STATISTICAL MODELING OF THE IMPACT OF MULTIPLICITY POOL TESTING AND THE ESTIMATION OF INFECTION AND RECOVERY RATES OF PARTIALLY KNOWN NETWORKS USING HYBRID SAMPLING

Abstract

Detection and control of epidemic outbreaks require effective testing measures, identification of highly-connected members in social networks, as well as the estimation of important epidemic parameters. Pool testing have been proven to be an efficient testing approach to control epidemic spread by reducing the total number of tests. However, pool testing can also be used to improve the accuracy of the testing process. One objective of this thesis is to improve the accuracy of pool testing using the same number of tests as that of individual testing taking into consideration the probability of testing errors and pool multiplicity classification thresholds. Statistical models are developed to evaluate the impact of pool multiplicity classification thresholds on pool testing accuracy using the receiver operating characteristic (ROC) curve and the area under the curve (AUC). The findings indicate that under certain conditions, pool testing multiplicity yields superior testing accuracy compared to individual testing without additional cost. Modelling the spread of epidemics requires the identification of well-connected nodes in partially known networks where network sampling can be leveraged to detect important nodes in these networks. This thesis extends prior research by developing a hybrid sampling method based on simple random sampling and network sampling to identify well-connected nodes in partially known networks. The performance of the proposed method is evaluated in terms of the Perron eigenvalue of the sampled subnetwork using simulation. The performance evaluation shows that the hybrid sampling method yields significantly superior performance compared to that of simple random sampling. The performance of the different levels of the partial combinations of the hybrid sampling is also evaluated where we find that the different hybrid levels give differing results under varying conditions. The findings reveal that by sampling only a small proportion of the individuals, the hybrid sampling very efficiently identifies well-connected ones. Finally, recent developments in social networks research enabled researchers to model the spread of infectious diseases using network structures. This thesis develops statistical models to estimate the infection rate and recovery rate in partially known networks. A joint sampling infection process is implemented and its outcomes are fed as input to two back tracing algorithms to estimate the health status of individuals during the periods before they are sampled. The infection and recovery rates for partially known networks are then estimated. The findings reveal that the identification of well-connected nodes using the proposed hybrid sampling method leads to significantly lower total number of infections and lower infection peak rates. The results also indicate that one of the two fill-up methods performs better than the other but incurs extra computational time.