Discrete mathematical modeling of the propagation of religious ideas: Optimal control approach

Abstract

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of the propagation of religious ideas. The population that we are going to study is divided into five compartments: Potential individuals who become religious, Religious individuals who are convinced of the religious ideas and indirectly affect society, Religious individuals who are convinced of the religious ideas and directly affect society, Religious individuals who are satisfied with the religious ideas and practise religious rites and Individuals who renounce religion and do not practice religious rites. Our objective is to find the best strategy to maximize the number of religious individuals who are convinced of the religious ideas and practise religious rites and to minimize the individuals who renounce religion and do not practise it. We use two control strategies that are: firstly, the efforts to raise religious awareness, early education on learning and practising religion, advocating the conformity of behavior with the religious ideas and secondly, the efforts made through intellectual seminars and deep religious debates on the part of great scholars and thinkers. Pontryagin’s maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the effectiveness of the optimization strategy.