Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru

Abstract

Rubella is generally a mild childhood disease, but infection during early pregnancy may cause spontaneous abortion or congenital rubella syndrome (CRS), which may entail a variety of birth defects. Consequently, understanding the age-structured dynamics of this infection has considerable public health value. Vaccination short of the threshold for local elimination of transmission will increase the average age of infection. Accordingly, the classic concern for this infection is the potential for vaccination to increase incidence in individuals of childbearing age. A neglected aspect of rubella dynamics is how age incidence patterns may be moulded by the spatial dynamics inherent to epidemic metapopulations. Here, we use a uniquely detailed dataset from Peru to explore the implications of this for the burden of CRS. Our results show that the risk of CRS may be particularly severe in small remote regions, a prediction at odds with expectations in the endemic situation, and with implications for the outcome of vaccination. This outcome results directly from the metapopulation context: specifically, extinction-re-colonization dynamics are crucial because they allow for significant leakage of susceptible individuals into the older age classes during inter-epidemic periods with the potential to increase CRS risk by as much as fivefold.

Figure 1.

Rubella incidence in Peru. (a) Raw time series for seven geographical units corresponding to 175 provinces across 13 years, showing the Costa central (black line), Costa norte (red line), Costa sur (green line), Selva (blue line), Sierra central (turquoise line), Sierra norte (purple line) and Sierra sur (grey line); (b) log-transformed time series +1 for the same geographical units; (c) map of Peru showing locations of each of the geographical units, with colours corresponding to colours used in the time series; arrow indicates North.

Figure 2.

(a) Distribution of incidence over age taken from the entire country and (b) relative age-specific force of infection (FOI) over age, fitted with a smoothing spline with 5 d.f. Transmission is highest in school-age children, peaking around age 13.

Figure 3.

Observed proportion of cases in individuals aged greater than 15 (indicator of CRS burden) against (a) log population size (no significant correlation, ρ = −0.009, d.f. = 114, p > 0.5 for the full dataset; and ρ = 0.05, d.f. = 111, p > 0.5 for the analysis with the three points where the proportion is equal to 1 are removed); (b) log distance from Lima + 1 (significant positive correlation, ρ = 0.24, d.f. = 114, p < 0.01 for the full dataset; and ρ = 0.24, d.f. = 111, p < 0.01 for the analysis with the three points where the proportion is 1 are removed); and (c) log average fadeout length in biweeks (significant positive correlation, ρ = 0.55, d.f. = 114, p < 1e-9 for the full dataset; and ρ = 0.40, d.f. = 111, p < 1e-5 for the analysis with three points removed). Grey bars indicate the expected proportion of cases occurring in individuals greater than 15 years of age in the endemic situation based on the estimated relative FOI over age.

Figure 4.

TSIR estimates of seasonal transmission rates showing (a) the pattern of transmission over the season, with standard errors shown as vertical dashed lines (the dip in transmission in July–August corresponds to the winter school holidays; and low transmission in December–March corresponds to the summer school vacation); and (b) the relationship between observed and expected numbers of total infected individuals in each biweek for the fitted model, where the observed is obtained by dividing through the reported numbers by the reporting rate (ρ = 0.005). The line indicates where x = y.

Figure 5.

Positive (red) and negative (blue) residuals around the mean log-coupling parameter. The locations indicated by red points are more connected than average; these tend to be concentrated along major roads (thick black lines) or in road-dense areas (black lines). Blue points are generally either off the broader roads or on smaller roads.

Figure 6.

The observed proportion of cases in individuals aged greater than 15 (indicator of CRS burden) is significantly negatively correlated with the estimated-coupling parameter (ρ = −0.27, d.f. = 114, p < 0.005), as more weakly coupled locations will have longer fadeouts, and fadeout length is strongly linked to the average age of infection (figure 2). The grey bar indicates the expected proportion of cases occurring in individuals greater than 15 years of age in the endemic situation based on the estimated relative FOI over age. The dashed line shows a smooth spline with 3 d.f., used to estimate the average metapopulation burden for different degrees of coupling.