Asymptotic Behavior of Angstmann–Henry–McGann Fractional SIS Model on Complete Networks

Abstract

This paper investigates the asymptotic behavior of the solution to a fractional-order Susceptible–Infected–Susceptible (SIS) epidemic model on complete networks. This model couples integer-order and tempered fractional-order derivatives; arises from the generalized continuous-time random walk (CTRW) framework introduced by Angstmann, Henry, and McGann; and is referred to as the Angstmann–Henry–McGann fractional-order SIS model. To handle the difficulties caused by the coupled derivatives in the attractivity analysis, we adopt an approach based on the asymptotic theory of Volterra integro-differential equations with positive-type kernels. By constructing an appropriate Lyapunov functional, we establish the global attractivity of the endemic equilibrium and further discuss its stability. The proposed framework could avoid the complications and difficulties that arise when directly manipulating the differential forms of the models (such as unifying derivatives or extending the state space).