Modeling Ebola Outbreak

Ebola spreading with time

Ebola spreading with time

The spread of infection causes exponentially more damage if it’s not contained and treated in a timely and isolative manner. Recent outbreak of Ebola is on the worst in history, which has topped at 30,000 cases by this point. To aid in fighting the current outbreak and any other infectious decease, we have developed a three models which act like a toolbox for fighting the infection and predicting its behavior. In our first model, we model the spread of infection using SEID model of ODEs. We used Markov Chains to identify the most infectious regions of Ebola outbreak, which should be treated first and isolated the most. A measure to prevent an outbreak of any infection from growing is to detect it early and respond to it as fast as possible with containment, treatment and isolation. Those goals are achievable much easier if the most infectious regions are identified and the behavior of the system could be modeled with a decently accurate prediction.

Team: me, Derek Driggs (Applied math BS/MS),  Ian Char (Applied Math, Computer Science)

In summary:

  1. We used a simple SEIR model for each region knowing region’s population size and infected population number from news.
    SEIR ODE model

    SEIR ODE model

     

  2. We made a model that analyzes regions of Africa as a closed network with migration between regions. Using such model, we were able to identify the most infectious regions of Africa (the ones that are most important to treat in order to contain the outbreak) using Markov Random Walk algorithm.

    The darker the color the most "infectious" is the region.

    The darker the color the most “infectious” is the region.

  3. Combining SEIR model with migration for each region and closed network model, we were able to estimate how the outbreak is going to behave with a specific number of medication given to certain regions.
    "Infectiousness" rank changed after a certain time period.

    “Infectiousness” rank changed after a certain time period.

    Number of infected people within each region grows according to the SEIR model with migration.

    The number of infected people within each region grows according to the SEIR model with migration.

Read more in our paper: EbolaModeling.pdf