Contagion and COVID-19 Prof. Srijan Kumar - - PowerPoint PPT Presentation

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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CSE 6240: Web Search and Text Mining. Spring 2020

Contagion and COVID-19

• Prof. Srijan Kumar

http://cc.gatech.edu/~srijan

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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R0: Reproduction Number

• Number of other people that a diseased

person will infect, in her lifetime

Reference: https://triplebyte.com/blog/modeling-infectious-diseases

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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How to Model COVID-19 Spread?

• Estimate the R0 from real data
• Case Study: Diamond Princess cruise ship
• Note that a lot is ongoing research and the

findings may change as new evidence emerges

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Findings

• The median with 95% Confidence Interval of

R0 of COVID-19 was about 2.28 (2.06-2.52) during the early stage experienced on the Diamond Princess cruise ship.

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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More Research, New Results

• Method: Study of virus spread in China. Fit

the SEIR model.

• Finding: median R0 value of 5.7 (95% CI 3.8–

8.9).

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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COVID-19 vs Others

Reference: https://triplebyte.com/blog/modeling-infectious-diseases

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Importance

• Estimating the number of cases and

casualties

• Policy development, e.g., stay-at-home
• rders
• Measuring the effect of interventions

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Modeling COVID-19 Spread

• Which model should we use?
• SIR
• SIS
• Next few slides: recap of SIR and SIS

models

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Simple model: Branching Process

• First wave: A person carrying a disease

enters the population and transmits to all she meets with probability 𝑟. She meets 𝑒 people, a portion of which will be infected.

• Second wave: Each of the 𝑒 people goes

and meets 𝑒 different people. So we have a second wave of 𝑒 ∗ 𝑒 = 𝑒% people, a portion

• f which will be infected.
• Subsequent waves: same process

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Example with k=3

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Spreading Models of Viruses

Virus Propagation: 2 Parameters:

• (Virus) Birth rate β:

– probability that an infected neighbor attacks

• (Virus) Death rate δ:

– Probability that an infected node heals

Infected Healthy N N1 N3 N2

• Prob. β
• Prob. δ

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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SIR Model

• SIR model: Node goes through phases

– Models chickenpox or plague:

• Once you heal, you can never get infected again
• Assuming perfect mixing: The network is a

complete graph

• The model dynamics are:

Susceptible Infected Recovered time Number of nodes

dI dt = βSI −δI dS dt = −βSI dR dt =δI

I(t) S(t) R(t) 𝛾 𝜀

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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SIS Model

• Susceptible-Infective-Susceptible (SIS)

model

• Cured nodes immediately become susceptible
• Virus “strength”: 𝒕 = 𝜸 / 𝜺
• Node state transition diagram:

Susceptible Infective

Infected by neighbor with prob. β Cured with

• prob. δ

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

SIS Model

• Models flu:

– Susceptible node

becomes infected

– The node then

heals and become susceptible again

• Assuming perfect

mixing (a complete graph):

Susceptible Infected

I SI dt dI d b

• =

I SI dt dS d b +

• =

time Number of nodes

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I(t) S(t)

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining

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Modeling COVID-19 Spread

• Which model should we use?

– SIR – SIS

• Answer: SIS