Bayesian calibration of simulation models for supporting management of the elimination of the macroparasitic disease, Lymphatic Filariasis

Abstract

Background: Mathematical models of parasite transmission can help integrate a large body of information into a consistent framework, which can then be used for gaining mechanistic insights and making predictions. However, uncertainty, spatial variability and complexity, can hamper the use of such models for decision making in parasite management programs.

Methods: We have adapted a Bayesian melding framework for calibrating simulation models to address the need for robust modelling tools that can effectively support management of lymphatic filariasis (LF) elimination in diverse endemic settings. We applied this methodology to LF infection and vector biting data from sites across the major LF endemic regions in order to quantify model parameters, and generate reliable predictions of infection dynamics along with credible intervals for modelled output variables. We used the locally calibrated models to estimate breakpoint values for various indicators of parasite transmission, and simulate timelines to parasite extinction as a function of local variations in infection dynamics and breakpoints, and effects of various currently applied and proposed LF intervention strategies.

Results: We demonstrate that as a result of parameter constraining by local data, breakpoint values for all the major indicators of LF transmission varied significantly between the sites investigated. Intervention simulations using the fitted models showed that as a result of heterogeneity in local transmission and extinction dynamics, timelines to parasite elimination in response to the current Mass Drug Administration (MDA) and various proposed MDA with vector control strategies also varied significantly between the study sites. Including vector control, however, markedly reduced the duration of interventions required to achieve elimination as well as decreased the risk of recrudescence following stopping of MDA.

Conclusions: We have demonstrated how a Bayesian data-model assimilation framework can enhance the use of transmission models for supporting reliable decision making in the management of LF elimination. Extending this framework for delivering predictions in settings either lacking or with only sparse data to inform the modelling process, however, will require development of procedures to estimate and use spatio-temporal variations in model parameters and inputs directly, and forms the next stage of the work reported here.

Fig. 1

Observed and fitted microfilariae (mf) age-prevalences of lymphatic filariasis (LF) for twenty-two study sites. The cyan lines denote the SIR BM model fits to observed baseline mf prevalences in different age-groups (red squares with binomial error-bars) from each of the 22 study sites. The age-groups in the figures are represented by the mid-point of the groups studied in each community. Study sites and details of survey data are described in Table 1. All mf prevalence values were standardized to reflect sampling of 1 ml blood volumes using a transformation factor of 1.95 and 1.15 respectively for values originally estimated using 20 or 100 μL blood volumes [49]

Fig. 2

Prior and posterior model parameter distributions for the data from each site. Results are shown for nine parameters (labels on top of each column), which were identified by a formal Kolmogorov-Smirnov (KS) two-sample test, to be significantly different from their flat priors across the majority of the study sites. Distribution plots for a parameter shown in gray denotes that the parameter did not differ significantly from the assigned flat priors for a study site

Fig. 3

Observed and fitted circulating filarial antigen (CFA) and microfilariae (mf) age-prevalences of lymphatic filariasis (LF) for five study sites. The model fits (cyan lines) to the observed baseline CFA and mf age-data (red squares with binomial error-bars) were obtained using a bivariate binomial likelihood function as derived and discussed in [44]. Note that both CFA and mf data were available only for five study sites

Fig. 4

Impact of annual mass drug administration (MDA) alone at 80 % coverage on the model-predicted community-level microfilariae (mf) prevalences of lymphatic filariasis (LF) for each study site. Note that the prevalence values on the y-axis are on a logarithmic scale. Simulations at MDA coverage of 80 % were carried out for three decades using the best-fit parameter vectors obtained by model-fitting to the baseline mf age-prevalence data in each site (cf. Fig. 1). The MDA start time is indicated by 0 on the x-axis. The horizontal dashed line in each plot represents the model-derived extinction threshold signifying 95 % probability of elimination (site-specific numerical values are provided in Table 2), whereas the vertical dashed line denotes the time-point since the start of mass treatment at which the modelled community-level mf prevalences had reduced/crossed below their respective 95 %-EP threshold values for all the best parameter vectors. Note that in these simulations, models were run forward for each site without the effect of drug treatments after the time-points indicated by the vertical lines were crossed

Fig. 5

Impact of annual mass drug administration (MDA) at 80 % coverage with supplemental vector control (VC) on the model-predicted community-level microfilariae (mf) prevalence of lymphatic filariasis (LF) for each study site. The supplemental VC was implemented at the population-level coverage of 80 %, and its effect was continued throughout the model simulation period, ie. even beyond the MDA stopping time-point indicated by the vertical lines. All other details as described in Fig. 4

Fig. 6

Impact of annual mass drug administration (MDA) alone at 80 % coverage on the model-predicted community-level microfilariae (mf), third-stage larvae (L3) and circulating filarial antigen (CFA) prevalences of lymphatic filariasis (LF) for the five study sites that provided both mf and CFA baseline age data. The intervention simulations were carried out with the best model parameters obtained by joint fitting to both CFA and mf baseline data. The horizontal dashed line in each plot represents the model-derived extinction threshold signifying 95 % probability of elimination for the respective state variables, whereas the vertical dashed line denotes the time-point since the start of mass treatment at which the modelled prevalences had reduced/crossed below their respective 95 %-EP threshold values for all the best parameter vectors in the case of mf and L3 prevalences; beyond this time-point model runs were carried out without the effect of drug treatments as in Figs. 4 and 5. Note that for CFA, thresholds were crossed only much after 30 years (data not shown)

Fig. 7

Risk of recrudescence of LF in communities as a result of the stopping of mass treatment following the WHO-recommended threshold of 1 % community-level microfilariae (mf) prevalence. Results shown in gray are for the LF intervention scenario when mass treatments (annual MDAs at 80 % coverage with no supplemental vector control) were stopped after the overall modelled mf prevalences crossed below the WHO-recommended threshold of 1 % (shown by solid horizontal line) in each site, whereas in the case of green curves, mass treatments were stopped after the modelled prevalences had reduced below the model-derived 95 %-EP thresholds (depicted by dashed horizontal line, for values cf. Table 2) in a site. Note that MDA stopping times for these thresholds varied within each site, with the vertical dotted line denoting the time-point when all model runs in a site had crossed the 95 %-EP threshold estimated for that site. Note that when modelled prevalences cross the 95 % EP in a site, all further simulated prevalences decayed steadily to the 0 state attractor, as predicted by theory [7]. The recrudescence probabilities (calculated as the percentage of the total model runs in which the mf prevalence rose above the 1 % threshold by the end of the simulation period) are provided in parentheses beside the names of the study sites

Fig. 8

Risk of recrudescence of LF in communities as a result of the stopping of mass treatment following the WHO-recommended threshold of 1 % community-level microfilariae (mf) prevalence. These results are shown for the biennial MDA with supplemental vector control. The coverage levels in this set of intervention runs, for both MDA and VC, were kept at 80 %. All other details, including color codes, are as given in Fig. 7