Dynamic Modeling of Reported COVID-19 Cases and Deaths with Continuously Varying Case Fatality and Transmission Rate Functions

Abstract

In this paper, we propose an enhanced SEIRD (Susceptible-Exposed-Infectious-Recovered-Death) model with time varying case fatality and transmission rates for confirmed cases and deaths from COVID-19. We show that when case fatalities and transmission rates are represented by simple Sigmoid functions, historical cases and fatalities can be fit with a relative-root-mean-squared-error accuracy on the order of 2% for most American states over the period from initial cases to July 20 (2020). We find that the model is most accurate for states that so far had not shown signs of multiple waves of the disease (such as New York), and least accurate for states where transmission rates increased after initially declining (such as Hawaii). For such states, we propose an alternate multi-phase model. Both the base model and multi-phase model provide a way to explain historical reported cases and deaths with a small set of parameters, which in the future can enable analyses of uncertainty and variations in disease progression across regions.

Spatial Interaction Analysis of Infectious Disease Import and Export Between Regions

“…The values of γ, σ, and ρ are set to 1/6.5 [44], 1/3.0 [44], and 1/7.5 respectively [45]. 𝛽 𝑖 (𝑡) and 𝛼 𝑖 (𝑡) are time-varying parameters following a Sigmoid function-based form [46] representing the reproduction number and fatality rate, respectively, at time t in region i. Spatial interaction between regions is represented by the daily number of people traveling from region 𝑗 to region 𝑖 and an adjustable factor 𝜇 𝑖 (𝑡) denoting rate at which an infectious traveler from region i transmits disease to individuals in other regions per day, at time 𝑡. We use the Standard Federal Regions [47] to aggregate the 50 United States into 10 parts.…”

Spatial Interaction Analysis of Infectious Disease Import and Export between Regions

“…The values of γ, σ, and ρ are set to 1/6.5 [43], 1/3.0 [43], and 1/7.5, respectively [44]. β i (t) and α i (t) are time-varying parameters following a Sigmoid function-based form [45] representing the reproduction number and fatality rate, respectively, at time t in region i. Spatial interaction between regions is represented by the daily number of people traveling from region j to region i and an adjustable factor µ i (t) denoting rate at which an infectious traveler from region i transmits disease to individuals in other regions per day, at time t.…”