Spatio-temporal models of infectious disease with high rates of asymptomatic transmission

TL;DR

This paper develops a spatio-temporal infectious disease model accounting for high asymptomatic transmission, capturing hot zone evolution and informing resource allocation during pandemics.

Contribution

It introduces a novel framework combining SIR dynamics with spatial diffusion and temporally varying parameters, specifically addressing asymptomatic spread and hot zone formation.

Findings

Model captures hot zone evolution over time.

Spatially varying diffusivity reflects population distribution.

Temporal transmission parameters adapt to behavioral and policy changes.

Abstract

The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and perspectives. A major contributor to the difficulty of containing the current pandemic is due to the highly asymptomatic nature of the disease. In this investigation, we develop a modeling framework to study the spatio-temporal evolution of diseases with high rates of asymptomatic transmission, and we apply this framework to a hypothetical country with mathematically tractable geography; namely, square counties uniformly organized into a rectangle. We first derive a model for the temporal dynamics of susceptible, infected, and recovered populations, which is applied at the county level. Next we use likelihood-based parameter estimation to derive temporally varying disease transmission parameters on the state-wide level. While these two methods give us some spatial structure and show the effects of behavioral and policy changes, they miss the evolution of hot zones that have caused significant difficulties in resource allocation during the current pandemic. It is evident that the distribution of cases will not be stagnantly based on the population density, as with many other diseases, but will continuously evolve. We model this as a diffusive process where the diffusivity is spatially varying based on the population distribution, and temporally varying based on the current number of simulated asymptomatic cases. With this final addition coupled to the SIR model with temporally varying transmission parameters, we capture the evolution of "hot zones" in our hypothetical setup.