A review of data needed to parameterize a dynamic model of measles in developing countries

Abstract

Background: Dynamic models of infection transmission can project future disease burden within a population. Few dynamic measles models have been developed for low-income countries, where measles disease burden is highest. Our objective was to review the literature on measles epidemiology in low-income countries, with a particular focus on data that are needed to parameterize dynamic models.

Methods: We included age-stratified case reporting and seroprevalence studies with fair to good sample sizes for mostly urban African and Indian populations. We emphasized studies conducted before widespread immunization. We summarized age-stratified attack rates and seroprevalence profiles across these populations. Using the study data, we fitted a "representative" seroprevalence profile for African and Indian settings. We also used a catalytic model to estimate the age-dependent force of infection for individual African and Indian studies where seroprevalence was surveyed. We used these data to quantify the effects of population density on the basic reproductive number R0.

Results: The peak attack rate usually occurred at age 1 year in Africa, and 1 to 2 years in India, which is earlier than in developed countries before mass vaccination. Approximately 60% of children were seropositive for measles antibody by age 2 in Africa and India, according to the representative seroprevalence profiles. A statistically significant decline in the force of infection with age was found in 4 of 6 Indian seroprevalence studies, but not in 2 African studies. This implies that the classic threshold result describing the critical proportion immune (pc) required to eradicate an infectious disease, pc = 1-1/R0, may overestimate the required proportion immune to eradicate measles in some developing country populations. A possible, though not statistically significant, positive relation between population density and R0 for various Indian and African populations was also found. These populations also showed a similar pattern of waning of maternal antibodies. Attack rates in rural Indian populations show little dependence on vaccine coverage or population density compared to urban Indian populations. Estimated R0 values varied widely across populations which has further implications for measles elimination.

Conclusions: It is possible to develop a broadly informative dynamic model of measles transmission in low-income country settings based on existing literature, though it may be difficult to develop a model that is closely tailored to any given country. Greater efforts to collect data specific to low-income countries would aid in control efforts by allowing highly population-specific models to be developed.

Figure 1

Percent infected by age for outbreak and endemic studies. The value shown at age 0 actually represents all children under the age of 1 year. Flat lines indicate an attack rate for an age group that spans more than one age. a) Epidemic studies in Africa. b) Endemic studies in Africa. c) Epidemic studies in India. d) Endemic studies in India.

Figure 2

Seroprevalence and force of infection by age. a) Representative seroprevalence profile for Africa. The parameters for the best-fit average seroprevalence profile are k₁ = 0.56, k₂ = 0.46 and k₃ = 2.64. b) Force of infection in Africa, computed from representative seroprevalence profile for Africa (panel 2a) using Equation (5). c) Representative seroprevalence profile for India. The parameters for the best-fit average seroprevalence profile are k₁ = 0.63, k₂ = 0.58, k₃ = 2.62. d) Force of infection in India, computed from representative seroprevalence profile for India (panel 2c) using Equation (5).

Figure 3

Plot of log(R₀) versus log(N) to determine the value of c. a) Linear regression for Africa. R² = 0.051, P < 0.6. b) Linear regression for India. R² = 0.2285, P < 0.14.