The pulse vaccination strategy 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
d S d t = μ N − μ S − β I N S , S ( n T + ) = ( 1 − p ) S ( n T − ) n = 0 , 1 , 2 , … {\displaystyle {\frac {dS}{dt}}=\mu N-\mu S-\beta {\frac {I}{N}}S,S(nT^{+})=(1-p)S(nT^{-})n=0,1,2,\dots }
d V d t = − μ V , V ( n T + ) = V ( n T − ) + p S ( n T − ) n = 0 , 1 , 2 , … {\displaystyle {\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 − p 1 − ( 1 − p ) E − μ T E − μ M O D ( t , T ) {\displaystyle S^{*}(t)=1-{\frac {p}{1-(1-p)E^{-\mu T}}}E^{-\mu MOD(t,T)}}
and that the eradication condition is:
R 0 ∫ 0 T S ∗ ( t ) d t < 1 {\displaystyle R_{0}\int _{0}^{T}{S^{*}(t)dt}<1}
See also Critical community size Epidemic model Herd immunity Pulse Polio Ring vaccination Vaccine-naive
References
External links
Immunisation Immunisation schedule for children in the UK. Published by the UK Department of Health. CDC.gov - 'National Immunization Program: leading the way to healthy lives', US Centers for Disease Control (CDC information on vaccinations) CDC.gov - Vaccines timeline History of Vaccines Medical education site from the College of Physicians of Philadelphia, the oldest medical professional society in the US Images of vaccine-preventable diseases