Ferreyra Emanuel Javier, Jonckheere Matthieu, Pinasco Juan Pablo
Instituto de Cálculo UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria (1428), Buenos Aires, Argentina.
IMAS UBA-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Av Cantilo s/n, Ciudad Universitaria (1428), Buenos Aires, Argentina.
Appl Math Optim. 2021;84(Suppl 2):1769-1818. doi: 10.1007/s00245-021-09810-7. Epub 2021 Jul 24.
We consider an SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of optimal controls for the limiting equations formulated in the framework of game theory, both in the centralized and decentralized setting. We show how the characteristics of the graph (degree distribution) influence the vaccination efficiency for optimal strategies, and we compute the limiting final size of the epidemic depending on the degree distribution of the graph and the parameters of infection, recovery and vaccination. We also present several simulations for two types of vaccination, showing how the optimal controls allow to decrease the number of infections and underlining the crucial role of the network characteristics in the propagation of the disease and the vaccination program.
我们考虑在稀疏配置模型随机图上具有疫苗接种策略的SIR模型。我们展示了节点数量增长时系统的收敛性，并刻画了缩放极限。然后，我们证明了在博弈论框架下制定的极限方程在集中式和分散式设置中最优控制的存在性。我们展示了图的特征（度分布）如何影响最优策略的疫苗接种效率，并根据图的度分布以及感染、恢复和疫苗接种参数计算了流行病的极限最终规模。我们还针对两种类型的疫苗接种进行了若干模拟，展示了最优控制如何减少感染数量，并强调了网络特征在疾病传播和疫苗接种计划中的关键作用。
