## Abstract

The symbiotic contact process can be thought of as a two type generalisation of the contact process which can be used to model the spread of two symbiotic diseases. Each site can either be infected with type A, type B, both, or neither. Infections of either type at a given site occur at a rate of lambda multiplied by the number of neighbours infected by that type. Recoveries of either type at a given site occur at rate 1 if only one type is present, or at a lower rate mu if both types are present, hence the symbiotic name. Both the contact process and the symbiotic contact process have two critical infection rates on a Galton-Watson tree, one determining weak survival, and the other strong survival. Here, weak survival refers to the event where at least one A infection and at least one B infection is present at all times. Strong survival is the event that the root of the tree is infected with both A and B infections at the same time infinitely often.

## References

- R. Durrett and D. Yao. The symbiotic contact process. Electronic Journal of Probability, 25(none):1 – 21, 2020.
- X. Huang and R. Durrett. The Contact Process on Random Graphs and Galton-Watson Trees, 2019.

## Presented at

- Workshop "Recent Trends in Spatial Stochastic Processes" in Eindhoven, Netherlands (October 2022)
- Ada Lovelace Day, in Bath, UK (October 2022)