From united nations- world health organization website https roberts

Modelling Ebola
with the SIR Model

1 Modelling Ebola with the SIR Model

When I was younger, my mother would come home detailing the mathematical concepts behind her current projects at the CDC (Center for Disease Control). But as a child I did not realize the concepts, let alone math behind her explanations. It was not until my highschool biology classes where I started to understand
epidemiology- the study of diseases- and the importance of the mathematical models my mom analyzes and creates. My biological interest in the field rose along with my understanding of calculus, until I finally found a fascination with such graphs and charts displaying the progression of diseases globally.

Specifically, I began to study the SIR Model which I will focus on in this investigation to show the behavior of disease and how to avoid infection.

Rt = the population of those who have recovered
from the illness meaning they cannot spread
or contract it once again. This includes those
who are deceased

Because the SIR Model only accounts for a proportion of the entire population as it only models a closed system (a constant population), only a fraction of those susceptible to infection can be modelled. This will be denoted by ​P ​and in relation to the set of variables above are as follows:

rt = P Rt Part of the population who is recovered

or removed from the disease

These assumptions together lessen the external probabilities of the unpredictable factors pertaining to the spread of disease.

3. The Math Behind the Model

The susceptible population with regards to time is:
st+1 = st − β t t

Therefore the derivation of the differential equation for the susceptible class is:
st+1 − st = st − β t t − st

3. Deriving the Differential Equation for the Recovered/ Removed Class The recovered/ removed population is the last category of the SIR model and accounts for those who have fully recovered from the disease in addition to those who have died from the disease. But both groups have no possibility of spreading or contracting the disease. Therefore this class has two components: those who are already in the population and those who are newly recovered as they have just passed the infection stage. The
recovered/ removed population with regards to time is:
rt+1 = rt + Φ t

And the respective differential equations are:

population as the net population seen here is zero meaning no person in the community enters or exits.

4. Modelling SIR with an Ebola in Guinea

=​ N ​= 12,000,000 people S0

There no are people initially infected because the disease is introduced: I0 =0 people

Therefore the Ebola virus in Guinea is modeled by the equations:

derived differential equations. From these equations, a graph modelling the Ebola virus through SIR was developed as seen in Figure 1 from data in the appendix.

see how the susceptible population is decreasing while the infected population increases

showing more people are becoming exposed to the virus and the spread of the virus is

In all, I gained a greater appreciation for the concepts highlighted in my exploration and applying math to real life situations such as the spread of disease. I also learned how to calculate and quantify gathered data and interpret critical points on graphs displaying

10 such data. Modeling SIR for diseases such as the present Coronavirus and Influenza will definitely help in efforts to eradicate.

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7. Appendix 2: Raw Data for SIR Model of Ebola