title: Modeling the Spread of Ebola.
abstract: OBJECTIVE
  This study aims to create a mathematical model to better understand the spread of Ebola, the mathematical dynamics of the disease, and preventative behaviors.
  
  
  METHODS
  An epidemiological model is created with a system of nonlinear differential equations, and the model examines the disease transmission dynamics with isolation through stability analysis. All parameters are approximated, and results are also exploited by simulations. Sensitivity analysis is used to discuss the effect of intervention strategies.
  
  
  RESULTS
  The system has only one equilibrium point, which is the disease-free state (S,L,I,R,D) = (N,0,0,0,0). If traditional burials of Ebola victims are allowed, the possible end state is never stable. Provided that safe burial practices with no traditional rituals are followed, the endemic-free state is stable if the basic reproductive number, R 0, is less than 1. Model behaviors correspond to empirical facts. The model simulation agrees with the data of the Nigeria outbreak in 2004: 12 recoveries, eight deaths, Ebola free in about 3 months, and an R 0 value of about 2.6 initially, which signifies swift spread of the infection. The best way to reduce R 0 is achieving the speedy net effect of intervention strategies. One day's delay in full compliance with building rings around the virus with isolation, close observation, and clear education may double the number of infected cases.
  
  
  CONCLUSIONS
  The model can predict the total number of infected cases, number of deaths, and duration of outbreaks among others. The model can be used to better understand the spread of Ebola, educate about prophylactic behaviors, and develop strategies that alter environment to achieve a disease-free state. A future work is to incorporate vaccination in the model when the vaccines are developed and the effects of vaccines are known better.
authors.affiliation: Department of Mathematics Education, Catholic Kwandong University, Kangleung, Korea.
authors.forename: Tae Sug
authors.initials: TS
authors.lastname: Do
authors.affiliation: Department of Mathematics and Computer Science, Manchester University, North Manchester, IN, USA.
authors.forename: Young S
authors.initials: YS
authors.lastname: Lee
keywords: Ebola; Nigeria; basic reproductive number; epidemiological model; stability analysis