Dynamics of viral mutation and evolution

We discuss our model of viral-host interaction, and the dynamics that is introduced by the multiple forces acting on the virus in that system. Two of the main forces, cell permissivity and immune response, result in two opposing strategies for viruses, one with either a large “match” to the cells or a small one, and these two, together with the other forces, give rise to a rich phase diagram. We find a first-order phase transition as a function of increasing cell permissivity at fixed immunity, featuring bi-modal quasispecies distributions at the phase boundary, and higher-order transitions in other areas of phase space as a function of varying immunity at fixed cell permissivity. We calculate the evolution of the viral load inside and outside cells, as well as the mutation of the viral quasispecies distribution, both as a function of time. The dynamics reveals two time scales of viral infection in our model, one portraying fast onset and the other of varying length to steady state. We map the three phases in our phase diagram based on their properties to acute (such as the flu and Covid-like diseases), chronic (hepatitis), and opportunistic diseases at very low immunity.