Most mathematical models introduced in the biological literature that describe inherently spatial phenomena of interacting populations consist of systems of ordinary differential equations, thus leaving out any spatial structure. The spatial component, however, is identified as an important factor in how communities are shaped, and spatial models can result in predictions that differ from non-spatial models. The aim of my research is to understand the role of space in ecology, epidemiology and population genetics through the mathematical analysis of a class of stochastic processes known as interacting particle systems. These processes are ideally suited to investigate the consequences of the inclusion of a spatial structure in the form of stochastic and local interactions. This includes generalizations of the contact process and the voter model in spatially heterogeneous environments and on inhomogeneous graphs.

Peer-Reviewed Publications

1. Coexistence for a multitype contact process with seasons. Ann. Appl. Probab. 19 (2009), 1921-1943, with Ben Chan and Rick Durrett.
2. Spatially explicit non-Mendelian diploid model. Ann. Appl. Probab. 19 (2009), 1880-1920, with Claudia Neuhauser.
3. Two-scale contact process and effects of habitat fragmentation on metapopulations. Markov Process. Related Fields. 14 (2008), 487-514, with Lamia Belhadji.
4. Coexistence in host-pathogen systems. Stochastic Process. Appl. 118 (2008), 1004-1021, with Rick Durrett.
5. Voter model and biased voter model in heterogeneous environments. J. Appl. Probab. 44 (2007), 770-787, with Claudia Neuhauser.
6. A spatially explicit model for competition among specialists and generalists in a heterogeneous environment. Ann. Appl. Probab. 16 (2006), 1385-1410, with Claudia Neuhauser.
7. Stochastic spatial models of host-pathogen and host-mutualist interactions I. Ann. Appl. Probab. 16 (2006), 448-474, with Claudia Neuhauser.
8. Individual versus cluster recoveries within a spatially structured population. Ann. Appl. Probab. 16 (2006), 403-422, with Lamia Belhadji.
9. Multitype contact process with frozen sites: a spatial model of allelopathy. J. Appl. Probab. 42 (2005), 1109-1119.
10. Phase transitions and duality properties of a successional model. Adv. Appl. Probab. 37 (2005), 265-278.

Recent Submissions

1. Two-scale multitype contact process: coexistence in spatially explicit metapopulations.
2. Ergodic theorems for a sexual reproduction contact process including genotypes, with Claudia Neuhauser.
3. Multitype voter model with confidence threshold.
4. Stochastic spatial models of host-pathogen and host-mutualist interactions II, with Claudia Neuhauser.
5. Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions, with Daniela Bertacchi and Fabio Zucca.

Work in Progress

1. Deterministic and stochastic models with migration and bistability, with Yun Kang.
2. Geometric properties of the spatial majority rule model, with Jared Neufer.