Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

Abstract

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed by individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S→I→R→S (SIRS). The open process S→I→R (SIR) is studied as a particular case of the SIRSprocess. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyse the role of noise in stabilizing the oscillations.

Stochastic Dynamics and Irreversibility

“…To characterize the behavior of x and y as functions of time we should also consider Fig. 14.3 Phase diagram of the predator-prey (a) and SIRS (b) models according to mean-field theory, in the plane c versus p, obtained by Satulovsky and Tomé (1994) and Souza and Tomé (2010), respectively. The solid line separates the absorbing (abs) phase and the species coexistence phase.…”

Critical behavior in a stochastic model of vector mediated epidemics

“…The SIR model exhibits a phase transition between non-spreading (NS) and spreading (S) regions7. Later, a variety of other models8910111213 were developed to cope with different specific epidemic conditions. Notable are the so-called contact models, particularly the Susceptible-Infected-Susceptible (SIS) model, whose critical properties have been widely analysed8910111415.…”

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

“…In the last years, a great number of works have shown the relevance of this kind of approach to describe biological population problems [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. We focus on the stochastic lattice model for a susceptible-infected-immunized system introduced by Satulovsky and Tomé [24,25]. This model exhibits a phase diagram with an active phase where epidemic spreads indefinitely and an inactive phase where the immunization process predominates and the epidemic spreading stops after reaching a finite portion of the system.…”