1. Network modeling of the Ebola Outbreak Ahmet Aksoy

2. Outline History and Introduction Symptoms Transmission and Prevention Epidemic model Types of Epidemic models Deterministic models Previous works Our contribution

3. History and Introduction Initially recognized in 1976 in the Democratic Republic of Congo (formerly Zaire) Member of the RNA virus family called Filoviridae Four known types of Ebola:  Ebola-Zaire  Ebola-Sudan  Ebola-Ivory Coast  Ebola-Reston First three are extremely deadly in humans Ebola-Reston causes disease in nonhuman primates

4. History and Introduction The 2014 West African Ebola virus outbreak, now more correctly referred to as an epidemic, is the largest ever to occur. It has spread to four West African countries (Guinea, Liberia, Sierra Leone, and Nigeria) It has infected over 2000 individuals as of August 28 2014 It has a case-fatality rate greater than 50% 2nd Dallas nurse with Ebola has occurred

5. Symptoms Symptoms usually occur 2-21 days after infection Death rate of 50-90% Symptoms within a few days:  flu-like (fever, headache, muscle ache, diarrhea, fatigue)  also sore throat, hiccups, itchy eyes, rash, vomiting blood Symptoms within a week:  bleeding into internal organs and from body openings, chest pain, shock, death

6. Transmission and prevention Transmission  Direct contact with blood, organs or semen of an infected person  Burial ceremonies that include direct contact with the body of an infected person  Encounters with infected animals- chimpanzees, gorillas, antelope, etc  Health care workers are at increased risk Prevention  Containment  Strict barrier nursing techniques  Properly disinfected tools  Education

7. Epidemic model What is an Epidemic model? An epidemic model is a simplified means of describing the transmission of communicable disease through individuals. What is the use of Epidemic models? Allows for viewing of expected effects of outbreaks, without a human toll Allows for scientists to experiment with “treatment” procedures (i.e. how to quarantine, etc.) Faster and more accurate (if programmed correctly) than humans

8. Types of Epidemic models Stochastic  A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time. Deterministic  Deterministic model is a mathematical model in which outcomes are determined through known relationships among states and events, without any room for random variation.

9. Deterministic models - The SIR model It has 3 compartments;  S(t) is used to represent the number of individuals not yet infected with the disease at time t, or those susceptible to the disease.  I(t) denotes the number of individuals who have been infected with the disease and are capable of spreading the disease to those in the susceptible category.  R(t) is the compartment used for those individuals who have been infected and then removed from the disease, either due to immunization or due to death. Those in this category are not able to be infected again or to transmit the infection to others.

10. Deterministic models - The SIR model The flow of this model may be considered as follows; S → I → R Using a fixed population, N = S(t) + I(t) + R(t), following equations have been derived:

11. Deterministic models - The SIRS model This model is simply an extension of the SIR model as we will see from its construction. The flow of this model may be considered as follows; S → I → R → S The only difference is that it allows members of the recovered class to be free of infection and rejoin the susceptible class.

12. Examples of how simple models can be useful and informative

14. S, Number of susceptible individuals; E, number of exposed individuals; I, number of infectious cases in the community; H, number of hospitalized cases; F, number of cases who are dead but not yet buried; R, number of individuals removed from the chain of transmission

16. A very simple mathematical model (the Incidence Decay with Exponential Adjustment, or “IDEA”, model) is for epidemic processes since only limited data (e.g., cumulative incidence curves) are available

17. Best fit model (dark curve) (R0 = 1.78, d = 0.009) to observed cumulative incidence for West Africa by generation (gray bars) Figure: Overall Observed vs. Expected Cumulative Incidence

18. Graphs demonstrate good model fits (dark curves) to observed generation by generation cumulative incidence of infection in Guinea (top panel), Liberia (middle panel), and Sierra Leone (bottom panel). Figure: Country Specific Model Fits, Observed vs. Expected Cumulative Incidence

19. Our contribution To create a model for the most recent state of the outbreak To use an epidemic model based on the network rather than the mathematical functions.

20. Thank you! Questions ?