Pathwise methods for the integration of a stochastic SVIR model

Abstract

We propose an approach for the precise numerical integration of a stochastic SVIR model defined by a stochastic differential equation (SDE) with non‐globally Lipschitz continuous coefficients and multiplicative noise. This equation, based on a compartmental epidemic model, describes a continuous vaccination strategy with environmental noise effects. By means of an appropriate invertible continuous transformation, we link the solution to the stochastic SVIR model to the solution of an auxiliary random differential equation (RDE) that has an Ornstein–Uhlenbeck process as the only input parameter of the system. In this way, based on this explicit conjugacy between both equations, new pathwise numerical schemes are constructed for the SVIR model. In particular, we propose an exponential method that outperforms other integrators in the literature and is able to approximate, with high stability, meaningful probabilistic features of the continuous system, including its stationary distribution and ergodicity. A simulation study is presented to illustrate the practical performance of the introduced methods, and a comparative analysis with other integrators commonly used for the simulation of epidemiological models is performed.