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 $R_v$, 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.

In this work we develop a model of viral infection in host tissues in order to study the influence of the immune response on the infection spreading speed and on the viral load characterizing, respectively, severity of symptoms and infection transmission rate. Dynamics of the interaction between viral infection and the immune response is studied with nonlocal reaction-diffusion equations for the concentrations of virus, interferon, immune cells and antibodies. Analytical results for infection spreading speed and viral load are completed by numerical simulations. At the first stage, progression of viral infection is confronted by the innate immune response mostly determined by the local interferon production. The modeling results show in this case that infection spreading speed does not depend on interferon concentration, while the total viral load decreases with the increase of its concentration. Next, we consider the influence of globally circulating interferon and show that, in contrast to local interferon diffusion, infection spreading speed decreases with increasing of global interferon level, and the total viral load also decreases. At the next stage, adaptive immune response mediated by antibodies and cytotoxic T cells (CTL) further influences infection progression. In this case, the infection propagation speed and the total viral load are decreased by the immune response. The humoral adaptive response (antibodies) increases the global interferon concentration through the viral load, while the cellular adaptive response (CTL) decreases it.

Viral infection spreads in cell culture or tissue as a reaction–diffusion wave. It is characterized by three main parameters: virus replication number, $R_v$, which determines whether infection progresses, wave speed, c, which correlates with the virus virulence, and viral load, $J\left(v\right)$, which determines the infection transmission rate. In this work, we study how the inflammation triggered by viral infection influences its progression. We obtain analytical expressions for $R_v,c$, and $J\left(v\right)$ and show how they depend on the intensity of inflammation characterized by one or two parameters. Analytical and numerical results show that inflammation decreases the viral replication number, virus virulence, and infectivity, though there are different cases depending on the parameters of the model.

We develop and analyze a reaction-diffusion model describing the early spatial dynamics of viral infection in tissue, incorporating key components of the innate immune system: inflammatory cytokines and circulating macrophages. The system couples three spatial partial differential equations (for uninfected cells, infected cells, and virus particles) with two ordinary differential equations (for cytokines and activated macrophages), and it includes time delays related to intracellular viral replication. In the absence of macrophage degradation, we derive analytical expressions for the total viral load and the wave speed, and we identify explicit immune control thresholds in terms of the virus replication number and the strength of the immune response. In the presence of macrophage degradation, simulations reveal that increasing macrophage turnover accelerates wave propagation and increases viral burden. These results highlight the critical role of innate immune feedback, modulated by effector degradation, in shaping the spatial outcome of infection. Depending on the values of viral replication number and the strength of the immune response, infection can be immediately suppressed, or it can propagate with gradual extinction due to the time-dependent immune response, or it can persistently propagate in the tissue in the form of a reaction-diffusion wave.

We develop and analyze a reaction-diffusion model describing the early spatial dynamics of viral infection in tissue, incorporating key components of the innate immune system: inflammatory cytokines and circulating macrophages. The system couples three spatial partial differential equations (for uninfected cells, infected cells, and virus particles) with two ordinary differential equations (for cytokines and activated macrophages), and includes time delays related to intracellular viral replication. In the absence of macrophage degradation, we derive analytical expressions for the total viral load and the wave speed, and identify explicit immune control thresholds in terms of the virus replication number and the strength of the immune response. In the presence of macrophage degradation, simulations reveal that increasing macrophage turnover accelerates wave propagation and increases viral burden. These results highlight the critical role of innate immune feedback, modulated by effector degradation, in shaping the spatial outcome of infection. Depending on the values of viral replication number and the strength of the immune response, infection can be immediately suppressed, or it can propagate with gradual extinction due to the time-dependent immune response, or it can persistently propagate in the tissue in the form of a reaction-diffusion wave.