During the COVID-19 epidemic, the Civil Aviation Administration of China (CAAC) proposed a rule of international airline incentives and circuit breakers to combat the spread of the new coronavirus. Implementing this rule based on the reward and punishment mechanism has played a crucial role in preventing the spread of COVID-19 in international air transportation. This paper proposes a linear piece-wise reward–punishment mechanism based on a mathematical infectious model to analyze the aviation administration’s implementation and preparation costs. When the number of infections surpasses or dips below penalty or reward thresholds, flights will encounter varying intensities of penalty or receive corresponding rewards. Using probabilistic methods and optimization rules to minimize the expected total costs of implementation and preparation for epidemic prevention, we explicitly find an optimal mechanism by choosing the vectors of thresholds on reward and punishment. Our technical results show that (i) the optimal reward threshold vector is one-dimensional, with this reward threshold coinciding with the first penalty threshold; (ii) the optimal punishment threshold vector is established by progressively incorporating penalty thresholds based on relative preparation costs; (iii) both the values and quantities of penalty thresholds decrease with preparation cost and higher reward or penalty intensities can increase the values of penalty thresholds.
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