Inference of a Susceptible-Infectious stochastic model

TL;DR

This paper develops a Generalized Method of Moments-based inference procedure for a time-inhomogeneous stochastic S-I epidemic model, enabling parameter estimation despite the challenges posed by time-dependent transmission rates.

Contribution

It introduces a novel estimation method for a stochastic S-I model with time-varying transmission, addressing limitations of classical inference techniques.

Findings

The proposed GMM-based method accurately estimates parameters in simulations.

Comparison shows GMM performs well against MLE in the time-homogeneous case.

Application to real data demonstrates practical utility of the approach.

Abstract

We consider a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious epidemic model in which the transmission intensity function is time-dependent. Such a model is well suited to describe some classes of micro-parasitic infections in which individuals never acquire lasting immunity and over the course of the epidemic everyone eventually becomes infected. The stochastic process related to the deterministic model is transformable into a non homogeneous Wiener process so the probability distribution can be obtained. Here we focus on the inference for such process, by providing an estimation procedure for the involved parameters. We point out that the time dependence in the infinitesimal moments of the diffusion process makes classical inference methods inapplicable. The proposed procedure is based on Generalized Method of Moments in order to find suitable estimate for the infinitesimal drift and variance of the transformed process. Several simulation studies are conduced to test the procedure, these include the time homogeneous case, for which a comparison with the results obtained by applying the MLE is made, and cases in which the intensity function are time dependent with particular attention to periodic cases. Finally, we apply the estimation procedure to a real dataset.