Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

Journal Article · 08 July 2010 · Journal of Difference Equations and Applications

DOI: https://doi.org/10.1080/10236190902766835 · OSTI ID:1343012

Kostova, Tanya ^[1]

---

1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1343012
• Report Number(s): LLNL-JRNL--404031
• Journal Information: Journal of Difference Equations and Applications, Journal Name: Journal of Difference Equations and Applications Journal Issue: 4 Vol. 15; ISSN 1023-6198
• Publisher: Taylor & FrancisCopyright Statement
• Country of Publication: United States
• Language: English