Nik Addleman and Jen Fox

  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

 S' = - ßSI = 0 I' = ßSI – γ I = 0 R' = γ I = 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