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

TL;DR

This paper develops exact solutions for generalized time-dependent SIS epidemic models using Lie-Hamilton systems, including quantum deformations, providing new analytical tools for understanding complex epidemic dynamics.

Contribution

It introduces a framework for exact solutions of time-dependent SIS models with quantum deformations, expanding the analytical understanding of epidemic Hamiltonians.

Findings

Exact solutions for generalized SIS Hamiltonians derived

Quantum deformations interpreted as perturbations of known systems

Explicit solutions obtained for deformed models

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.