Optimizing Healthcare Delivery for Infectious Disease Testing

Abstract

Early detection of infectious diseases and isolation of the infected individuals are paramount for disease spread and controlling epidemics or pandemics. This can be achieved by timely testing of individuals at risk as part of secondary preventive care. Given the known effectiveness of screening and testing in the propagation of infectious diseases, testing operations should be planned and managed effectively. This thesis presents a series of novel mathematical models to optimize healthcare delivery for testing operations by addressing the unique characteristics of specific infectious diseases. The research focuses on two key applications: COVID-19 testing centers and MRSA surveillance testing protocols.

The first problem focuses on determining the locations and capacities of COVID-19 specimen collection centers to efficiently improve accessibility to polymerase chain reaction (PCR) testing during surges in testing demand. We develop a two-echelon multi-period location and capacity allocation model that determines the optimal number and locations of pop-up testing centers, capacities of the existing centers as well as assignments of demand regions to these centers, and centers to labs. The objective is to minimize the total number of delayed appointments and specimens subject to budget, capacity, and turnaround time constraints, which will in turn improve the accessibility to testing. We apply our model to a case study for locating COVID-19 testing centers in the Region of Waterloo, Canada using data from the Ontario Ministry of Health, public health databases, and medical literature. We also test the performance of the model under uncertain demand and analyze its outputs under various scenarios. Our analyses provide practical insights to the public health decision-makers on the timing of capacity expansions and the locations for the new pop-up centers. According to our results, the optimal strategy is to dynamically expand the existing specimen collection center capacities and prevent bottlenecks by locating pop-up facilities. The optimal locations of pop-ups are among the densely populated areas that are in proximity to the lab and a subset of those locations are selected with the changes in demand.

The second problem addresses surveillance protocols for hospital-acquired methicillin-resistant \textit{Staphylococcus} aureus (MRSA). Roommates of nosocomial MRSA cases have a high risk of MRSA acquisition. Following infection prevention and control guidelines, these individuals are isolated and undergo surveillance testing. However, the optimal post-exposure surveillance testing and isolation strategies for contacts of index MRSA cases are unknown. We develop a Markov decision process (MDP) model to optimize the testing decisions for individuals exposed to MRSA cases in hospitals to minimize loss of quality-adjusted life years and number of MRSA colonizations. We solve the model optimally using data from clinical literature and conduct sensitivity analyses on key parameters, including disutility values and disease parameters, such as prevalence and transmission probability. The optimal testing decisions recommend varying both the frequency and timing of tests based on initial test results and room configurations. Although implementing these optimal testing decisions may present challenges due to their complexity, they offer valuable insights for improving MRSA management in healthcare facilities, potentially leading to better health outcomes and cost savings compared to current guidelines and practices. We evaluate and compare the performances of various practical MRSA testing protocols, including different testing schedules and modalities using the proposed modeling framework enabling us to incorporate the test sensitivities on different days. We suggest alternative testing protocols with close-to-optimal performance that balances cost-effectiveness with clinical efficacy, aligned with decision-makers' objectives. Furthermore, the model's applicability extends beyond MRSA to other hospital-acquired infections with similar surveillance testing protocols, demonstrating its potential for infection prevention and control strategies.

The proposed MDP model helps identify the gap between optimal testing decisions, current practices, and alternative testing protocols. While it is effective for small and medium-sized hospitals, its scalability could be limited for larger institutions. To address this limitation, we propose a hybrid framework that integrates a Hidden Markov Model (HMM) with a discrete-event simulation (DES). The HMM mimics MRSA transmission and progression dynamics within isolated rooms, while the DES implements alternative testing protocols and reports related performance metrics. This hybrid framework provides computational efficiency for evaluating testing strategies in large healthcare settings. By incorporating varying test sensitivities for culture and PCR tests across different days, the proposed framework enables the evaluation of diverse MRSA surveillance testing protocols using hospital data and clinical literature. Furthermore, this approach allows us to address controversial policy questions related to MRSA testing strategies, such as the marginal benefit of day 0 testing, the ideal timing for initial and follow-up testing, and the most effective test modalities. Our analyses also identify the most effective testing protocols under specific parameter settings, which is particularly valuable given the significant variation in MRSA testing protocols across regions and institutions. By addressing these variations, the hybrid framework becomes a valuable tool for enhancing MRSA surveillance and supporting evidence-based decision-making in healthcare settings.