Abstract
This paper adapts a multi-dimensional Random Variable Transformation technique to derive a comprehensive stochastic description of the Susceptible-Infected-Recovered epidemiological model. An approximate solution of a system of nonlinear differential equations, that characterizes this model, is deterministically obtained and, from this approximation, we derive the first probability density functions for the solution processes of susceptible, infected and recovered percentages. These probability density functions are used to find the approximate mean and variance functions, as well as the confidence intervals. Taking a general situation, the infection contact rate, the recovery rate and the initial conditions are taken to be random variables with arbitrary distributions. To test the validity of the theoretical findings associated to the proposed random epidemiological model, some numerical results are tabulated and graphically presented through an illustrative example.