The analysis of a fractional network-based epidemic model with saturated treatment function and fuzzy transmission

For understanding the in uence of malware attacking on complex heterogeneous networks, this work studies a fractional network-based SIRS epidemic model with fuzzy transmission and saturated treatment function. Firstly, we apply the next-generation method to obtain the basic reproductive ratio R0, that is an important threshold value in the investigation of asymptotic behavior of the proposed epidemic model. The obtained theoretical results indicates that the value R0 signi cantly depends on the topology structure of the underlying network and the malware load. In addition, we give a threshold value R~0 R0 that not only determines the existence of endemic equilibrium E∗ but also ensures the clean of malware programs on the network. At last, the sensitivity analysis of the threshold value R0 and some graphical simulations are presented to illustrate for the theoretical results.