Contact process with viral load

TL;DR

This paper introduces two new variants of the contact process incorporating viral load and dormant states, analyzing their phase transitions and invariant laws using Poisson constructions and duality relationships.

Contribution

It presents novel contact process models with viral load dynamics and dormant infection states, including phase transition analysis and duality-based insights.

Findings

Phase transition of survival in the viral load model

Existence of a non-trivial upper invariant law

Duality relationship between the two variants

Abstract

In this article, we present two novel variants of the contact process. In the first variant individuals carry a viral load. An individual with viral load zero is classified as healthy and otherwise infected. If an individual becomes infected it begins with a viral load of one, which then evolves according to a Birth-Death process. In this model, viral load indicates severity of the infection such that individuals with a higher load can be more infectious. Moreover, the recovery times of individual is not necessarily exponentially distributed and can even be chosen to follow a power-law distribution. In the second variant individuals are permanently infected albeit in two states: actively infected or dormant. The dynamics of these individual states are again governed by a Birth-Death process. Dormant infections do not interact with neighbouring individuals but may reactivate spontaneously. Active infections reactivate dormant neighbours at a constant rate and may become dormant themselves. We present for both variants a Poisson construction. For the first model, we study the phase transition of survival and discuss existence of a non-trivial upper invariant law. Additionally, we derive a duality relationship between the two variant, which we use to uncover a phase transition regarding invariant distributions in the second variant.