Viral infection spreads in the infected tissue or in cell culture as a reaction-diffusion wave due to virus replication in the infected cells and its transport between the cells. The speed of wave propagation correlates with the virus virulence and the severity of the disease, while the total viral load with its infectivity, that is, the rate of transmission from infected to uninfected individuals. The first barrier to the progression of viral infection after its penetration into the organism is provided by the innate immune response mediated mainly by immune cells and interferon. The effectiveness of this response determines whether infection progression in the organism will be stopped at this stage or it will further develop stimulating the adaptive immune response. The interferon mediated immune response down-regulates virus penetration in the host cells and its replication inside the cells. In this work, we consider the interferon influence on the infection spreading in the tissue, and on virus infectivity and virulence. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.