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

## Abstract

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.

- Authors:

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

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1343012

- Report Number(s):
- LLNL-JRNL-404031

Journal ID: ISSN 1023-6198

- Grant/Contract Number:
- AC52-07NA27344

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Difference Equations and Applications

- Additional Journal Information:
- Journal Volume: 15; Journal Issue: 4; Journal ID: ISSN 1023-6198

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 99 GENERAL AND MISCELLANEOUS; epidemic network; network dynamics; connectivity; epidemic control; dynamical system; reproduction number

### Citation Formats

```
Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks. United States: N. p., 2010.
Web. doi:10.1080/10236190902766835.
```

```
Kostova, Tanya. Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks. United States. doi:10.1080/10236190902766835.
```

```
Kostova, Tanya. Fri .
"Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks". United States. doi:10.1080/10236190902766835. https://www.osti.gov/servlets/purl/1343012.
```

```
@article{osti_1343012,
```

title = {Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks},

author = {Kostova, Tanya},

abstractNote = {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.},

doi = {10.1080/10236190902766835},

journal = {Journal of Difference Equations and Applications},

number = 4,

volume = 15,

place = {United States},

year = {2010},

month = {7}

}

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Cited by: 6 works

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