A stochastic SIR model with contact-tracing: large population limits and statistical inference

TL;DR

This paper develops a stochastic SIR epidemic model with contact-tracing, demonstrating its convergence to a PDE system in large populations and exploring its implications for statistical inference and real-world HIV data analysis.

Contribution

It introduces a novel stochastic SIR model incorporating contact-tracing effects and proves its convergence to a PDE system for large populations, aiding inference methods.

Findings

Model converges to PDE system as population size increases

Preliminary statistical inference results are established

Application to HIV data in Cuba demonstrates model relevance

Abstract

A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing information related to persons with whom they have had possibly infectious contacts. The population evolves through demographic, infection and detection processes, in a way that its temporal evolution is described by a stochastic Markov process, of which the component accounting for the contact-tracing feature is assumed to be valued in a space of point measures. For adequate scalings of the demographic, infection and detection rates, it is shown to converge to the weak deterministic solution of a PDE system, as a parameter n, interpreted as the population size roughly speaking, becomes large. From the perspective of the analysis of infectious disease data, this approximation result may serve as a key tool for exploring the asymptotic properties of standard inference methods such as maximum likelihood estimation. We state preliminary statistical results in this context. Eventually, relation of the model to the available data of the HIV epidemic in Cuba, in which country a contact-tracing detection system has been set up since 1986, is investigated and numerical applications are carried out.