UBC Math Bio Seminar: JC Loredo-Osti

The many ways to model an infectious disease go from simple predator-prey Lotka-Volterra compartmentalised models to highly dimensional models. These models are also commonly expressed as the solution to a system of deterministic differential equations. One issue with models that are highly parametrised, which makes them unsuitable for the early stages of an outbreak, is that estimation with a few data points may be impractical. In terms of sampling, small populations are peculiar, e.g., one may find very effective contact tracing along quite noisy data collection and management due to the lack of resources, and a scarcity of methodological developments crafted for those populations. In this presentation, I will argue that in small jurisdictions, stochastic branching and self-exciting processes or variations of basic compartmentalised models are more relevant because of the volatile nature of the disease dynamics, particularly at early stages of an outbreak. Then, we will focus on continuous-time Markov chain compartmentalised models and their parameter estimation through the likelihood. Finally, we comment on the connection of SIR-like models with Hawkes processes.