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The surprisingly mercurial Covid-19 pandemic has highlighted the need to notonly accelerate research on infectious disease, but to also study them usingnovel techniques and perspectives. A major contributor to the difficulty ofcontaining the current pandemic is due to the highly asymptomatic nature of thedisease. In this investigation, we develop a modeling framework to study thespatio-temporal evolution of diseases with high rates of asymptomatictransmission, and we apply this framework to a hypothetical country withmathematically tractable geography; namely, square counties uniformly organizedinto a rectangle. We first derive a model for the temporal dynamics ofsusceptible, infected, and recovered populations, which is applied at thecounty level. Next we use likelihood-based parameter estimation to derivetemporally varying disease transmission parameters on the state-wide level.While these two methods give us some spatial structure and show the effects ofbehavioral and policy changes, they miss the evolution of hot zones that havecaused significant difficulties in resource allocation during the currentpandemic. It is evident that the distribution of cases will not be stagnantlybased on the population density, as with many other diseases, but willcontinuously evolve. We model this as a diffusive process where the diffusivityis spatially varying based on the population distribution, and temporallyvarying based on the current number of simulated asymptomatic cases. With thisfinal addition coupled to the SIR model with temporally varying transmissionparameters, we capture the evolution of "hot zones" in our hypothetical setup.

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