# Pulse vaccination strategy

The pulse vaccination strategy is vaccinating a calculated proportion of an entire population in a single pulse. It is a method used to eradicate an epidemic by repeatedly vaccinating a group at risk, over a defined age range, until the spread of the pathogen has been stopped. It is most commonly used during measles and polio epidemics to quickly stop the spread and contain the outbreak.

## Mathematical model

Where T= time units is a constant fraction p of susceptible subjects vaccinated in a relatively short time. This yields the differential equations for the susceptible and vaccinated subjects as[citation needed]

${\frac {dS}{dt}}=\mu N-\mu S-\beta {\frac {I}{N}}S,S(nT^{+})=(1-p)S(nT^{-})n=0,1,2,\dots$ ${\frac {dV}{dt}}=-\mu V,V(nT^{+})=V(nT^{-})+pS(nT^{-})n=0,1,2,\dots$ Further, by setting I = 0, one obtains that the dynamics of the susceptible subjects is given by:

$S^{*}(t)=1-{\frac {p}{1-(1-p)E^{-\mu T}}}E^{-\mu MOD(t,T)}$ and that the eradication condition is:

$R_{0}\int _{0}^{T}{S^{*}(t)dt}<1$ 