Colombo Rinaldo M, Garavello Mauro
INdAM Unit, University of Brescia, via Branze, 38, 25123 Brescia, Italy.
Department of Mathematics and its Applications, University of Milano - Bicocca, via R. Cozzi, 55, 20126 Milano, Italy.
Math Biosci Eng. 2019 Nov 14;17(2):1074-1089. doi: 10.3934/mbe.2020057.
We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.
我们提出了一个基于结构化SIR模型的建模框架，在该框架中可以测试和比较不同的疫苗接种策略。疫苗接种可以按照规定的年龄或规定的时间对易感人群的规定部分进行接种。这些接种规定的不同选择会导致疾病完全不同的演变。一旦引入合适的“成本”，相应地寻求“最佳”疫苗接种策略就很自然了。严格的结果确保了各种合理成本对控制参数的Lipschitz连续依赖性，从而确保了最优控制的存在，并建议例如通过最速下降法来寻找它们。
