Renewal contact process with dormancy

TL;DR

This paper studies a contact process with dormancy, showing that its growth rate and survival probability depend on the possibility of infection between dormant individuals and the renewal process governing wake-up times.

Contribution

It introduces a model where wake-up times follow a renewal process and analyzes how infection dynamics affect growth and survival.

Findings

Growth is at most logarithmic without inter-dormant infection.

Process survives with positive probability if inter-dormant infection is possible.

Survival and growth depend on the infection mechanism and wake-up process.

Abstract

We consider the contact process with dormancy, where wake-up times follow a renewal process. Without infection between dormant individuals, we show that the process under certain conditions grows at most logarithmically. On the other hand, if infections between dormant individuals are possible, the process survives with positive probability even on finite graphs.