Stochastic modeling and decision making in two healthcare applications: inpatient flow management and influenza pandemics
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Delivering health care services in an efficient and effective way has become a great challenge for many countries due to the aging population worldwide, rising health expenses, and increasingly complex healthcare delivery systems. It is widely recognized that models and analytical tools can aid decision-making at various levels of the healthcare delivery process, especially when decisions have to be made under uncertainty. This thesis employs stochastic models to improve decision-making under uncertainty in two specific healthcare settings: inpatient flow management and infectious disease modeling. In Part I of this thesis, we study patient flow from the emergency department (ED) to hospital inpatient wards. This line of research aims to develop insights into effective inpatient flow management to reduce the waiting time for admission to inpatient wards from the ED. Delayed admission to inpatient wards, also known as ED boarding, has been identified as a key contributor to ED overcrowding and is a big challenge for many hospitals. Part I consists of three main chapters. In Chapter 2 we present an extensive empirical study of the inpatient department at our collaborating hospital. Motivated by this empirical study, in Chapter 3 we develop a high fidelity stochastic processing network model to capture inpatient flow with a focus on the transfer process from the ED to the wards. In Chapter 4 we devise a new analytical framework, two-time-scale analysis, to predict time-dependent performance measures for some simplified versions of our proposed model. We explore both exact Markov chain analysis and diffusion approximations. Part I of the thesis makes contributions in three dimensions. First, we identify several novel features that need to be built into our proposed stochastic network model. With these features, our model is able to capture inpatient flow dynamics at hourly resolution and reproduce the empirical time-dependent performance measures, whereas traditional time-varying queueing models fail to do so. These features include unconventional non-i.i.d. (independently and identically distributed) service times, an overflow mechanism, and allocation delays. Second, our two-time-scale framework overcomes a number of challenges faced by existing analytical methods in analyzing models with these novel features. These challenges include time-varying arrivals and extremely long service times. Third, analyzing the developed stochastic network model generates a set of useful managerial insights, which allow hospital managers to (i) identify strategies to reduce the waiting time and (ii) evaluate the trade-off between the benefit of reducing ED congestion and the cost from implementing certain policies. In particular, we identify early discharge policies that can eliminate the excessively long waiting times for patients requesting beds in the morning. In Part II of the thesis, we model the spread of influenza pandemics with a focus on identifying factors that may lead to multiple waves of outbreak. This line of research aims to provide insights and guidelines to public health officials in pandemic preparedness and response. In Chapter 6 we evaluate the impact of seasonality and viral mutation on the course of an influenza pandemic. In Chapter 7 we evaluate the impact of changes in social mixing patterns, particularly mass gatherings and holiday traveling, on the disease spread. In Chapters 6 and 7 we develop agent-based simulation models to capture disease spread across both time and space, where each agent represents an individual with certain socio-demographic characteristics and mixing patterns. The important contribution of our models is that the viral transmission characteristics and social contact patterns, which determine the scale and velocity of the disease spread, are no longer static. Simulating the developed models, we study the effect of the starting season of a pandemic, timing and degree of viral mutation, and duration and scale of mass gatherings and holiday traveling on the disease spread. We identify possible scenarios under which multiple outbreaks can occur during an influenza pandemic. Our study can help public health officials and other decision-makers predict the entire course of an influenza pandemic based on emerging viral characteristics at the initial stage, determine what data to collect, foresee potential multiple waves of attack, and better prepare response plans and intervention strategies, such as postponing or cancelling public gathering events.