Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 1

CSE 6240: Web Search and Text Mining. Spring 2020

Contagion and COVID-19

Prof. Srijan Kumarhttp://cc.gatech.edu/~srijan

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 2

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 3

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 4

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 5

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 6

COVID-19 vs Others

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

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 7

Importance• Estimating the number of cases and

casualties• Policy development, e.g., stay-at-home

orders• Measuring the effect of interventions

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 8

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 9

Simple model: Branching Process• First wave: A person carrying a disease

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

• Second wave: Each of the 𝑑 people goes and meets 𝑑 different people. So we have a second wave of 𝑑 ∗ 𝑑 = 𝑑% people, a portion of which will be infected.

• Subsequent waves: same process

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 10

Example with k=3

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 11

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

NN1

N3

N2Prob. β

Prob. δ

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 12

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

Num

ber o

f nod

esdIdt= βSI −δI

dSdt

= −βSI dRdt

= δI I(t)

S(t) R(t)

𝛽 𝛿

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 13

SIS Model

• Susceptible-Infective-Susceptible (SIS) model

• Cured nodes immediately become susceptible• Virus “strength”: 𝒔 = 𝜷/𝜹• 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 InfectedISI

dtdI db -=

ISIdtdS db +-=

time

Num

ber o

f nod

es

14

I(t)

S(t)

Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining 15

Modeling COVID-19 Spread• Which model should we use?

– SIR– SIS

• Answer: SIS