Thermostated Susceptible-Infected-Susceptible epidemic model

The evolution of epidemics based on the Susceptible-Infected-Susceptible (SIS) model relies on the density of infected individuals ρ. Recent results show that the mean density 〈ρ〉 and its variance σ2 can be regarded as canonical variables and obey Hamilton's equations. Using the Hamiltonian formulation, we study the SIS system coupled to a Nosé thermal bath. We reinterpret classical parameters like temperature in an epidemiological context. In contrast to classical epidemiological models, the thermal bath modifies the dynamical behavior of the system by introducing fluctuations, such as those seen in some infectious waves. We study the stability and show that 〈ρ〉 tends to be half of the value predicted by the original SIS model. © 2022 Elsevier Inc.