Cell & Systems Modeling Final Project
The 2014 2016 Western Africa Ebola epidemic marked the largest outbreak of the disease ever recorded. During this time, some 28 , 616 confirmed or suspected cases were reported across Sierra Leone, Guinea, and Liberia. Even with the intervention of concerted humanitarian aid and directed relief efforts, 11 , 310 people in total died as a result. 1 As a result the World Health Organization (WHO) named Ebola an emerging disease likely to induce a major epidemic in December 2015. 2
In order to learn what fundamental attributes drive the spread of disease, it is beneficial to create models that simulate reallife events. A common model of disease spread is the SEIR model. SEIR models work by categorizing members of some population as either S usceptible, E xposed, I nfected, or R emoved. By defining rates by which members transition between each of these categories and altering the parameters that affect these rates, we can observe how a population exposed to disease changes over time. One such parameter is the reproduction number, R 0 , t he average n umber of s econdary cases spawned by a primary case. In Ebola, this measure has been estimated to be two, meaning an infected individual will pass the disease to two others. 3 SEIR models are often described by ordinary differential equations (ODEs), and related work of this nature is discussed further below.
One drawback of standard ODEbased SEIR models is that they do not directly account for the stochastic nature by which infected members of a population can interact with each other. As infected individuals travel, they risk spreading disease among the rest of the population. While the disease progression for Ebola is relatively quick and dramatic, the initial symptoms are fairly benign, such as fever and fatigue. Thus it is conceivable that there exists a window whereby symptomatic individuals could still interact with others before becoming immobile. Another drawback with ODEbased SEIR models is that they do not account for spatial constraints that could impact disease spread. Chowell et. al. ( 2015 ) performed statistical analyses on data generated during the West African Ebola outbreak and found that disease spreads at a polynomial rate on a local level, but exponentially at a broader global scale. 4 This suggests that there could be some underlying phenomena related to the way populations are distributed in space that could affect disease transmission, and merits further investigation.
This work presents the design and implementation of a novel agentbased model of Ebola disease spread that aims to improve upon traditional SEIR models by incorporating stochasticity and spatial constraints that are motivated by reallife conditions. In our model, virtual Agents inhabit nodes of a connected grid and may move randomly to a neighboring node at each time step. By ascribing each Agent one of the SEIR conditions and allowing them to change state based on their interactions with other agents at a common node, we can connect emergent properties that arise in our model to realworld interactions. On the whole, we would like to determine how effectively our model can emulate the spread of Ebola.
In constructing a new model, there are a number of considerations we must make to evaluate its validity. First, we want to make sure that it correctly captures known behaviors. As an example, if we increase t he disease m odel’s reproduction number, R 0 , the m odel s hould p redict that p eople n ot only become infected at a quicker rate but are also removed much faster. Furthermore, we want to test the model’s robustness by observing its behavior as we vary input parameters, such as the probabilities that Agents move away from a node, or the times for which an Agent inhabits a given SEIR condition. This is important since a model that is too sensitive may have too small a parameter search space to yield biologically significant results and, conversely, a model that lacks sensitivity may never demonstrate meaningful behaviors.
Finally, we want to utilize our choice of model parameters to elucidate behaviors associated with constraining the movement of Agents as well as constraining the grid’s structure. These two constraints are the best means by which we attempt to transform our abstract model into a clearer picture of reality. Constraining infected Agent movement is analogous to the relative immobility of sick individuals, and constraints on the graph’s connectivity impose barriers to movement and add a layer of nonuniformity more representative of the real world. By comparing our model with and without these constraints, we can determine whether or not Agentbased models can uncover largescale behavior of disease spread.