Markov Model Predicts Changes in STH Prevalence during Control Activities Even with a Reduced Amount of Baseline Information

Background
Estimating the reduction in levels of infection during implementation of soil-transmitted helminth (STH) control programmes is important to measure their performance and to plan interventions. Markov modelling techniques have been used with some success to predict changes in STH prevalence following treatment in Viet Nam. The model is stationary and to date, the prediction has been obtained by calculating the transition probabilities between the different classes of intensity following the first year of drug distribution and assuming that these remain constant in subsequent years. However, to run this model longitudinal parasitological data (including intensity of infection) are required for two consecutive years from at least 200 individuals. Since this amount of data is not often available from STH control programmes, the possible application of the model in control programme is limited. The present study aimed to address this issue by adapting the existing Markov model to allow its application when a more limited amount of data is available and to test the predictive capacities of these simplified models.
Method
We analysed data from field studies conducted with different combination of three parameters: (i) the frequency of drug administration; (ii) the drug distributed; and (iii) the target treatment population (entire population or school-aged children only). This analysis allowed us to define 10 sets of standard transition probabilities to be used to predict prevalence changes when only baseline data are available (simplified model 1). We also formulated three equations (one for each STH parasite) to calculate the predicted prevalence of the different classes of intensity from the total prevalence. These equations allowed us to design a simplified model (SM2) to obtain predictions when the classes of intensity at baseline were not known. To evaluate the performance of the simplified models, we collected data from the scientific literature on changes in STH prevalence during the implementation of 26 control programmes in 16 countries. Using the baseline data observed, we applied the simplified models and predicted the onward prevalence of STH infection at each time-point for which programme data were available. We then compared the output from the model with the observed data from the programme.
Results
The comparison between the model-predicted prevalence and the observed values demonstrated a good accuracy of the predictions. In 77% of cases the original model predicted a prevalence within five absolute percentage points from the observed figure, for the simplified model one in 69% of cases and for the simplified model two in 60% of cases. We consider that the STH Markov model described here could be an important tool for programme managers to monitor the progress of their control programmes and to select the appropriate intervention. We also developed, and made freely available online, a software tool to enable the use of the STH Markov model by personnel with limited knowledge of mathematical models.