Becker N G, Starczak D N
School of Statistical Science, La Trobe University, Bundoora, Victoria, Australia.
Math Biosci. 1997 Jan 15;139(2):117-32. doi: 10.1016/s0025-5564(96)00139-3.
The effectiveness of a vaccination program depends on how the vaccinations are spread over the households of the community. Here we formulate the optimal allocation of vaccinations as a linear programming problem, when the objective is to prevent epidemics with the minimum vaccination coverage. A vaccine efficacy of less than 100%, as is usual in practice, is allowed for. Optimal vaccine allocations attempt to leave the same number of susceptibles in every household if the disease has a very high transmission rate within households. This means that proportionately more individuals need to be vaccinated in larger households if the vaccine efficacy is < 100%. The linear programming formulation can accommodate heterogeneity among individuals of the proportionate mixing form and can also minimize the initial reproduction number for a given achievable vaccination coverage.
疫苗接种计划的有效性取决于疫苗在社区家庭中的分配方式。在此，我们将疫苗接种的最优分配问题表述为一个线性规划问题，目标是在实现最小疫苗接种覆盖率的情况下预防流行病。考虑到实际中疫苗效力通常低于100% 的情况，我们允许这种情况存在。如果疾病在家庭内部具有非常高的传播率，最优疫苗分配试图使每个家庭中的易感人群数量相同。这意味着，如果疫苗效力 < 100%，则较大家庭中需要接种疫苗的个体比例相应更高。线性规划公式可以适应比例混合形式个体之间的异质性，并且还可以在给定的可实现疫苗接种覆盖率下使初始繁殖数最小化。
