1. Nik Addleman and Jen Fox

2.   Susceptible, Infected and Recovered S' = - ßSI I' = ßSI - γ I R' = γ I  Assumptions  S and I contact leads to infection  Infection is a disease, allows for recovery (or death…)  Fixed population Traditional SIR Model

3.  S' = - ßSI = 0 I' = ßSI – γ I = 0 R' = γ I = 0 Jacobian Analysis Equilibrium points: I = S = 0, R = R*

4.   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

5.   Vaccinations  Vaccinated members of susceptible pop. are not as likely to contract disease  Temporary infective/immunity periods Extensions

6.   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

7.   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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9.   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

10.  Susceptible

11.  Infectious … etc

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15.   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