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# ws26 - Math 464 Worksheet 26 In this worksheet will will...

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Math 464, Worksheet 26 In this worksheet will will add vaccination to the SIR model. As before, population of size N is divided into three groups: S (susceptible), R (recovered/resistant), and I (infectious). Assumptions are that Total population is constant. Infection rate is βI/N per person per time step. Recovery rate is γ per person per time step. Birth and death rates are b per person per time step. All newborns are susceptible. Everyone is in exactly one group. From the susceptible group, there are v vaccinations per person per time step. Schematically, it looks like this: b S b βI/N b b v I b γ R b Part I 1. Develop a model. Write your model as a system of difference equations. Eliminate R using that fact that total population is a constant. NOTE: If you prefer numerical constants over symbolic parameters, you can use the numbers from prior SIR models: b = 0 . 02 , β = 0 . 24 , γ = 0 . 1 , and N = 100 However you have to keep v as a symbolic parameter.

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