these sub-cultures. For example, flight data can be used to simulate how people move between geographic areas and help researchers visually track how a disease spreads [Balcan].

The GLEaM model divides the population into three categories: susceptible, latent, and recovered. The susceptible group is the sub-population that is vulnerable to the epidemic. The latent group is the sub-population that is infected and is yet to recover. Since the GLEaM model analyzes spatial data, the latent sub-population is further divided into traveling and not traveling. The recovered group is the sub-population that has recovered from the epidemic or has passed away. The GLEaM model aids researchers in tracking changes in these sub-populations in order to simulate the spread of an epidemic [Balcan].

This model, as mentioned before, uses transportation and mobility data to simulate the movement of people into and out of these sub-cultures. The GLEaM model simulates the mobility of individuals from one sub-population to another by using real mobility data to define the number of people traveling from a sub-population ** j** to a sub-population

**as an integer random variable [Balcan].**

*k*There are two main steps that are performed to integrate this transportation and mobility data into the model. We describe these below.

- The first step is to define a new geographic resolution, which is simply dividing travel points and population grids into smaller components that can be tracked easily. This means we have to create a system where we can track travel points and see where the population is concentrated in a geographic location. Commuting patterns, such as flight or travel data, are used to connect the travel points on the geographic resolution [Balcan].
- The second step is to analyze the disease model. The rate
**λ**at which a susceptible individual in sub-population_{j}acquires the infection is determined by interactions with infectious persons either in the home sub-population*j*or in its neighboring sub-populations on the commuting network. If the infectious person is symptomatic, then the infection rate is given by*j***β**. If the infectious person is asymptomatic, the infection rate is reduced and given by**r**. After the end of the latency period_{β }β**ε**, each latent individual becomes infected. The probability of becoming asymptomatic infectious is given by^{-1}**p**and the probability of traveling is given by_{a,}**p**. So, an individual becomes symptomatic with probability (1 –_{t}**p**). These equations are used to see how the population flows through each category in the GLEaM model [Balcan]._{a}

Following these two steps, researchers can track how the disease spreads by following the population flow through each category, and through the travel points on the geographic resolution. They can differentiate the subsets of the population that are able and unable to travel. This analysis gives insight into how the disease affects a geographic location, thus helping policy makers decide the course of action to take to mitigate future negative effects of the epidemic [Balcan].

Graph theory from Networks class can be directly applied to this form of research. As mentioned before, the GLEaM model tracks movement from subcultures. So, in graph theory, nodes would represent the transportation hubs and the edges would represent the connections to the different hubs with flow on them with the number of people traveling. By using graph theory and flow theory, researchers can better gauge how an epidemic will spread in a given area over time. This is very beneficial in trying to prevent the spread of an epidemic or to see how an epidemic evolves over time.

http://www.sciencedirect.com/science/article/pii/S1877750310000438