Study of an optimal control model for the panic propagation in a flying aircraft

Abstract

The aim of this paper is to study a discrete mathematical model of panic spreading on an airplane inspired by SIRS model, and the optimal control strategies, applied to reduce the number of panicked passengers during the flight. The population is divided into three compartments: Panic-prone panicked, and recovered passengers. Two control strategies were used, which are psychological therapies, applied by trained flight personnel, to both susceptible and panicked passengers. The discrete-time Pontryagin maximum principle was used to characterize the optimal controls. All numerical simulations were performed using MATLAB. The obtained results demonstrated which of the strategies is effective.