Keeling Matt J, Ross J V
WIDER Centre, University of Warwick, UK; Mathematics Institute, University of Warwick, UK; School of Life Sciences, University of Warwick, UK.
School of Mathematical Sciences, University of Adelaide, Australia.
Epidemics. 2015 Jun;11:7-13. doi: 10.1016/j.epidem.2015.01.002. Epub 2015 Jan 24.
One of the fundamental problems in public health is how to allocate a limited set of resources to have the greatest benefit on the health of the population. This often leads to difficult value judgements about budget allocations. However, one scenario that is directly amenable to mathematical analysis is the optimal allocation of a finite stockpile of vaccine when the population is partitioned into many relatively small cliques, often conceptualised as households. For the case of SIR (susceptible-infectious-recovered) dynamics, analysis and numerics have supported the conjecture that an equalising strategy (which leaves equal numbers of susceptible individuals in each household) is optimal under certain conditions. However, there exists evidence that some of these conditions may be invalid or unsuitable in many situations. Here we consider how well the equalising strategy performs in a range of other scenarios that deviate from the idealised household model. We find that in general the equalising strategy often performs optimally, even far from the idealised case. However, when considering large subpopulation sizes, frequency-dependent transmission and intermediate levels of vaccination, optimality is often achieved through more heterogeneous vaccination strategies.
公共卫生领域的一个基本问题是如何分配有限的资源，以便对人群健康产生最大益处。这常常导致在预算分配方面做出艰难的价值判断。然而，一种直接适用于数学分析的情形是，当人群被划分为许多相对较小的群体（通常被概念化为家庭）时，对有限疫苗储备进行最优分配。对于易感-感染-康复（SIR）动力学的情况，分析和数值计算支持了这样的推测：在某些条件下，一种均衡策略（即在每个家庭中留下相等数量的易感个体）是最优的。然而，有证据表明，其中一些条件在许多情况下可能是无效的或不合适的。在这里，我们考虑均衡策略在一系列偏离理想化家庭模型的其他情形中的表现如何。我们发现，一般来说，均衡策略通常表现最优，即使远离理想化情形。然而，当考虑较大的亚群体规模、频率依赖性传播和中等水平的疫苗接种时，最优性通常通过更具异质性的疫苗接种策略来实现。
