Geodesic
A Lie algebra approach to susceptible-infected-susceptible epidemics
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 92D30, 17B80, 60J22
Keywords: epidemic dynamics, Lie algebra, Riccati equation, susceptible-infected-susceptible 
@article{EJDE_2012__2012__a7,
     author = {Shang,  Yilun},
     title = {A {Lie} algebra approach to susceptible-infected-susceptible epidemics},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1321.92077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a7/}
}
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Shang,  Yilun. A Lie algebra approach to susceptible-infected-susceptible epidemics. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a7/