Modeling household transmission dynamics: Application to waterborne diarrheal disease in Central Africa

Abstract

Introduction: We describe a method for analyzing the within-household network dynamics of a disease transmission. We apply it to analyze the occurrences of endemic diarrheal disease in Cameroon, Central Africa based on observational, cross-sectional data available from household health surveys.

Methods: To analyze the data, we apply formalism of the dynamic SID (susceptible-infected-diseased) process that describes the disease steady-state while adjusting for the household age-structure and environment contamination, such as water contamination. The SID transmission rates are estimated via MCMC method with the help of the so-called synthetic likelihood approach.

Results: The SID model is fitted to a dataset on diarrhea occurrence from 63 households in Cameroon. We show that the model allows for quantification of the effects of drinking water contamination on both transmission and recovery rates for household diarrheal disease occurrence as well as for estimation of the rate of silent (unobserved) infections.

Conclusions: The new estimation method appears capable of genuinely capturing the complex dynamics of disease transmission across various human, animal and environmental compartments at the household level. Our approach is quite general and can be used in other epidemiological settings where it is desirable to fit transmission rates using cross-sectional data.

Software sharing: The R-scripts for carrying out the computational analysis described in the paper are available at https://github.com/cbskust/SID.

Fig 1. Synthetic inference based on some data X_obs and the SID likelihood PXM(θ^).

The count data X₁, … X_M represents household level diarrhea cases among adults and juveniles under and contaminated (V = 1) and clean (V = 0) environments and is used to fit the generative model (observed likelihood) ${\ell }_M\left(\widehat{\eta }\right)$ based on (1). The generated pseudo-data $X_1^M,\dots X_n^M$ are then used to fit the SID model $P_X^M\left(\widehat{\theta }\right)$ based on (2) and (3).

Fig 2. The graphical representation of the SID model from Table 2 with marked two compartments J (juveniles) and A (adults).

Solid lines denote transitions within compartments. Dashed lines indicate transitions due to interactions (both within and across compartments) between susceptible (S) and infected (I) individuals.

Fig 3. Model validation.

The distributions of the posterior means of the counts of asymptomatic individuals in juvenile (J) and adult compartments based on the fitted SID model (2) and (3) vs the actual observed values from M = 63 Maroua households (cf. Table 1) marked by vertical lines.