TY - JOUR
T1 - Optimal control intervention strategies in low- and high-risk problem drinking populations
AU - Lee, S.
AU - Jung, E.
AU - Castillo-Chavez, Carlos
N1 - Funding Information:
Jung’s work was supported by Konkuk University. This project has been partially supported by grants from the National Science Foundation (NSF – Grant DMPS-0838704 ), the National Security Agency (NSA – Grant H98230-09-1-0104 ), the Alfred T. Sloan Foundation and the Office of the Provost of Arizona State University .
Funding Information:
Carlos Castillo-Chavez is Regents and Joaquin Bustoz Jr. Professor, School of Human Evolution and Social Change, Arizona State University, Tempe. He earned B.S., M.S. and Ph.D. degrees in Mathematics from the University of Wisconsin at Stevens Point (B.S.), Milwaukee (M.S.), and Madison (Ph.D.). Professor Castillo-Chavez’ research interests focus on the application of computational, modeling and mathematical approaches to problems in population biology with emphasis on ecology, epidemiology and social dynamics. His research has been funded by NIH, NSF, NSA, and the Sloan Foundation, and has been presented at universities, institutes and government agencies around the world. Professor Castillo-Chavez’ publications have appeared in a variety of journals including American Journal of Veterinary Research , American Scientist , Emerging Infectious Diseases , JAMA , Mathematical Biosciences , Nature , Physica A , Physics Rev. E. , Scientometrics , SIAM Journal on Applied Mathematics , Statistics in Medicine , Substance Use & Misuse , The Journal of Mathematical Biology , and The Journal of Theoretical Biology . Professor Castillo-Chavez is a fellow of the American Association for the Advancement of Science (AAAS), is the recipient of two White House Awards (1992, 1997) and the 2007 AAAS Mentor award.
Funding Information:
Eunok Jung is an Associate Professor of Mathematics at Konkuk University, Republic of Korea. She earned both her B.A. and M.S. from Korea University and Ph.D. in mathematics from New York University. Professor Jung’s research interests focus on mathematical models in biofluid dynamics, such as valveless pump systems and heart model in the circulatory system, and optimal control problems applied to the cardiopulmonary resuscitation, tuberculosis, laser, and avian influenza. Her research has been funded by the Korea Research Foundation, the Korea Science and Engineering Foundation, and an Oak Ridge National Laboratory seed money grant. Her recent work has been published in The Journal of Theoretical Biology , SIAM Journal on Scientific Computing , SIAM Journal on Applied Mathematics , Mathematical Medicine and Biology , Computer Methods in Applied Mechanics and Engineering , Bulletin of Mathematical Biology , Academic Emergency Medicine , Mathematical Models and Methods in Applied Sciences and Physics Rev. E .
PY - 2010/12
Y1 - 2010/12
N2 - A mathematical model of drinking that incorporates the impact of relapse, in a rather simple setting, is analyzed primarily under the impact of two time-dependent controls (policies) put in place over a finite time horizon. The model divides the population of interest in three drinking classes: occasional or moderate drinkers (S), problem drinkers (D) and temporarily recovered (R). In this SDR framework, individuals are assumed to mix at random within their shared drinking environments. The transmission process is modeled as a social " contact" process between D, S, and R-individuals within an unchanging shared drinking environment. High relapse rates in this framework, including those resulting from temporarily effective detoxification programs, under some circumstances can do more harm than good. The impact of two intervention strategies aimed at distinct processes is explored in high- and low-risk drinking cultures as defined in this manuscript. The first intervention's goal is to reduce the intensity of " social influence" while the second tries to slow down the rate of peer-induced relapse. The use of time-dependent controls in low-risk drinking environments may remain effective beyond their lifespan (implementation time horizon). However, the effectiveness intervention programs in high-risk environments ends soon after the control efforts have been terminated. That is, the system returns to its previous problem drinking state once the controls have been removed. Control measures will have a long-term effect only when carried out in conjunction with policies that generate dramatic changes in the population's behavioral norms. That is, changes that reduce significantly the risks of abusive drinking in shared drinking environments must be implemented or costly programs put in place if change is going to be lasting. A brief discussion of the relationship between the use of costly measures and the achievement of shifts in drinking norms will be discussed.
AB - A mathematical model of drinking that incorporates the impact of relapse, in a rather simple setting, is analyzed primarily under the impact of two time-dependent controls (policies) put in place over a finite time horizon. The model divides the population of interest in three drinking classes: occasional or moderate drinkers (S), problem drinkers (D) and temporarily recovered (R). In this SDR framework, individuals are assumed to mix at random within their shared drinking environments. The transmission process is modeled as a social " contact" process between D, S, and R-individuals within an unchanging shared drinking environment. High relapse rates in this framework, including those resulting from temporarily effective detoxification programs, under some circumstances can do more harm than good. The impact of two intervention strategies aimed at distinct processes is explored in high- and low-risk drinking cultures as defined in this manuscript. The first intervention's goal is to reduce the intensity of " social influence" while the second tries to slow down the rate of peer-induced relapse. The use of time-dependent controls in low-risk drinking environments may remain effective beyond their lifespan (implementation time horizon). However, the effectiveness intervention programs in high-risk environments ends soon after the control efforts have been terminated. That is, the system returns to its previous problem drinking state once the controls have been removed. Control measures will have a long-term effect only when carried out in conjunction with policies that generate dramatic changes in the population's behavioral norms. That is, changes that reduce significantly the risks of abusive drinking in shared drinking environments must be implemented or costly programs put in place if change is going to be lasting. A brief discussion of the relationship between the use of costly measures and the achievement of shifts in drinking norms will be discussed.
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U2 - 10.1016/j.seps.2010.07.006
DO - 10.1016/j.seps.2010.07.006
M3 - Article
AN - SCOPUS:77955922724
SN - 0038-0121
VL - 44
SP - 258
EP - 265
JO - Socio-Economic Planning Sciences
JF - Socio-Economic Planning Sciences
IS - 4
ER -