Uncertainty and sensitivity analysis of the basic reproduction number of diphtheria: a case study of a Rohingya refugee camp in Bangladesh, November-December 2017

Abstract

Background: A Rohingya refugee camp in Cox's Bazar, Bangladesh experienced a large-scale diphtheria epidemic in 2017. The background information of previously immune fraction among refugees cannot be explicitly estimated, and thus we conducted an uncertainty analysis of the basic reproduction number, R₀.

Methods: A renewal process model was devised to estimate the R₀ and ascertainment rate of cases, and loss of susceptible individuals was modeled as one minus the sum of initially immune fraction and the fraction naturally infected during the epidemic. To account for the uncertainty of initially immune fraction, we employed a Latin Hypercube sampling (LHS) method.

Results: R₀ ranged from 4.7 to 14.8 with the median estimate at 7.2. R₀ was positively correlated with ascertainment rates. Sensitivity analysis indicated that R₀ would become smaller with greater variance of the generation time.

Discussion: Estimated R₀ was broadly consistent with published estimate from endemic data, indicating that the vaccination coverage of 86% has to be satisfied to prevent the epidemic by means of mass vaccination. LHS was particularly useful in the setting of a refugee camp in which the background health status is poorly quantified.

Keywords: Bangladesh; Basic reproduction number; Corynebacterium diphtheriae; Diphtheria; Epidemiology; Mathematical model; Outbreak; Refugee; Statistical estimation; Vaccination.

Figure 1. Daily incidence of diphtheria cases in Rohingya refugee camp, 2017.

Daily number of new cases as extracted from the latest open data (World Health Organization (WHO), 2017a). The vertical axis represents the total of confirmed, probable and suspected cases. By December 11, 2017, the count represents suspected cases. On and after December 12, 2017, the case definition was improved, and probable cases replaced the majority.

Figure 2. Estimated values of the basic reproduction number and case ascertainment rate.

Univariate probability distribution of (A) the basic reproduction number, (B) a₁ by December 11 and (C) a₂ by December 12 from Latin Hypercube sampling (n = 1,000). During the Latin Hypercube sampling, the vaccination coverage, ν, has a symmetric triangular distribution ranging from 0.0 to 0.7.

Figure 3. Estimated correlations in each pair of estimated parameters, and comparison between observed and predicted epidemic curves.

(A), (B) and (C) represent a two-dimensional plot of estimated parameters. During the Latin Hypercube sampling (n = 1,000), the vaccination coverage, ν, has a symmetric triangular distribution ranging from 0.0 to 0.7. (D) shows the comparison between observed and predicted epidemic curves. Bars constituting the epidemic curve show the observed data, while dots indicate predicted epidemic curve from Latin Hypercube sampling (n = 1,000).

Figure 4. Sensitivity of R₀ with respect to the serial interval.

R₀ was estimated with variable values of the coefficient of variations (CV) of the serial interval. Mean serial interval was fixed at eight days. Variations of R₀ along the vertical axis reflects the uncertainty associated with the initially immune fraction v of the Rohingya refugee population.