Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks

The outbreak of corona virus disease 2019 has profoundly affected people’s way of life.It is increasingly necessary to investigate epidemics over social networks.This paper studies susceptible-infected-removed(SIR)epidemics via the semi-tensor product.First,a formal susceptible-infected-removed epidemic dynamic model over probabilistic dynamic networks(SIRED-PDN)is given.Based on an evolutionary rule,the algebraic form for the dynamics of individual states and network topologies is given,respectively.Second,the SIRED-PDN can be described by a probabilistic mix-valued logical network.After providing an algorithm,all possible final spreading equilibria can be obtained for any given initial epidemic state and network topology by seeking attractors of the network.And the shortest time for all possible initial epidemic state and network topology profiles to evolve to the final spreading equilibria can be obtained by seeking the transient time of the network.Finally,an illustrative example is given to show the effectiveness of our model.

A Dynamic Probabilistic Marking Approach with Multi-Tag for Tracing ICMP-Based DoS Attacks

This paper presents a dynamic probabilistic marking algorithm with multiple routing address tags, which allows the vic- tim to traceback the origin of ICMP （Internet Control Message Pro- tocol）-based direct and reflective DoS attacks. The proposed ap- proach makes full use of scalable data space of ICMP packet to achieve multiple information tags. The difference between this pro- posal and previous proposals lies in two points. First, the number of packets needed by the victim to reconstruct the attack path is greatly reduced because of three key mechanisms： multi-tag, uniform left- over probability, and tag location choice based on the module of accommodated tag numbers within a packet. Second, the true origin of both direct and reflective ICMP-based DoS attacks can be traced.