Question

1. (Ellner and Guckenheimer) An isolated village experiences an outbreak of influenza in which 812 of the 1100 residents contract the infection. Estimate Ro assuming that the outbreak started with a single case contracted from outside the village, with all others susceptible at the start of the outbreak 2. (Ellner and Guckenheimer) Starting with a constant population SIR model with births, suppose that newborns are vaccinated, with the result that a fraction p 〈 l of the newborns are born as removed (or recovered) rather than susceptible. a) Write down the resulting system of differential equations. Your population size should stil be constant, and when p 0 your equations should reduce to the original SIR model with births. b) Show that as p is increased from 0, the number of infectives at the endemic steady state decreases until it eventually hits 1 = 0 at some value pく1 (find this value). This is sometimes called herd immunity: even though some individuals have not been immunized by vaccination, the disease cannot sustain itself in the population as a whole.

Answer 1

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