Cumulative viral load, an indicator of virulence, is controlled by the host's immune response.

A viral strain may infect a host, proliferate rapidly, become controlled by immune reactions, and eventually be eliminated from the body. The virulence, or the magnitude of harm to the host due to infection, depends on the abundance and duration of the viral strain in the body, and the importance of the damaged tissue of the host. In this study, we investigated how the cumulative viral load (time-integral of the number of infected cells) depends on various factors, such as the viral growth rate, the effectiveness of immune cells to kill infected cells, speed of immune activation, formation of memory cells, and longevity of immune cells. In addition, viruses may produce a mutant with different antigen types, escape the immune reaction targeting the original type, and inflate virulence. We derived four simple formulas for the cumulative viral load that holds in different parameter regions. We analyzed the sensitivity of the cumulative viral load to the parameters in the model. Additionally, we discussed the reported correlation between virulence and molecular evolution rate. We conclude that viral virulence can be mitigated by enhancing the speed and effectiveness of immune reactions and by reducing the viral growth rate.