Inferring person-to-person networks of Plasmodium falciparum transmission: are analyses of routine surveillance data up to the task?

Abstract

Background: Inference of person-to-person transmission networks using surveillance data is increasingly used to estimate spatiotemporal patterns of pathogen transmission. Several data types can be used to inform transmission network inferences, yet the sensitivity of those inferences to different data types is not routinely evaluated.

Methods: The influence of different combinations of spatial, temporal, and travel-history data on transmission network inferences for Plasmodium falciparum malaria were evaluated.

Results: The information content of these data types may be limited for inferring person-to-person transmission networks and may lead to an overestimate of transmission. Only when outbreaks were temporally focal or travel histories were accurate was the algorithm able to accurately estimate the reproduction number under control, R_c. Applying this approach to data from Eswatini indicated that inferences of R_c and spatiotemporal patterns therein depend upon the choice of data types and assumptions about travel-history data.

Conclusions: These results suggest that transmission network inferences made with routine malaria surveillance data should be interpreted with caution.

Fig. 1

Schematic of a hypothetical transmission network A hypothetical transmission network is presented along with the corresponding notation. In the schematic, white circles denote unobserved cases, and black circle denote observed cases. Arrows represent transmission between two cases

Fig. 2

Marginal posterior distributions of parameters from Eswatini surveillance data. Histograms represent the marginal posterior distribution of each parameter, colour-coded by the inference settings used. D is the diffusion coefficient with units sq km day⁻¹, τ_s is the probability that an imported case reports travel, and τ_l is the probability that a locally acquired case reports travel. Grey shapes represent the prior distributions placed on each parameter. Inference settings in which a given parameter was not estimated are indicated by NA

Fig. 3

Spatial and temporal scales of transmission in Eswatini. Kernel density plots of the spatial (km) and temporal (days) scales of transmission are reported and colour-coded for each inference setting. Dashed lines indicate the corresponding null distribution, generated from all random pairs of cases in the Eswatini surveillance data set. The null distribution was different if we believed the travel history, because classification of cases on the basis of travel history reduced the pairs of cases that could be randomly sampled. The grey shape is the serial interval distribution used in the likelihood

Fig. 4

Spatial distribution of importation and transmission risk in Eswatini. Maps of the proportion of cases that are imported and the reproduction number under control (R_c) were generated for each inference setting using a generalized additive model with a Gaussian process basis function setting using the mgcv package in R [50, 51]. In each plot, darker colours indicate greater importation or transmission risk

Fig. 5

Maximum a posteriori transmission networks in Eswatini. The maximum a posteriori transmission networks (i.e., the transmission network in the posterior distribution with the highest likelihood) is shown for each inference setting: A spatial and temporal data while estimating the accuracy of the travel history; B spatial and temporal data while believing the travel history; C spatial and temporal data alone; D temporal data while estimating the accuracy of the travel history; and E temporal data while believing the travel history. In each transmission network, circles represent nodes, and arrows represent directed edges

Fig. 6

Marginal posterior distributions for parameters inferred from simulated data. The marginal posterior distributions are reported for each inference setting from its respective simulated data set. Each line denotes the true value of the parameter, and the grey shapes represent the prior distributions of the parameters. Inference settings in which a given parameter was not estimated are indicated by NA

Fig. 7

Inference accuracies for validation exercises. Accuracy metrics are reported for each inference setting applied to its respective simulated data set. Case Classification, represented by squares, refers to the proportion of cases that are correctly classified as imported or locally acquired. Transmission Linkage, denoted by circles, is the proportion of locally acquired cases for which the true parent is correctly identified. Outbreak, represented by triangles, is the proportion of locally acquired cases for which the inferred parent belongs to the correct outbreak. Bars denote the 95% credible intervals, and the grey line is the true R_c value of the network

Fig. 8

Comparison of R_c estimates across inference settings. The inference algorithm was applied to 2,000 simulated data sets. The estimated R_c is compared to the true R_c for each of the inference settings: A spatial and temporal data while estimating the accuracy of the travel history; B spatial and temporal data while believing the travel history; and C spatial and temporal data alone. Each point represents a simulated data set. The darker, accented points are simulated data sets with epidemiological features that improved performance. In A and C, the darker, accented points were simulated data sets where the mean temporal interval between imported infections was greater than two times the mean serial interval. In B, the darker, accented points were simulated data sets where the proportion of cases reporting travel was within 0.05 of the proportion of imported cases