中文摘要：

当一种疾病侵袭带有免疫策略人群时,用带有感染年龄的SIR模型去描述这类疾病的传播更为准确.利用庞特里亚金极大值原理（PMP）,研究了带有有限资源的SIR模型的最优接种控制问题,得到了最优策略的存在性条件.

英文摘要：

If a disease invades the vaccinated population, it is more accurate to use an SIR model with infection age to describe the transmission of disease. By Pontryagin Maximum Principle, the optimal vaccination strategy of SIR model with limited resources was investigated, and the conditions for the existence of optimal strategy were obtained.