论文标题
依赖年龄的SIR模型的国家反馈控制法律设计
State feedback control law design for an age-dependent SIR model
论文作者
论文摘要
考虑了一个依赖年龄的SIR模型，目的是开发国家反馈疫苗接种法以消除疾病。使用线性稳定性的原理对系统进行动力分析，并表明，如果基本繁殖数大于1，则无疾病平衡是不稳定的。该结果证明了疫苗接种法的发展。使用两种方法。第一个是基于根据年龄的局部整数差异方程（PIDE）模型的分界化。在这种情况下，使用Isidori的理论发现了线性化反馈定律。确定稳定性和积极性的条件。第二种方法得出了为PIDE模型开发的线性反馈定律。该法律是从对ODE案件获得的法律中得出的。使用半群理论，还获得了稳定条件。最后，提出数值模拟以加强理论论点。
An age-dependent SIR model is considered with the aim to develop a state-feedback vaccination law in order to eradicate a disease. A dynamical analysis of the system is performed using the principle of linearized stability and shows that, if the basic reproduction number is larger than 1, the disease free equilibrium is unstable. This result justifies the developement of a vaccination law. Two approaches are used. The first one is based on a dicretization of the partial integro-differential equations (PIDE) model according to the age. In this case a linearizing feedback law is found using Isidori's theory. Conditions guaranteeing stability and positivity are established. The second approach yields a linearizing feedback law developed for the PIDE model. This law is deduced from the one obtained for the ODE case. Using semigroup theory, stability conditions are also obtained. Finally, numerical simulations are presented to reinforce the theoretical arguments.
