Modeling infectious disease dynamics: the challenge of non-stationarity
The spread of disease through human populations is complex. The characteristics of disease propagation evolve with time, as a result of a multitude of environmental and anthropic factors, including social distancing. This non-stationarity is a key factor in the complexity of disease propagation.
In the absence of appropriate external data sources, to correctly describe disease propagation, I propose a flexible methodology, based on stochastic models for disease dynamics, and on Brownian processes for parameter evolution. Using such a diffusion process has the advantage of not requiring a specific mathematical function for the parameter dynamics. Coupled with Bayesian inference using Particle MCMC, this approach allows us to reconstruct both the time evolution of some key parameters of an epidemiological dynamic and its incidence.
I will demonstrate the efficiency of this methodology on toy epidemiological models where the parameters and the observation process are known, and also on more complex epidemics, such as flu, dengue and Covid-19.