Optimal control problems in public health

Feng Lin, Purdue University

Abstract

The health care delivery system in the United States is poorly planned to meet the growing needs of its population. This research establishes the foundations of developing decision-support tools in the emerging field of health care engineering, with special emphasis on public health. It demonstrates the potential of applying engineering methods, especially optimal control theory, to facilitate decision making in the complex health care delivery systems. Two compelling problems of public health are studied: (1) how to optimally implement non-pharmaceutical interventions to mitigate an influenza pandemic; and (2) how to allocate limited long-term care budget effectively. (1) Pandemic planning: Optimal implementation of non-pharmaceutical interventions during influenza pandemic. Non-pharmaceutical interventions (NPIs) are the first line of defense against pandemic influenza. These interventions dampen virus spread by reducing contact between infected and susceptible persons. Because they curtail essential societal activities, NPIs must be applied judiciously. Their effectiveness also depends on the degree of public compliance, as NPIs require people to change their daily behaviors. The public “buy-in” depends on their awareness and perception of the severity of the outbreak. It is also likely to degrade as time evolves due to compliance fatigue. In this work, we use an epidemiologic compartmental model to develop optimal triggers for NPI implementation. The objective is to minimize the expected persondays lost from influenza related deaths and NPI implementation. In the first part of this work, optimal policies for a deterministic control model are derived. A multivariate sensitivity analysis is performed to study the effects of input parameters on the optimal control policy. Additional studies investigate the effects of departures from the modeling assumptions, including exponential terminal time and linear NPI implementation cost. Next, a stochastic control model is developed from the deterministic model to investigate the effect of public compliance and uncertainties of system dynamics on the NPI policies. The public compliance is modeled as functions of time and incidence of infection. Diffusion terms are introduced to capture the uncertainties in the dynamic of the system. Optimal NPI policies are derived for different compliance functions and diffusion terms. Numerical results for interpreting policy characteristics are presented along with guidelines for practical implementation. Our findings highlight the importance of timely surveillance and effective risk communications during pandemic outbreak. The application of optimal control theory can provide valuable insight to develop effective control strategies for pandemic. (2) Long-term care planning: Capacity planning of publicly funded community based care. Long-term care (LTC) provides medical and non-medical services to people with chronic disease or disability, many of whom are older adults eligible for receiving care through public funding sources. At present, the annual spending on LTC in the U.S. is over $200 billion and this number is increasing rapidly. The federal and state governments paying for LTC are under increasing financial pressure. Although nursing home care has been a viable option, it often provides expensive and more than necessary care. Home and community based services (HCBS) offers a flexible alternative by providing care at home and in the community. However, little is known on how much infrastructure is needed for providing community-based care. This research formulates an optimal control problem to determine the optimal infrastructure capacity of HCBS program from a societal expenditure viewpoint. A compartmental model is established to describe the population dynamics in the publicly funded LTC system. Two models are considered in determining whether to provide LTC in the community or in a nursing home. The objective of the optimal control problem is to minimize the overall expenditure, including spending on long-term and acute care services, over a given time period. We consider two alternative models when determining whether to provide LTC in the community or in a nursing home. Analytical properties are presented along with computational examples for dementia patients based on published data. A full-factorial sensitivity analysis is performed to study the sensitivity of various parameters. The compartmental model is validated against the published data, which indicates that it is a reasonable abstraction of the LTC system for the elderly. Reduction in total expenditure suggested by the model indicates that future development of the LTC system should increase HCBS capacity, but unrestricted HCBS expansion is not desirable. Also, HCBS cost should not exceed a certain proportion of nursing home cost for the HCBS program to remain economic.

Degree

Ph.D.

Advisors

Lawley, Purdue University.

Subject Area

Industrial engineering|Public health|Health care management

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