Electron. J. Diff. Equ., Vol. 2012 (2012), No. 233, pp. 1-7.

A Lie algebra approach to susceptible-infected-susceptible epidemics

Yilun Shang

The susceptible-infected-susceptible (SIS) epidemic model can be represented by a continuous-time Markov chain, which is governed by a set of deterministic differential equations (Kolmogorov forward equations). In this paper, a Lie algebra approach is applied to solve an SIS model where infection rate and recovery rate are time-varying. The method presented here has been used widely in chemical and physical sciences but not in epidemic applications due to insufficient symmetries.

Submitted August 24, 2012. Published December 21, 2012.
Math Subject Classifications: 92D30, 17B80, 60J22.
Key Words: Epidemic dynamics; Lie algebra; Riccati equation; susceptible-infected-susceptible.

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Yilun Shang
Institute for Cyber Security
University of Texas at San Antonio
San Antonio, Texas 78249, USA
email: shylmath@hotmail.com

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