Abstract

SIR models, also with age structure, can be used to describe the evolution of an infectious disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolution of the S and R populations. It is then natural to seek the “best” vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies.

中文翻译：

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非本地SIR模型中的良好位置和控制

摘要

具有年龄结构的SIR模型可用于描述传染病的演变。疫苗接种运动会影响部分易感个体的这种免疫过程，从本质上将他们转变为康复个体。我们假设疫苗接种在规定的时间或年龄进行，这会导致S和R种群进化的不连续性。因此，就成本和/或有效性而言，寻求“最佳”疫苗接种策略是很自然的。本文提供了带有疫苗接种运动的SIR模型的基本适定性和稳定性结果，从而确保了最佳剂量策略的存在。