Thermostated Susceptible-Infected-Susceptible epidemic model

The evolution of epidemics based on the Susceptible-Infected-Susceptible (SIS) model re-lies on the density of infected individuals rho. Recent results show that the mean density (rho) and its variance Sigma 2 can be regarded as canonical variables and obey Hamilton's equations. Using the Hamiltonian formulation, we study the SIS system coupled to a Nose 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 (rho) tends to be half of the value predicted by the original SIS model.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The evolution of epidemics based on the SIS model relies on the density of infected individuals rho. Recent research shows that the mean density rho and its variance Sigma 2 can be considered as canonical variables and follow Hamilton's equations. By using the Hamiltonian formulation, the SIS system coupled to a Nose thermal bath is studied. Classical parameters like temperature are reinterpreted in an epidemiological context. Unlike classical epidemiological models, the thermal bath introduces fluctuations that modify the system's dynamical behavior, such as those observed in some infectious waves. The stability is investigated, and it is shown that rho tends to be half of the value predicted by the original SIS model.