Oxford Mathematician explains SIR disease model for COVID-19 (Coronavirus)

The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population. I first explain where the model comes from, including the assumptions that are made and how the equations are derived, before going on to use the results of the model to answer three important questions:

Will the disease spread?

What is the maximum number of people that will have the disease at one time?

How many people will catch the disease in total?

The answers to these questions are discussed in the context of the current COVID-19 (Coronavirus) outbreak. The model tells us that to reduce the impact of the disease we need to lower the ‘contact ratio’ as much as possible – which is exactly what the current social distancing measures are designed to do.

Produced by Dr Tom Crawford at the University of Oxford.

How is s determined for a Novel disease ? Is s anyone who hasn’t been vaccinated and hasn’t had the disease , or does the person have to have antibodies to be included in s ? What happens if some of the I are Not immune and go back into s , rather than going to r ?

S is anyone that is susceptible to a particular disease. So people that are vaccinated (if a vaccine exists) would be excluded, as would anyone that has had the disease before and has antibodies that prevent them from catching it again etc. You make a valid point about people potentially not being immune after having the disease and recovering, and they could certainly go back to the susceptible category. However, in this basic model I’ve explained we purposefully choose not to include this possibility. In the real-world models being used by scientists around the world, this would be included.

N = 1000 # Total Population in an particular Area of a country
I_0 = 5 # Initial Infectives (misclassified as COVID negative)
S_0 = N – I_0 = 995 # Initial Susceptible
R_0 = 1.51 # COVID19 Reproduction number of the country on April 10

Now, according to your explanation, can I claim that: ‘If I_0 = 5 people were misclassified as COVID negative during RTPCR test & they moved freely; then there’s a possibility that those 5 person can infect maximum of 69~70 people” ??

Actually, I was writing for an article. Can I use this & is my claim valid?

Be careful – the numbers for I_0 and S_0 need to be given as proportions of the total population, so I_0 = 5/1000 and S_0 = 995/1000. This will change your value for q.

[…] Watch the first video on the basic SIR model here. […]

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How is s determined for a Novel disease ? Is s anyone who hasn’t been vaccinated and hasn’t had the disease , or does the person have to have antibodies to be included in s ? What happens if some of the I are Not immune and go back into s , rather than going to r ?

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S is anyone that is susceptible to a particular disease. So people that are vaccinated (if a vaccine exists) would be excluded, as would anyone that has had the disease before and has antibodies that prevent them from catching it again etc. You make a valid point about people potentially not being immune after having the disease and recovering, and they could certainly go back to the susceptible category. However, in this basic model I’ve explained we purposefully choose not to include this possibility. In the real-world models being used by scientists around the world, this would be included.

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[…] Watch Tom explain the ‘SIR Model for Disease Spread’ here. […]

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Hey, Dr. Tom, I loved your video. Do you think if I could get the pdf of the SIR model in the way you explained. Please let me know.

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Thanks Sruthi – I don’t have a pdf I’m afraid, but the model is described in the textbook ‘Mathematical Biology’ by JD Murray.

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N = 1000 # Total Population in an particular Area of a country

I_0 = 5 # Initial Infectives (misclassified as COVID negative)

S_0 = N – I_0 = 995 # Initial Susceptible

R_0 = 1.51 # COVID19 Reproduction number of the country on April 10

q = R_0/S_0 = 0.001518

I_max = I_0 + S_0 – (1/q)*(1+ln(q*S_0)) = 69.58 ~ 70

Now, according to your explanation, can I claim that: ‘If I_0 = 5 people were misclassified as COVID negative during RTPCR test & they moved freely; then there’s a possibility that those 5 person can infect maximum of 69~70 people” ??

Actually, I was writing for an article. Can I use this & is my claim valid?

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Be careful – the numbers for I_0 and S_0 need to be given as proportions of the total population, so I_0 = 5/1000 and S_0 = 995/1000. This will change your value for q.

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