Optimal but unequitable prophylactic distribution of vaccine.
The final epidemic size (R(∞)) remains one of the fundamental outcomes of an epidemic, and measures the total number of individuals infected during a "free-fall" epidemic when no additional control action is taken. As such, it provides an idealised measure for optimising control policies before an epidemic arises. Although the generality of formulae for calculating the final epidemic size have been discussed previously, we offer an alternative probabilistic argument and then use this formula to consider the optimal deployment of vaccine in spatially segregated populations that minimises the total number of cases. We show that for a limited stockpile of vaccine, the optimal policy is often to immunise one population to the exclusion of others. However, as greater realism is included, this extreme and arguably unethical policy, is replaced by an optimal strategy where vaccine supply is more evenly spatially distributed.
Mathematics Institute & School of Life Sciences, University of Warwick, Coventry, United Kingdom. M.J.Keeling@warwick.ac.uk
Matt J
MJ
Keeling
Andrew
A
Shattock
D018890:Chemoprevention / Q000706:statistics & numerical data*; D058872:Epidemics / Q000517:prevention & control*; D015276:Health Care Rationing / Q000706:statistics & numerical data*; D006297:Health Services Accessibility / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D011336:Probability; D014611:Vaccination / Q000706:statistics & numerical data*; D014612:Vaccines
D014612:Vaccines