arXiv subjects
Publications and source records attributed to O. E. Aiello.
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master Equation formalism. One shows that it is a very precise and efficient way to determine the epidemic threshold; using its most primitive concept, we can find exact results.
In this work we introduce a new approach to Dynamical Monte Carlo methods to simulate markovian processes. We apply this approach to formulate and study an epidemic generalized SIRS model. The results are in excellent agreement with the fourth order Runge-Kutta method in a region of deterministic solution. Introducing local stochastic interactions, the Runge-Kutta method is no longer applicable. Thus, we solve the system described by a set of stochastic differential equations by a Dynamical Monte Carlo technique and check the solutions self-consistently with a stochastic version of the Euler method. We also analyzed the results under the herd-immunity concept.
A new approach to Dynamical Monte Carlo Methods is introduced to simulate markovian processes. We apply this approach to formulate and study an epidemic Generalized SIRS model. The results are in excellent agreement with the forth order Runge-Kutta Method in a region of deterministic solution. We also demonstrate that purely local interactions reproduce a poissonian-like process at mesoscopic level. The simulations for this case are checked self-consistently using a stochastic version of the Euler Method.