Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

Abstract

In recent years, many research works have been focusing on the propagation dynamics of infectious diseases in complex networks, and some interesting results have been obtained. The main purpose of this paper is to investigate the stability of a fractional SIS model on complex networks with linear treatment function. Based on the basic reproduction number, the stability of the disease-free equilibrium point and the endemic equilibrium point is analyzed in detail. That is, when R 0 ≤ 1, the disease-free equilibrium point is globally asymptotically stable and the disease will die out ultimately; when R 0 > 1, there exists a unique endemic equilibrium point, and both the disease-free equilibrium point and the endemic equilibrium point are stable and the disease will not spread to all individuals. Finally, numerical simulations are presented to demonstrate the theoretical results. Moreover, the influence of the fractional-order parameter and the coefficient of the linear treatment function on the decay rate of the infectious is depicted separately.

Global stability of a fractional-order logistic growth model with infectious disease

“…It is clear that the total population N(t) satisfies N(t) = S(t) + I(t). Some similar works are done by scholars [10,[22][23][24][25][26][27][28][29]. The novelty of our model compared with their models lies on the utilization of logistic growth rate rather than the constant growth rate.…”

COVID-19 pandemic and chaos theory

“…In analogy with our paper that considered a fractional SEIR model, other papers were published that described fractionally various infectious diseases, using other mathematical models. In [20] , the propagation dynamics of infectious diseases on complex networks with a linear treatment function is described using a fractional Susceptible–Infected–Susceptible model. [18] provides a new fractional Susceptible–Infected–Recovered–Susceptible, Susceptible–Infected model that uses the Caputo–Fabrizio fractional operator for the inclusion of memory in order to study the transmission of malaria disease.…”

Stability Analysis of an Incommensurate Fractional-Order SIR Model

“…More recently, there has been increased interest in extending SIR models through the inclusion of fractional derivatives [27]. Modified SIR mathematical modeling through CFOS are in recent years analyzed in [28,29,30]. In here, the time-dependent changes in sizes of susceptible, infected and recovered individuals in a population in case of an infectious disease were investigated by mathematically modeling with IFOS.…”