In this paper, the problem of social distancing in the spread of infectious diseases in the human network is extended by optimal control and differential game approaches. Hear, SEAIR model on simulation network is used. Total costs for both approaches are formulated as objective functions. SEAIR dynamics for group k that contacts with k individuals including susceptible, exposed, asymptomatically infected, symptomatically infected and improved or safe individuals is modeled. A novel random model including the concept of social distancing and relative risk of infection using Markov process is proposed. For each group, an aggregate investment is derived and computed using adjoint equations and maximum principle. Results show that for each group, investments in the differential game are less than investments in an optimal control approach. Although individuals' participation in investment for social distancing causes to reduce the epidemic cost, the epidemic cost according to the second approach is too much less than the first approach.

中文翻译：

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社交距离的最优控制和差异化博弈解决方案，以应对网络上传染病的流行。

在本文中，通过最优控制和微分博弈方法扩展了人类网络中传染病传播中的社会距离问题。听说，使用了仿真网络上的 SEAIR 模型。两种方法的总成本都被表述为目标函数。与k接触的组k的SEAIR 动力学对包括易感、暴露、无症状感染、有症状感染和改善或安全个体在内的个体进行建模。提出了一种新的随机模型，包括使用马尔可夫过程的社会距离和相对感染风险的概念。对于每个组，使用伴随方程和最大原理推导出和计算总投资。结果表明，对于每一组，微分博弈的投资少于最优控制方法的投资。虽然个人参与社会疏远投资会降低流行病成本，但第二种方法的流行病成本比第一种方法要低得多。