The model consists of sets of three nested equations (one set for each strain i): y, z, and w. See \citet{Louren_o_2015} for a more comprehensive discussion of the model framework, including a graphical representation. yi represents the proportion of the population currently infectious with strain i. zi represents the proportion of the population that has been exposed to strain i. These individuals harbor complete immunity to future infections with strain i and include those currently infected, i.e. yi, those that have recovered but were previously infectious, and those that were exposed, but protected from becoming infectious due to partial cross-protective immunity. Finally, wi represents the proportion of the population which has been exposed to any strain j which has at least one allele in common with strain i (including strain i itself), i.e. \(j\cap i\ne\text{Ø}\). These individuals have at least partial immunity to strain i. N.b. these equations are nested such that any individual in yi is also in zi and any individual in zi is also in wi, and \(y_i\le z_i\le w_i\ \forall\ \) strain i. In traditional Susceptible-Infected (SI), Susceptible-Infected-Recovered (SIR), etc. single-strain mathematical frameworks: the y class is analogous to the I class, while w and z are composed of combinations of I and R classes. The susceptible population is not modelled explicitly in this framework.