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Deprecated: Implicit conversion from float 265.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Comput+Mech 2020 ; 66 (5): 1131-1152 Nephropedia Template TP
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Diffusion-reaction compartmental models formulated in a continuum mechanics framework: application to COVID-19, mathematical analysis, and numerical study #MMPMID32836602
Viguerie A; Veneziani A; Lorenzo G; Baroli D; Aretz-Nellesen N; Patton A; Yankeelov TE; Reali A; Hughes TJR; Auricchio F
Comput Mech 2020[]; 66 (5): 1131-1152 PMID32836602show ga
The outbreak of COVID-19 in 2020 has led to a surge in interest in the research of the mathematical modeling of epidemics. Many of the introduced models are so-called compartmental models, in which the total quantities characterizing a certain system may be decomposed into two (or more) species that are distributed into two (or more) homogeneous units called compartments. We propose herein a formulation of compartmental models based on partial differential equations (PDEs) based on concepts familiar to continuum mechanics, interpreting such models in terms of fundamental equations of balance and compatibility, joined by a constitutive relation. We believe that such an interpretation may be useful to aid understanding and interdisciplinary collaboration. We then proceed to focus on a compartmental PDE model of COVID-19 within the newly-introduced framework, beginning with a detailed derivation and explanation. We then analyze the model mathematically, presenting several results concerning its stability and sensitivity to different parameters. We conclude with a series of numerical simulations to support our findings.