The Analysis of A Fractional Network-Based Epidemic Model with Saturated Treatment Function and Fuzzy Transmission

In this work, a fractional network-based SIRS epidemic model with saturated treatment function and fuzzy transmission are introduced to characterize the malware attacking on complex heterogeneous networks. By using next-generation method, the threshold value R۰, namely basic reproductive ratio, is obtained, that determines not only the existence of endemic equilibrium E∗ but also the asymptotic stability of the model’s equilibrium points. The theoretical results indicates that the value R۰ significantly depends on the topology structure of the underlying network and the malware load. Some graphical simulations are presented to illustrate the analytical results.

Keywords:

fractional network-based epidemic model , fuzzy transmission , basic reproduction number , malware-freeequilibrium , endemic equilibrium , asymptotic stability.