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Modeling the Spread of Ebola in Liberia 2015-2015 Using Differential Equations

Undergraduate #254
Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics

Chad Sadler - Virginia State University
Co-Author(s): Jasmine Jackson, Virginia State University, Petersburg, VA



Ebola Hemorrhagic Fever, currently known as Ebola Virus Disease (EVD) is an extremely infectious disease and can be fatal to humans. The disease spreads through direct contact with an infected person or their bodily fluids (breaking of the skin, mucus, fluids, and contaminated objects, such as syringes). Once infected with the disease, individuals go through an incubation stage where there are no symptoms and they are not considered infectious. After the incubation stage, the infected will develop symptoms such as a fever, flu-like symptoms, severe headaches, fatigue, muscle pains, vomiting, diarrhea and bleeding of the stomach. Ebola has a high risk of death and kills an average of 45% of those who become infected. Ebola first appeared in 1976 in two simultaneous outbreaks, in The Democratic Republic of Congo, and Sudan. Currently, West Africa is experiencing the largest outbreak since 1976. The virus originated from Sierra Leone and Liberia. In this paper, we will focus on the spread of the virus in Liberia. By using differential equations and the SEIHFR disease transmission model, it is possible to model the spread of Ebola given the proper data.

Through data mining, research, and finding the least squares fit of our differential equation model we were able to find key parameters for our model and effectively model the 2014-2015 Ebola epidemic in Liberia. We then conducted a multivariate sensitivity analysis to determine the importance of key parameters. We found that the time between the start of the outbreak to human intervention, as well as the time it takes for intervention measures to become completely efficient are the two most important parameters when it comes to controlling the size of an epidemic. That is not to say that other parameters are not important, however. In the paper we will discuss how each of the parameters interact and how that is very important to controlling the epidemic. While Ebola is a highly infectious and deadly disease, it is possible to save as many lives as possible through quick intervention and proper handling of infected individuals. Through careful research, we determined that while the most important parameters in terms of lowering the size of the epidemic were the time to intervention, and the time it takes for intervention measures to become completely efficient. By controlling all parameters simultaneously and effectively it is possible to bring the epidemic to an end as quickly as possible, saving thousands of lives. This can be achieved in a number of ways such as spreading knowledge about the disease, proper barrier nursing techniques, safe burial ceremonies, quarantining individuals suspected to be infected and many other techniques. In the paper we will discuss how we came to these conclusions and the tools that we used.

Funder Acknowledgement(s): NSF: HBCU-UP Program

Faculty Advisor: Zhifu Xie,

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This material is based upon work supported by the National Science Foundation (NSF) under Grant No. DUE-1930047. Any opinions, findings, interpretations, conclusions or recommendations expressed in this material are those of its authors and do not represent the views of the AAAS Board of Directors, the Council of AAAS, AAAS’ membership or the National Science Foundation.

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