A Study of Fractional Order SIS Model with Fear Effect and Beddington-De Angelis Incidence Rate

Fractional SIS Model with Fear Effect

Résumé

Many studies have demonstrated that during epidemics, fear can significantly influence human behaviour, often leading to a decline in birth rates. In this work, we propose a fractional-order SIS compartmental model that incorporates the effects of fear and employs a Beddington-De Angelis type incidence rate. This incidence function captures the impact of preventive measures taken by both susceptible and infected individuals, thereby reflecting more realistic disease transmission dynamics. Following the formulation of the model, we establish fundamental properties such as positivity and boundedness of solutions. We then compute the basic reproduction number, R0, and demonstrate the existence of an endemic equilibrium when R0 > 1. Furthermore, we analyze the local stability of both the disease-free and endemic equilibria using the linearized system. To support our analytical results, we conduct numerical simulations using the Adams-Bashforth-Moulton Predictor-Corrector method.