Risk-based evaluation and management of cyber-physical-social systems during pandemic crisis

Abstract

This research focuses on risk-based evaluation and management of cyber-physical-social systems during a pandemic crisis. The ongoing novel coronavirus (COVID-19) epidemic has caused serious challenges for the world’s countries. The health and economic crisis caused by the COVID-19 pandemic highlights the necessity for a deeper understanding and investigation of the best mitigation policy. While different control strategies in the early stages, such as lockdowns and school and business closures, have helped decrease the number of infections, these strategies have had an adverse economic impact on businesses and some controversial impacts on social justice. Therefore, optimal timing and scale of closure and reopening strategies are required to prevent both different waves of the pandemic and the negative socio-economic impact of control strategies. To maximize the effectiveness of the controlling policies during a major crisis like a pandemic, we propose two mathematical frameworks which optimize the contorting policy while considering three sets of important factors, including the epidemiologic, economic, and social impact of the pandemic. Each formulation quantifies the epidemiologic impact using a modified SIRD (susceptible-infected-recovered-deceased) model which captures the number of infected, recovered, immune, and deceased populations. The two formulations propose different approaches for measuring the social and economic impacts of the pandemic. In the first formulation, the economic impact is a twofold measure, first the unmet demand because of supply perturbation (due to industry closure), and the second is the local business shrinkage because of demand perturbation (due to the state closure). The modified SIRD model is combined with a multi-commodity maximum network flow problem (MNFP) in which the unmet demand is measured in a network of states and industries. The proposed formulation is implemented on a dataset that includes 11 states, the District of Columbia (including the states in New England and the mid-Atlantic), and 19 industries in the US. In the second formulation, the economic impact is measured using the supply side multi-regional inoperability input-output model, accounting for the inoperability of each industry to satisfy the demand of final consumers and other industries, due to its closure. Also, the second formulation measures the social impact of the pandemic policy, by incorporating the vulnerability of social communities to get infected due to state opening or to lose their job due to the closure of the state. We test the efficacy of proposed formulations on the real data set of COVID-19 applicable to 50 states, the District of Columbia, and 19 industries. Both formulations are multi-objective mixed integer programming with three objectives which are solved using the augmented ε-constraint approach. The final pandemic policy is selected from the set of Pareto-optimal solutions based on the least cubic distance of the solution from the optimal value of each objective. The Pareto-optimal solutions suggest that for any control decision (state and industry closure or reopening), the economic impact and the epidemiologic impact change in the opposite direction, and it is more effective to close most states while keeping the majority of industries open. For each Pareto optimal solution, the unmet demand and the propagation of inoperability to the industries and states can be tracked down. This will give a holistic view of the impact of the pandemic policy on the health, economy, and social justice aspects of the country.