Modeling and Bifurcation Research of a Worm Propagation Dynamical System with Time Delay

Table 1

Notations and definitions of the model.

Notations	Definitions
𝑁	Total number of hosts in the network
𝑅𝑁	Total number of removable devices in the network
𝑆(𝑡)	Number of susceptible hosts at time 𝑡
𝐼(𝑡)	Number of infectious hosts at time 𝑡
𝐷(𝑡)	Number of delayed hosts at time 𝑡
𝑄(𝑡)	Number of quarantined hosts at time 𝑡−𝜏
𝑅(𝑡)	Number of removed hosts at time 𝑡
𝑅𝑆(𝑡)	Number of susceptible removable devices at time 𝑡
𝑅𝐼(𝑡)	Number of infectious removable devices at time 𝑡
𝛽1	Infection ratio of infectious hosts
𝛽2	Contact infection rate between computers and removable devices
𝛾1	Recovery rate of infectious hosts
𝛾2	Recovery rate of infectious removable devices
𝜔	Reassembly rate of immunized hosts
𝜃1	Quarantine rate of susceptible hosts
𝜃2	Quarantine rate of infectious hosts
𝛿	Immunization rate of quarantined hosts
𝜏	Time delay of detection by anomaly intrusion detection system