CSE 6240: Web Search and Text Mining. Spring 2020 Contagion and COVID-19 Prof. Srijan Kumar http://cc.gatech.edu/~srijan 1 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
R 0 : Reproduction Number • Number of other people that a diseased person will infect, in her lifetime Reference: https://triplebyte.com/blog/modeling-infectious-diseases 2 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
How to Model COVID-19 Spread? • Estimate the R 0 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 3 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
Findings • The median with 95% Confidence Interval of R 0 of COVID-19 was about 2.28 (2.06-2.52) during the early stage experienced on the Diamond Princess cruise ship. 4 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
More Research, New Results • Method: Study of virus spread in China. Fit the SEIR model. • Finding: median R 0 value of 5.7 (95% CI 3.8– 8.9). 5 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
COVID-19 vs Others Reference: https://triplebyte.com/blog/modeling-infectious-diseases 6 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
Importance • Estimating the number of cases and casualties • Policy development, e.g., stay-at-home orders • Measuring the effect of interventions 7 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
Modeling COVID-19 Spread • Which model should we use? • SIR • SIS • Next few slides: recap of SIR and SIS models 8 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
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 of which will be infected. • Subsequent waves : same process 9 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
Example with k=3 10 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
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 Healthy Prob. δ N 2 Prob. β N 1 N Infected N 3 11 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
SIR Model • SIR model: Node goes through phases 𝜀 𝛾 S usceptible I nfected R ecovered – Models chickenpox or plague: • Once you heal, you can never get infected again • Assuming perfect mixing: The network is a complete graph S(t) • The model dynamics are: R(t) dS Number of nodes dR dt = − β SI dt = δ I I(t) dI dt = β SI − δ I time 12 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
SIS Model • Susceptible-Infective-Susceptible (SIS) model • Cured nodes immediately become susceptible • Virus “strength”: 𝒕 = 𝜸 / 𝜺 • Node state transition diagram: Infected by neighbor with prob. β Susceptible Infective Cured with prob. δ 13 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
SIS Model • Models flu: – Susceptible node I(t) becomes infected – The node then Number of nodes heals and become susceptible again • Assuming perfect mixing (a S(t) complete graph): dS = - b + d SI I dt time dI S usceptible I nfected = b - d SI I dt 14 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
Modeling COVID-19 Spread • Which model should we use? – SIR – SIS • Answer: SIS 15 Srijan Kumar, Georgia Tech, CSE6240 Spring 2020: Web Search and Text Mining
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