A generalization of a SIS epidemic model with fluctuations

Abstract

In a recent paper (Nakamura and Martinez, 2019), the classical epidemic compartmental susceptible-infectious-susceptible (SIS) model has been upgraded to a form which permits fluctuations in terms of the mean and the variance of infected individuals. This novel model happens to admit a Hamiltonian realization involving a constant rho(0) that is related to the reproduction number R-0. In this work, we generalize rho(0) as a t-dependent function to arrive at a non-autonomous system of differential equations that we call SISt model. We make use of the theory of Lie systems to provide a (nonlinear) superposition rule for the general solution of SISt model. To conclude, we present a quantum version of the same model, giving rise to a parametric family of SISt systems. We provide a superposition rule for the general solution of the quantum extension as well.