Parameters for polio and measles. The disease transmission rate r is calculated from the basic reproduction number R0, disease recovery rate g and birth rate b using eqn (4). Polio R0, measles R0 and measles g are taken from Anderson and May (1991). Polio g is from Tebbens et al. (2005). The value of b is from Hamilton et al. (2015). The value s = 0 is chosen for simplicity, and we expect s to be low in real populations. The value of v was chosen so that it takes about 7 days on average for a newly pro-vaccine individual to become vaccinated. The parameters r, g, v, and s are reported in units of days−1; b uses units of per capita births per day. R0 is dimensionless. The values in the table were used to produce Figure 3