SummaryBackgroundSince late 2015, an epidemic of yellow fever has caused more than 7334 suspected cases in Angola and the Democratic Republic of the Congo, including 393 deaths. We sought to understand the spatial spread of this outbreak to optimise the use of the limited available vaccine stock.MethodsWe jointly analysed datasets describing the epidemic of yellow fever, vector suitability, human demography, and mobility in central Africa to understand and predict the spread of yellow fever virus. We used a standard logistic model to infer the district-specific yellow fever virus infection risk during the course of the epidemic in the region.FindingsThe early spread of yellow fever virus was characterised by fast exponential growth (doubling time of 5–7 days) and fast spatial expansion (49 districts reported cases after only 3 months) from Luanda, the capital of Angola. Early invasion was positively correlated with high population density (Pearson's r 0·52, 95% CI 0·34–0·66). The further away locations were from Luanda, the later the date of invasion (Pearson's r 0·60, 95% CI 0·52–0·66). In a Cox model, we noted that districts with higher population densities also had higher risks of sustained transmission (the hazard ratio for cases ceasing was 0·74, 95% CI 0·13–0·92 per log-unit increase in the population size of a district). A model that captured human mobility and vector suitability successfully discriminated districts with high risk of invasion from others with a lower risk (area under the curve 0·94, 95% CI 0·92–0·97). If at the start of the epidemic, sufficient vaccines had been available to target 50 out of 313 districts in the area, our model would have correctly identified 27 (84%) of the 32 districts that were eventually affected.InterpretationOur findings show the contributions of ecological and demographic factors to the ongoing spread of the yellow fever outbreak and provide estimates of the areas that could be prioritised for vaccination, although other constraints such as vaccine supply and delivery need to be accounted for before such insights can be translated into policy.FundingWellcome Trust.

An individual's learning rule is completely uncoupled if it does not depend directly on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient (welfare-maximizing) pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: (i) the sum of payoffs over all agents, and (ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.

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Despite notable scientific and medical advances, broader political, socioeconomic and behavioural factors continue to undercut the response to the COVID-19 pandemic1,2. Here we convened, as part of this Delphi study, a diverse, multidisciplinary panel of 386 academic, health, non-governmental organization, government and other experts in COVID-19 response from 112 countries and territories to recommend specific actions to end this persistent global threat to public health. The panel developed a set of 41 consensus statements and 57 recommendations to governments, health systems, industry and other key stakeholders across six domains: communication; health systems; vaccination; prevention; treatment and care; and inequities. In the wake of nearly three years of fragmented global and national responses, it is instructive to note that three of the highest-ranked recommendations call for the adoption of whole-of-society and whole-of-government approaches1, while maintaining proven prevention measures using a vaccines-plus approach2 that employs a range of public health and financial support measures to complement vaccination. Other recommendations with at least 99% combined agreement advise governments and other stakeholders to improve communication, rebuild public trust and engage communities3 in the management of pandemic responses. The findings of the study, which have been further endorsed by 184 organizations globally, include points of unanimous agreement, as well as six recommendations with >5% disagreement, that provide health and social policy actions to address inadequacies in the pandemic response and help to bring this public health threat to an end.