Fabio Lopes: Coexistence time for two competing SIS epidemics

The stochastic SIS epidemic model is a well-known continuous-time Markov chain with finite state space, describing the spread of an epidemic in a homogeneously mixing population of size N. This process eventually reaches an absorbing state (“extinction”) and its extinction time is well-understood. Namely, we can identify a phase transition depending on the infectious rate of the epidemic. There is a subcritical phase where the process goes extinct in time O_P(log N), and a supercritical phase where the extinction time grows exponentially in the population size. In this work we consider two SIS epidemics with distinct supercritical infectious rates competing under cross-immunity. We show that with high probability the process with the lower infectious rate dies out first and the two epidemics coexist for a time that is O_P(log N). Furthermore, we derive a conjecture for the limiting distribution of the coexistence time.

This is the last paper of my thesis, and I am currently working on the conjecture. It would therefore be very helpful with feedback from the audience.