Local and global survival for infections with recovery

Rangel Baldasso, Alexandre Stauffer

Research output: Contribution to journalArticlepeer-review


We establish two open problems from Kesten and Sidoravicius (Kesten and Sidoravicius, 2006). Particles are initially placed on Z d with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared as infected. Infection transmits instantaneously to healthy particles on the same site and infected particles become healthy with a positive rate. We prove that, for small enough recovery rates, the infection process survives and visits the origin infinitely many times on the event of survival. Second, we establish the existence of density parameters for which the infection survives for all choices of the recovery rate.

Original languageEnglish
Pages (from-to)161-173
Number of pages13
JournalStochastic Processes and their Applications
Early online date14 Mar 2023
Publication statusE-pub ahead of print - 14 Mar 2023


  • math.PR
  • 60K37, 60K35, 82C22


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