Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 233, pp. 1-7.

Title: A Lie algebra approach to susceptible-infected-susceptible epidemics
        
Author: Yilun Shang (Univ. of Texas, San Antonio,TX, USA)

Abstract:
 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.