Figure 4.
Results of spatially targeting vaccination in a deterministic metapopulation models of the 408 districts of Great Britain, linked by commuter movements from the 2001 census. Five simple alternatives for targeting unvaccinated individuals are considered, either randomly (shown as ‘1’ and white), or proportional to the proportion of susceptible (‘S’ and green), infected (‘I’ and red), recovered (‘R’ and grey) or vaccinated individuals (which is never optimal) in the district. For each parameter combination (of which 1926 are shown), 100 replicates were performed; for each replicate the transmission rate within each district and the distribution of cases is chosen randomly (within the prescribed values) and simulations were performed with all five alternative strategies. The letter (and colour) in each square corresponds to the strategy that generates the minimum number of cases the majority of times in the 100 replicates; letters in bold (with bold boxes) correspond to simple strategies that significantly outperform vaccination based on the proportion of infected. Rows correspond to different levels of heterogeneity in transmission, H = 0, 0.1, 0.2, 0.4; columns correspond to when the vaccination campaign starts, defined in terms of the number of recovered individuals, (a) early vaccination (begun when R = 100, 100 recovered cases nationally), (b) vaccination begins when R = 0.1N, and (c) vaccination starts late (begun when R = 0.2N). (R0 = 1.4, 1/γ = 4 days, βd = R0γ exp(Hξd); where ξd is a random variable, normally distributed with mean 0 and a variance of 1.)