  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.
