  Although traditional models of epidemic spreading focus on the number of
infected, susceptible and recovered individuals, a lot of attention has been
devoted to integrate epidemic models with population genetics. Here we develop
an individual-based model for epidemic spreading on networks in which viruses
are explicitly represented by finite chains of nucleotides that can mutate
inside the host. Under the hypothesis of neutral evolution we compute
analytically the average pairwise genetic distance between all infecting
viruses over time. We also derive a mean-field version of this equation that
can be added directly to compartmental models such as SIR or SEIR to estimate
the genetic evolution. We compare our results with the inferred genetic
evolution of SARS-CoV-2 at the beginning of the epidemic in China and found
good agreement with the analytical solution of our model. Finally, using
genetic distance as a proxy for different strains, we use numerical simulations
to show that the lower the connectivity between communities, e.g., cities, the
higher the probability of reinfection.
