Download Ebola

Network modeling of the Ebola
Outbreak
Ahmet Aksoy
Outline

History and Introduction

Symptoms

Transmission and Prevention

Epidemic model

Types of Epidemic models

Deterministic models

Previous works

Our contribution
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
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
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
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
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
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.
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.
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:
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.
Examples of how simple models can be
useful and informative
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


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

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

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
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.
Thank you!

Questions ?