Department of Mathematics, Purdue University, West Lafayette, IN, USA; Division of Mathematical Sciences, National Science Foundation, Alexandria, VA, USA.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing, PR China.
Theor Popul Biol. 2020 Apr;132:24-32. doi: 10.1016/j.tpb.2020.01.005. Epub 2020 Feb 3.
Because demographic realism complicates analysis, mathematical modelers either ignore demography or make simplifying assumptions (e.g., births and deaths equal). But human populations differ demographically, perhaps most notably in their mortality schedules. We developed an age-stratified population model with births, deaths, aging and mixing between age groups. The model includes types I and II mortality as special cases. We used the gradient approach (Feng et al., 2015, 2017) to explore the impact of mortality patterns on optimal strategies for mitigating vaccine-preventable diseases such as measles and rubella, which the international community has targeted for eradication. Identification of optimal vaccine allocations to reduce the effective reproduction number R under various scenarios is presented. Numerical simulations of the model with various types of mortality are carried out to ascertain the long-term effects of vaccination on disease incidence. We conclude that both optimal vaccination strategies and long-term effects of vaccination may depend on demographic assumptions.
由于人口统计学的现实情况使分析变得复杂，数学模型构建者要么忽略人口统计学，要么做出简化假设（例如，出生和死亡人数相等）。但是，人口在人口统计学上存在差异，最显著的可能是在其死亡率表上。我们开发了一种具有出生、死亡、老龄化和年龄组之间混合的年龄分层人口模型。该模型包括 I 型和 II 型死亡率作为特例。我们使用梯度方法（Feng 等人，2015 年，2017 年）来探索死亡率模式对缓解麻疹和风疹等可通过疫苗预防的疾病的最佳策略的影响，国际社会已将这些疾病作为消除的目标。提出了在各种情况下确定最佳疫苗分配以降低有效繁殖数 R 的方法。对具有各种类型死亡率的模型进行数值模拟，以确定疫苗接种对疾病发病率的长期影响。我们得出的结论是，最佳疫苗接种策略和疫苗接种的长期效果都可能取决于人口统计学假设。
