Mathematical modeling of respiratory viral infection and applications to SARS-CoV-2 progression |
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| Authors: | Latifa Ait Mahiout Nikolai Bessonov Bogdan Kazmierczak Vitaly Volpert |
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| Affiliation: | 1. Laboratoire d'équations aux dérivées partielles non linéaires et histoire des mathématiques, Ecole Normale Supérieure, Algiers, Algeria;2. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia;3. Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland;4. Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, France |
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| Abstract: | Viral infection in cell culture and tissue is modeled with delay reaction-diffusion equations. It is shown that progression of viral infection can be characterized by the viral replication number, time-dependent viral load, and the speed of infection spreading. These three characteristics are determined through the original model parameters including the rates of cell infection and of virus production in the infected cells. The clinical manifestations of viral infection, depending on tissue damage, correlate with the speed of infection spreading, while the infectivity of a respiratory infection depends on the viral load in the upper respiratory tract. Parameter determination from the experiments on Delta and Omicron variants allows the estimation of the infection spreading speed and viral load. Different variants of the SARS-CoV-2 infection are compared confirming that Omicron is more infectious and has less severe symptoms than Delta variant. Within the same variant, spreading speed (symptoms) correlates with viral load allowing prognosis of disease progression. |
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| Keywords: | reaction-diffusion equations spreading speed SARS-CoV-2 variants viral infection viral load |
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