Probabilistic solution of random Riccati-type differential equations appearing in epidemiological models

Abstract

[EN] This paper deals with the probabilistic solution of random Riccati-type differential equations that appear in a class of epidemiological models usually referred to as SIS-type models. Taking advantage of Random Variable Transformation technique, the first probabilistic density function of the solution stochastic process of that class of random differential equations is determined by two different ways. This permits to characterize, from a probabilistic point of view, the solution in every time instant and to compute its expectation, variance and confidence intervals. The obtained results are very general since all the model input parameters are assumed to be random variables with an arbitrary joint probability density function.