A fractional SIS model for a random process about infectivity and recovery

Abstract

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number [Formula: see text] of the model and studied the influence of orders a and b on [Formula: see text]. Second, we found that frSIS has a disease-free equilibrium point [Formula: see text] and an endemic equilibrium point [Formula: see text]. Moreover, we proved frSIS global stability of the model using [Formula: see text]. If [Formula: see text], the model of [Formula: see text] is globally asymptotically stable. If [Formula: see text], the model of [Formula: see text] is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease.