  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.
