Spatial Stochastic modeling for population dynamic

Data Science Seminar

Wai-Tong (Louis) Fan (Indiana University)

Abstract

Spatial-temporal data on population dynamics offer important evidence of how populations evolve over time and space, whether the populations consist of groups of living organisms, the cancer cells of a tumor, or the virus particles within a single host cell. To explain these data and make predictions, mechanistic models are essential for understanding population dynamics. These models are necessarily spatial and stochastic, due to the noisy nature of the data, making them challenging to study. Individual-based models can capture fine details, including the randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE). However, they are sensitive to minor changes and often intractable. The challenge lies in how to simultaneously retain key information from microscopic models while ensuring the efficiency and robustness of macroscopic models.

In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between individual-based models and PDEs. These connections will illuminate how certain stochastic partial differential equations (SPDEs) emerge as robust models—uniquely characterized by their resilience to changes in minute details. I will present an innovative class of SPDEs that offer insights about virus infection spread and about expanding populations in general. These robust models hold considerable promise for advancing the application of spatial-temporal data analysis in understanding dynamic populations.