Modern Applications of the SIR Epidemic Model

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Nik Addleman and Jen Fox Nik Addleman and Jen Fox

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Modern Applications of the SIR Epidemic Model. Nik Addleman and Jen Fox. Traditional SIR Model. Susceptible, Infected and Recovered S' = - ßSI I' = ßSI - γI R' = γI Assumptions S and I contact leads to infection Infection is a disease, allows for recovery (or death…) - PowerPoint PPT Presentation

Transcript of Modern Applications of the SIR Epidemic Model

Page 1: Modern Applications of the SIR Epidemic Model

Nik Addleman and Jen FoxNik Addleman and Jen Fox

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Susceptible, Infected and Recovered

S' = - ßSII' = ßSI - γI R' = γI

Assumptions S and I contact leads to infection Infection is a disease, allows for recovery (or

death…) Fixed population

Traditional SIR Model

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S' = - ßSI = 0

I' = ßSI – γI = 0R' = γI = 0

Jacobian Analysis

Equilibrium points: I = S = 0, R = R*

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Infectious contact

rate β = # daily contacts

* transmission probability given a contact

Infectious Period γ= time until

recovered and no longer infectious

Example of SIR Model

S

t

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Vaccinations

Vaccinated members of susceptible pop.are not as likely to contract disease

Temporary infective/immunity periods

Extensions

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Modeling Seasonal Influenza Outbreak in a

Closed College Campus. (K. L. Nichol et al.)

Compartmentalized, fixed-population ODE model Modification of the SIR model Minimize Total Attack Rate

Experimentally determine parameters

Modeling Influenza

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Students and Faculty Vaccinated versus Unvaccinated Symptomatic and Asymptomatic infections

Different β and γ values for various populations Categories (following slide)

Four susceptible categories Eight infected One recovered

Compartments

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Determining parameters

β varies between students/faculty and symptomatic/asymptomatic

γ has different values for symptomatic/asymptomatic and vaccinated/unvaccinated populations

Vaccine 80% effective

Apply to all compartments

Constructing Equations

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Susceptible

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Infectious

… etc

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Can use SIR model to determine best way to

cut down on infections

Stay home when you are sick because you are infectious. Gross.

Get vaccinated! Even late vaccinations are effective Vaccine helps you and those around you 60% vaccination means none of us gets sick

Conclusions

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