Mathematical Epidemiology through Transport Phenomena Viewpoint: Generalized Coordinates to Categorize People and Preliminary Numerical Results towards COVID-19
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Keywords

Population modeling
Infectious disease dynamics
Epidemic modeling
General transport equation
Numerical simulation

Abstract

With historical roots linked to life sciences, species diffusion has inspired dynamic models for infectious disease spreading. However, drawbacks have been raised towards the inclusion of people’s displacement effects, whose ordered motion might refer to species convection within transport phenomena perspective. By transcending usual geometric role of spatial coordinates, the present work proposes a surrogate mathematical description via dimensionless generalized coordinates as intended to categorize people, whether or not infected, in terms of age and comorbidities. Accordingly, while diffusive infection refers to random motion of categorized people, convective infection can be additionally invoked and assigned to “streamwise” (i.e. ontology-driven) people’s motion. With infected-people fraction as dimensionless dependent variable, the governing partial differential equation equally considers source and sink terms referring respectively to contamination-reinfection and recovery-death rates. Such epidemic transport model is preliminary applied to SARS-CoV-2 spreading (i.e. COVID-19 dynamics) among categorized people and trial numerical simulations are performed in view of extant infection data from Florida (USA), here taken as case study. Prospective extensions for the proposed epidemic transport model are addressed (e.g. diffusive infection in inhomogeneous media and human’s displacement rheology).

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