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\title{Mathematical modelling of respiratory viral infection and applications
to SARS-CoV-2 progression}



\author[1]{Latifa Ait Mahiout}%
\author[2]{Nikolai Bessonov}%
\author[3]{Bogdan Kazmierczak}%
\author[4]{Vitaly Volpert}%
\affil[1]{Ecole Normale Superieue Kouba Sciences de l'Education}%
\affil[2]{Institut Problem Masinovedenia RAN}%
\affil[3]{Institute of Fundamental Technological Research Polish Academy of Sciences}%
\affil[4]{University of Lyon}%


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  \date{June 18, 2024}


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\begin{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.%
\end{abstract}%



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