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对于一个免疫策略来讲,付出(单位时间内接种疫苗的数量)和效果(再生数的大小)是两个重要概念.在给定的费用下找到带有最小再生数的策略和在给定的再生数下找到最小费用的策略是两个最优问题.对一个确定的免疫策略来说,人群中的易感群体和染病群体会趋于相对稳定的状态.当一种疾病侵袭已免疫人群时,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.因此,本文研究了一类带有感染年龄的SIR模型,得到了最优化策略的存在性.
For an immunization strategy, two important concepts are the amount of vaccination (the number of vaccinations per unit time) and the effect (the size of the number of reproductions). Find the strategy with the smallest number of reproductions for a given cost and the strategy The strategy of finding the minimum cost under the regenerative number is the two optimal problems.For a given immune strategy, the susceptible population and the infected population in the population tend to be relatively stable state.When a disease has been attacked the population has been immunized , It is more accurate to describe the spread of such diseases by using SIR model with infected age.Therefore, this paper studies a kind of SIR model with age of infection and obtains the existence of optimization strategy.