Generalized time-dependent SIS Hamiltonian models: Exact solutions and quantum deformations

Abstract

The theory of Lie-Hamilton systems is used to construct generalized time-dependent SIS epidemic Hamiltonians with a variable infection rate from the 'book' Lie algebra. Although these are characterized by a set of non-autonomous nonlinear and coupled differential equations, their corresponding exact solution is explicitly found. Moreover, the quantum deformation of the book algebra is also considered, from which the corresponding deformed SIS Hamiltonians are obtained and interpreted as perturbations in terms of the quantum deformation parameter of previously known SIS systems. The exact solutions for these deformed systems are also obtained.

arXiv comment11 pages. Some misprints corrected. Based on the contribution presented at "The XII International Symposium on Quantum Theory and Symmetries" (QTS12), July 24-28, 2023, Czech Technical University in Prague, Czech Republic. To appear in Journal of Physics: Conference Series

References in corpus (4)

• On the complete integrability and linearization of certain second order nonlinear ordinary differential equations
• Superposition rules, Lie theorem and partial differential equations
• Lie-Hamilton systems on the plane: properties, classification and applications
• Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations

Cited by in corpus (2)

• Quasi-rectifiable Lie algebras for partial differential equations
• Generalized Buchdahl equations as Lie-Hamilton systems from the 'book' and oscillator algebras: Quantum deformations and their general solution