@article{Campoamor-Stursberg2023, 
author = {Rutwig Campoamor-Stursberg and Eduardo Fernández-Saiz and Francisco J. Herranz},
title = {Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {10},
pages = {24025-24052},
keywords = {Lie systems, Lie-Hamilton systems, nonlinear differential equations, SIS models, exact solutions, nonlinear superposition rules},
url = {https://www.sciopen.com/article/10.3934/math.20231225},
doi = {10.3934/math.20231225},
abstract = {Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by              b        2   and              h        4  , respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry              h        6  , according to the embedding chain              b        2    ⊂            h        4    ⊂            h        6  , for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.}
}