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The paper analyzes the optimal lockdown policy using the SQAIRD model over a network with three population groups (young, adult, and old). We show that different lockdown policies may be justified by different socioeconomic structures (objective cost functions that are either convex or concave). We also show that a lockdown policy is always better than a laissez-faire policy, and a targeted policy specific to each group outperforms a uniform policy. In our benchmark example, we consider the case of Italy. Our simulations show that: (a) a lockdown policy is always better than the laissez-faire policy because it limits the costs generated by the pandemic in an uncontrolled situation; (b) a group-specific targeted lockout policy is more effective than a uniform policy to the extent that the groups differ. The latter is a less expensive targeted policy (as it optimally minimizes direct, indirect, and vaccination costs), and it is equally effective in controlling the pandemic. One finding of particular interest is that the optimal lockdown rate should be higher for the young and elderly than for adults. This is motivated by the fact that younger individuals are more likely to spread the virus in question asymptomatically. [ABSTRACT FROM AUTHOR]

Infectious diseases are one of the most important problems of the modern world, for example, the periodic outbreaks of coronavirus infections caused by COVID-19, influenza, and many other respiratory diseases have significantly affected the economics of many countries. Hence, it is therefore important to minimize the economic damage, which includes both loss of work and treatment costs, quarantine costs, etc. Recent studies have presented many different models describing the dynamics of virus spread, which help to analyze the epidemic outbreaks. In the current work we focus on finding solutions that are robust to noise and take into account the dynamics of future changes in the process. We extend previous results by using a nonlinear model-predictive-control (MPC) controller to find effective controls. MPC is a computational mathematical method used in dynamically controlled systems with observations to find effective controls. [ABSTRACT FROM AUTHOR]

The analysis of global epidemics, such as SARS, MERS, and COVID-19, suggests a hierarchical structure of the epidemic process. The pandemic wave starts locally and accelerates through human-to-human interactions, eventually spreading globally after achieving an efficient and sustained transmission. In this paper, we propose a hierarchical model for the virus spread that divides the spreading process into three levels: a city, a region, and a country. We define the virus spread at each level using a modified susceptible–exposed–infected–recovery–dead (SEIRD) model, which assumes migration between levels. Our proposed controlled hierarchical epidemic model incorporates quarantine and vaccination as complementary optimal control strategies. We analyze the balance between the cost of the active virus spread and the implementation of appropriate quarantine measures. Furthermore, we differentiate the levels of the hierarchy by their contribution to the cost of controlling the epidemic. Finally, we present a series of numerical experiments to support the theoretical results obtained. [ABSTRACT FROM AUTHOR]