Epidemiological model for the inhomogeneous spatial spreading of COVID-19 and other diseases

Abstract

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, “reaction-diffusion”, spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection “heat-maps” show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas—such as those underway in a few countries.

Spatio-temporal spread of COVID-19: Comparison of the inhomogeneous SEPIR model and data from South Carolina

“…We briefly review the key features of our in-homogeneous SEPIR model, described in detail in Ref. [18]. To model the spread of COVID-19 and other epidemics, the population is divided into five compartments, termed as "sub-populations": susceptible, exposed, pre-symptomatic (that are infectious), infectious (that are symptomatic), and recovered.…”

“…In this limit, inter-nodal interactions give rise to diffusion-like infection terms in the rate equations. After proper rescaling, the model equations can be written as [18] ∂h…”

“…The spatially-dependent parameters k(x) and D k (x) originate both from infections within each node (influencing k alone), and from infections between neighboring nodes (influencing both k and D k ) [18,20].…”

“…We have recently advanced a general mathematical framework for epidemiological models that can treat the spatial spreading of an epidemic [18]. The framework accounts for possible spatial in-homogeneity of all associated "compartments", which we termed "sub-populations", such as the infectious and the susceptible sub-populations.…”

Automated Pipeline for Continual Data Gathering and Retraining of the Machine Learning-Based COVID-19 Spread Models

“…Governments have issued restrictions on public activities, mandatory testing, and lockdowns [3]. Researchers across the world have attempted to assist in the combat against this disease in various ways -either through the development of spread models [4], vaccine development [5,6] or through the modeling of various influences the pandemic may have on society [7,8]. One of the tools that have shown high usability was artificial intelligence models -either for spread prediction [9] or for patient diagnosis [10].…”