The Analysis of an SIRS Epidemic Model with Discrete Delay on Scale-Free Network

Abstract

A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity, while the disease is uniformly persistent when the basic reproductive number is more than unity. Numerical simulations are given to demonstrate the main results.

Identification of disease propagation paths in two-layer networks

“…The single-layer network model of disease was first investigated in disease models 13 . The models involved include SIS (susceptible-infected-susceptible) 10 – 13 , SIR (susceptible-infected-removed) 12 , 14 , SIRS (susceptible-infected- removed- susceptible) 15 , SEIR (susceptible-exposed-infected-recovered) 16 , SEIRS (susceptible-exposed-infected-recovered-susceptible) 17 , SIQRS (susceptible-infected-quarantined-recovered-susceptible) 18 , SIVRS (susceptible-infected-variant-recovered-susceptible) 19 , 20 , etc. The propagation characteristics of the SIS model under the condition of infected individual mobility 10 , the nonlinear infectivity and adaptive weighted SIS model 13 , the network-based SIS epidemic model with global behavior notes 21 , the SIS epidemic model with infectious latency 22 , the epidemic situation of nodes with a square lattice 13 , and so on are among the most studied models.…”