It is recognized that social heterogeneities in terms of the contact distribution have a strong influence on the spread of infectious diseases. Nevertheless, few data are available on the group composition of social contacts, and their statistical description does not possess universal patterns and may vary spatially and temporally. It is therefore essential to design robust control strategies, mimicking the effects of non-pharmaceutical interventions, to limit efficiently the number of infected cases. In this work, starting from a recently introduced kinetic model for epidemiological dynamics that takes into account the impact of social contacts of individuals, we consider an uncertain contact formation dynamics leading to slim-tailed as well as fat-tailed distributions of contacts. Hence, we analyse the effects of an optimally robust control strategy of the system of agents. Thanks to classical methods of kinetic theory, we couple uncertainty quantification methods with the introduced mathematical model to assess the effects of social limitations. Finally, using the proposed modelling approach and starting from available data, we show the effectiveness of the proposed selective measures to dampen uncertainties together with the epidemic trends.
Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic using Robust Multi-objective Optimization and Stochastic Fractal Search
传统上，反问题的制定和解决方案中的参数识别认为，模型，变量和数学参数是免费的不确定性。这一方面简化了估计过程，但没有考虑设计变量相对较小的变化对目标函数的影响。本文采用SIDR（Susceptible，Infected，Dead and Available）模型来模拟新型冠状病毒病（COVID-19）的动态行为，通过构造鲁棒反问题，即考虑设计变量的敏感性，来估计其参数。为此，制定了一个强大的多目标优化问题，考虑最小化的不确定性相关的估计过程和最大化的鲁棒性参数。为了解决这个问题，多目标随机分形搜索算法是与有效平均的概念，用于评估的鲁棒性。考虑中国疫情的实际数据得到的结果表明，设计变量的敏感性评估可以提供更可靠的结果。
Epidemic Control Modeling using Parsimonious Models and Markov Decision Processes
University of Southampton（南安普顿大学）；Number Theory Software Pvt Ltd（数论软件私人有限公司）；Federal University of Rio de Janeiro（里约热内卢联邦大学）；Digital University Kerala（喀拉拉数字大学）
