Models of RNA virus evolution and their roles in vaccine design

Ojosnegros, Samuel; Beerenwinkel, Niko

Virus dynamics models have been successfully employed to the study of simian immunodeficiency viruses (SIV), HIV, and HBV, among others [144, [146] [147] [148] [149] [150] . The dynamics of this model are shown in [151] , in which infection is treated as a microepidemic and host cells play the role of infected or susceptible individuals. Whether the virus infection can spread in the cell pool or not depends on a condition very similar to the spread of an epidemic in a population of individuals. The parameters of the model must satisfy the inequality R 0 > 1, where R 0 is the basic reproductive number, defined as the number of newly infected cells that arise from any one infected cell when almost all cells are uninfected [144, 151] . For a' = cp/b, this number is given by For generic parameters, if R 0 > 1 uninfected cells become infected and produce progeny viruses exponentially. Activation of the immune system (a' > 1) reduces the value of R 0 and slows down the spread of the infection. At the beginning of the infection, before the immune response is mounted (a' ≈ 0), and after the initial peak of viral load, viruses and infected and uninfected cells reach a stable equilibrium termed viral set point ( Figure 3 ). While monitoring viral load of SIV in infected macaques, a correlation between the viral load at initial stages of the infection and the viral set point was observed [152, 153] . One can demonstrate that the equilibrium abundance of viruses, v*, and the logarithm of the virus load during the exponential growth phase, follow the linear relationship This result is important in HIV research, because several studies indicate that there is a positive correlation between viral load and disease progression. Individuals who display a lower viral load during the first stage of the infection have higher chances to survive and control the infection [154] .