The contact process with an asymptomatic state

TL;DR

This paper studies a variant of the contact process distinguishing asymptomatic and symptomatic individuals, revealing how infection rates and symptom development influence epidemic thresholds.

Contribution

It introduces a contact process model with asymptomatic states and analyzes how symptom development and infectiousness affect epidemic spread.

Findings

Epidemics occur if infection rates are high enough, regardless of asymptomatic to symptomatic transition.

If asymptomatic individuals are not infectious and become symptomatic slowly, epidemics can be prevented.

Local interactions influence epidemic thresholds differently than mean-field approximations.

Abstract

In order to understand the cost of a potentially high infectiousness of symptomatic individuals or, on the contrary, the benefit of social distancing, quarantine, etc. in the course of an infectious disease, this paper considers a natural variant of the popular contact process that distinguishes between asymptomatic and symptomatic individuals. Infected individuals all recover at rate one but infect nearby individuals at a rate that depends on whether they show the symptoms of the disease or not. Newly infected individuals are always asymptomatic and may or may not show the symptoms before they recover. The analysis of the corresponding mean-field model reveals that, in the absence of local interactions, regardless of the rate at which asymptomatic individuals become symptomatic, there is an epidemic whenever at least one of the infection rates is sufficiently large. In contrast, our analysis of the interacting particle system shows that, when the rate at which asymptomatic individuals become symptomatic is small and the asymptomatic individuals are not infectious, there cannot be an epidemic even when the symptomatic individuals are highly infectious.