Modern Applications of the SIR Epidemic Model
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Transcript of Modern Applications of the SIR Epidemic Model
Nik Addleman and Jen FoxNik Addleman and Jen Fox
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
S' = - ßSI = 0
I' = ßSI – γI = 0R' = γI = 0
Jacobian Analysis
Equilibrium points: I = S = 0, R = R*
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
Vaccinations
Vaccinated members of susceptible pop.are not as likely to contract disease
Temporary infective/immunity periods
Extensions
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
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
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
Susceptible
Infectious
… etc
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