A new stochastic SIS-type modelling framework for analysing epidemic dynamics in continuous space

TL;DR

This paper introduces a novel stochastic SIS epidemic model in continuous space using a spatial Lambda-Fleming-Viot process, providing a new framework for analyzing epidemic dynamics with genetic data.

Contribution

It develops a mathematically rigorous, low-parameter stochastic model for spatial epidemics, linking genealogies to epidemic outcomes and enabling inference from demographic and genetic data.

Findings

Extinction probability largely independent of initial conditions

Identification of a candidate basic reproduction number R0

Mathematical construction based on martingale problems and Poisson processes

Abstract

We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $\Lambda$-Fleming-Viot (SLFV) process. The model can be described by as little as three parameters, and is dual to a spatial branching process with competition linked to genealogies of infected individuals. Therefore, it is a possible modelling framework to develop computationally tractable inference tools for epidemics in a continuous space using demographic and genetic data.We provide mathematical constructions of the process based on well-posed martingale problems as well as driving space-time Poisson point processes. With these devices and the duality relation in hand, we unveil some of the drivers of the transition between extinction and survival of the epidemic. In particular, we show that extinction is in large parts independent of the initial condition, and identify a strong candidate for the reproduction number R 0 of the epidemic in such a model.