  Identifying the infection status of each individual during infectious
diseases informs public health management. However, performing frequent
individual-level tests may not be feasible. Instead, sparse and sometimes
group-level tests are performed. Determining the infection status of
individuals using sparse group-level tests remains an open problem. We have
tackled this problem by extending graph-coupled hidden Markov models with
individuals infection statuses as the hidden states and the group test results
as the observations. We fitted the model to simulation datasets using the Gibbs
sampling method. The model performed about 0.55 AUC for low testing frequencies
and increased to 0.80 AUC in the case where the groups were tested every day.
The model was separately tested on a daily basis case to predict the statuses
over time and after 15 days of the beginning of the spread, which resulted in
0.98 AUC at day 16 and remained above 0.80 AUC until day 128. Therefore,
although dealing with sparse tests remains unsolved, the results open the
possibility of using initial group screenings during pandemics to accurately
estimate individuals infection statuses.
