Using models to shape measles control and elimination strategies in low- and middle-income countries: A review of recent applications

Abstract

After many decades of vaccination, measles epidemiology varies greatly between and within countries. National immunization programs are therefore encouraged to conduct regular situation analyses and to leverage models to adapt interventions to local needs. Here, we review applications of models to develop locally tailored interventions to support control and elimination efforts. In general, statistical and semi-mechanistic transmission models can be used to synthesize information from vaccination coverage, measles incidence, demographic, and/or serological data, offering a means to estimate the spatial and age-specific distribution of measles susceptibility. These estimates complete the picture provided by vaccination coverage alone, by accounting for natural immunity. Dynamic transmission models can then be used to evaluate the relative impact of candidate interventions for measles control and elimination and the expected future epidemiology. In most countries, models predict substantial numbers of susceptible individuals outside the age range of routine vaccination, which affects outbreak risk and necessitates additional intervention to achieve elimination. More effective use of models to inform both vaccination program planning and evaluation requires the development of training to enhance broader understanding of models and where feasible, building capacity for modelling in-country, pipelines for rapid evaluation of model predictions using surveillance data, and clear protocols for incorporating model results into decision-making.

Keywords: Elimination; Epidemiology; Mathematical models; Measles; Measles vaccination; Rubella.

Fig. 1

Schematic of inputs (solid lines) and outputs (dashed lines) from a Susceptible [S] – Infected [I] – Recovered [R] dynamic transmission model for measles and rubella. The colors represent different types of parameters/data: socio-demographic are blue, epidemiologic are green, and red represents inferred epidemiologic profiles. The model can be structured by time, age, or space, or any combination of these dimensions. *R₀ or the basic reproduction number is the average number of people a typical case will infect in a completely susceptible population. Estimates for the R₀ of rubella range from 2 to 12, with an estimated median of just over 5 , and the measles R₀ is typically reported between 12 and 18, although can range from 1 to 770 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

Illustrative comparison of the expected proportion vaccinated against measles and the expected proportion immune as a function of age. (a) The fitted proportion of children that have previously received measles vaccine (all sources, including RI and SIAs) at each month of age between 0 and 59 months per state in Nigeria, as estimated from the 2013 Demographic and Health Survey. All clusters within each state were combined and the proportion reflects both maternal recall and vaccination cards. (b) The proportion of children of age 60 months that have been previously vaccinated per state in Nigeria according to Nigeria's 2013 Demographic and Health Survey. (c) The expected proportion of children that are measles-immune at each month of age between 0 and 59 months per state in Nigeria in 2013, assuming vaccination coverage as in a) and a constant force of infection (FOI) in all states; the assumed FOI is consistent with a mean age of infection of 5 years in the absence of vaccination. (d) The expected proportion of children aged 60 months immune to measles (due to either prior vaccination or infection) per state in Nigeria in 2013; vaccination coverage and FOI assumption as in (c).

Fig. 3

Benefits of modeling to understand outbreak risk. (A) From readily available data, we can derive the proportions vaccinated by age cohort; here we see the vaccination profile as of 2018 in Madagascar vaccinated by routine (WHO-UNICEF estimates) and campaign (administrative coverage reported to WHO) activities. It is important to note that administrative coverage data typically over-estimate campaign coverage, and a post-campaign coverage survey is preferred when available . (B) To infer population susceptibility prior to the 2018–19 measles outbreak, we can use modeling to estimate age profiles of measles susceptibility, natural immunity, and vaccinal immunity; here we portray the epidemiologic profile of the Malagasy population estimated using pseudo-dynamic transmission models . (C) Incorporating estimates of susceptibility heterogeneity, we can use modeling to estimate outbreak risk. Here we demonstrate the estimated measles R in the Malagasy population in 2018 across different assumed R₀ values (5–20) and susceptibility clustering levels (defined as the relative probability of infected individuals coming into contact with susceptible individuals, e.g., ϕ = 1 in a homogeneously mixing population and ϕ = 2 when infected individuals are twice as likely to contact susceptible individuals) .

Fig. 4

Schematic demonstrating effects of population size and connectivity on transmission dynamics. Number of incident cases (bars) and number of susceptible population (dotted line) in a (A) very large susceptible population that is highly connected, (B) large susceptible population with moderate connectivity, (C) medium-size susceptible population with lower connectivity and (D) in a small susceptible population with low connectivity. (E) The connectivity and susceptible population size of the four populations shown in A–D. Populations are connected to the other populations proportional to the thickness of the arrow and whose susceptible population size is proportional to the size of the dot. Persistence and fade-out are determined by the number of susceptible individuals in the population and contact between susceptible and infected individuals. Therefore, populations with more susceptible individuals experience persistence. After fade-out, successful re-introduction (represented by the red arrow) of infected individuals is determined by connectivity and the size of the susceptible pool. Larger susceptible pools in well-connected populations will likely experience shortened delay between fade-out and successful re-introduction. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5

Estimating the impact of SIAs. (a) A hypothetical population of 15 individuals arranged by age (circles) illustrating the sources of measles immunity and their interplay. In the top row, maternal antibodies protect some of the youngest children (purple), while routine immunization covers 6 of the 13 eligible (yellow) with one vaccine failure (square). In the second row, natural infection affects 4 individuals across the age range (red). Finally, an SIA targeting the 10 individuals from 9 months to 5 years-old covers 9 (teal). Of the 5 individuals still susceptible (grey) at the time of the SIA, 2 are immunized in the campaign, implying that the SIA’s efficacy is 40%. (b) Dynamic models have been used to estimate SIA efficacy by computing goodness of fit to incidence data as SIA efficacy changes. In this illustrative example, 40% SIA efficacy (purple) does the best job of explaining measles incidence (black dots) after the SIA (grey dashed line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)