Institute of Fundamental Technological Research

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 infec-
tion 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 tis-
sue 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.

reaction-diffusion equations,spreading speed,SARS-CoV-2 variants,viral infection,viral load

A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. Conditions of the coexistence of the two variants or competitive exclusion of one of them are found, and different stages of infection progression are identified.

viral infection, mutation, cell culture, reaction-diffusion equations, time delay