Optimal Implementation of Intervention to Control the Self-harm Epidemic

AbstractObjectivesDeliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls.MethodsWe considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method.ResultsSimulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls.ConclusionThe long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals

Applying the Wiener-Hermite random technique to study the evolution of excess weight population in the region of Valencia (Spain)

This paper proposes a stochastic model to study the evolution of normal and excess weight population between 24 - 65 years old in the region of Valencia (Spain). An approximate solution process of the random model is obtained by taking advantage of Wiener-Hermite expansion together with a perturbation method (WHEP). The random model takes as starting point a classical deterministic SIS¿type epidemiological model in order to improve it in several ways. Firstly, the stochastic model enhances the deterministic one because it considers uncertainty in its formulation, what it is con- sidered more realistic in dealing with a complex problem as obesity is. Secondly, WHEP approach provides valuable information such as average and variance functions of the approximate solution stochastic process to random model. This fact is remarkable because other techniques only provide predictions in some a priori chosen points. As a conse- quence, we can compute and predict the expectation and the variance of normal and excess weight population in the region of Valencia for any time. This information is of paramount value to both doctors and health authorities to set optimal investment policies and strategies.Cortés López, JC.; Romero Bauset, JV.; Roselló Ferragud, MD.; Villanueva Micó, RJ. (2012). Applying the Wiener-Hermite random technique to study the evolution of excess weight population in the region of Valencia (Spain). American Journal of Computational Mathematics. 2(4):274-281. doi:10.4236/ajcm.2012.24037S2742812

Modeling Social Transmission Dynamics of Unhealthy Behaviors for Evaluating Prevention and Treatment Interventions on Childhood Obesity

Research evidence indicates that obesity has spread through social networks, but lever points for interventions based on overlapping networks are not well studied. The objective of our research was to construct and parameterize a system dynamics model of the social transmission of behaviors through adult and youth influence in order to explore hypotheses and identify plausible lever points for future childhood obesity intervention research. Our objectives were: (1) to assess the sensitivity of childhood overweight and obesity prevalence to peer and adult social transmission rates, and (2) to test the effect of combinations of prevention and treatment interventions on the prevalence of childhood overweight and obesity. To address the first objective, we conducted two-way sensitivity analyses of adult-to-child and child-to-child social transmission in relation to childhood overweight and obesity prevalence. For the second objective, alternative combinations of prevention and treatment interventions were tested by varying model parameters of social transmission and weight loss behavior rates. Our results indicated child overweight and obesity prevalence might be slightly more sensitive to the same relative change in the adult-to-child compared to the child-to-child social transmission rate. In our simulations, alternatives with treatment alone, compared to prevention alone, reduced the prevalence of childhood overweight and obesity more after 10 years (1.2–1.8% and 0.2–1.0% greater reduction when targeted at children and adults respectively). Also, as the impact of adult interventions on children was increased, the rank of six alternatives that included adults became better (i.e., resulting in lower 10 year childhood overweight and obesity prevalence) than alternatives that only involved children. The findings imply that social transmission dynamics should be considered when designing both prevention and treatment intervention approaches. Finally, targeting adults may be more efficient, and research should strengthen and expand adult-focused interventions that have a high residual impact on children

Predicting cocaine consumption in Spain: A mathematical modelling approach

This is an author's accepted manuscript of an article published in “Drugs: Education, Prevention, and Policy "; Volume 18, Issue 2, 2011; copyright Taylor & Francis; available online at: http://dx.doi.org/10.3109/09687630903443299In this article, we analyse the evolution of cocaine consumption in Spain and we predict consumption trends over the next few years. Additionally, we simulate some scenarios which aim to reduce cocaine consumption in the future (sensitivity analysis). Assuming cocaine dependency is a socially transmitted epidemic disease, this leads us to propose an epidemiological-type mathematical model to study consumption evolution. Model sensitivity analysis allows us to design strategies and analyse their effects on cocaine consumption. The model predicts that 3.5% of the Spanish population will be habitual cocaine consumers by 2015. The simulations carried out suggest that cocaine consumption prevention strategies are the best policy to reduce the habitual consumer population. In this article, we show that epidemiological-type mathematical models can be a useful tool in the analysis of the repercussion of health policy proposals in the short-time future. © 2011 Informa UK Ltd.Sánchez, E.; Villanueva Micó, RJ.; Santonja, FJ.; Rubio, M. (2011). Predicting cocaine consumption in Spain: A mathematical modelling approach. Drugs: Education, Prevention, and Policy. 18(2):108-115. doi:10.3109/09687630903443299S108115182Blower, S. M., & Dowlatabadi, H. (1994). Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: An HIV Model, as an Example. International Statistical Review / Revue Internationale de Statistique, 62(2), 229. doi:10.2307/1403510Dutra, L., Stathopoulou, G., Basden, S. L., Leyro, T. M., Powers, M. B., & Otto, M. W. (2008). A Meta-Analytic Review of Psychosocial Interventions for Substance Use Disorders. American Journal of Psychiatry, 165(2), 179-187. doi:10.1176/appi.ajp.2007.06111851Gorman, D. M., Mezic, J., Mezic, I., & Gruenewald, P. J. (2006). Agent-Based Modeling of Drinking Behavior: A Preliminary Model and Potential Applications to Theory and Practice. American Journal of Public Health, 96(11), 2055-2060. doi:10.2105/ajph.2005.063289Jódar, L., Santonja, F. J., & González-Parra, G. (2008). Modeling dynamics of infant obesity in the region of Valencia, Spain. Computers & Mathematics with Applications, 56(3), 679-689. doi:10.1016/j.camwa.2008.01.011JOHNSON, B., ROACHE, J., AITDAOUD, N., JAVORS, M., HARRISON, J., ELKASHEF, A., … BLOCH, D. (2006). A preliminary randomized, double-blind, placebo-controlled study of the safety and efficacy of ondansetron in the treatment of cocaine dependence. Drug and Alcohol Dependence, 84(3), 256-263. doi:10.1016/j.drugalcdep.2006.02.011Levin, F. R., Evans, S. M., Brooks, D. J., & Garawi, F. (2007). Treatment of cocaine dependent treatment seekers with adult ADHD: Double-blind comparison of methylphenidate and placebo. Drug and Alcohol Dependence, 87(1), 20-29. doi:10.1016/j.drugalcdep.2006.07.004Marino, S., Hogue, I. B., Ray, C. J., & Kirschner, D. E. (2008). A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology, 254(1), 178-196. doi:10.1016/j.jtbi.2008.04.011Martcheva, M., & Castillo-Chavez, C. (2003). Diseases with chronic stage in a population with varying size. Mathematical Biosciences, 182(1), 1-25. doi:10.1016/s0025-5564(02)00184-0Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Computer Journal, 7(4), 308-313. doi:10.1093/comjnl/7.4.308Olsson, A., Sandberg, G., & Dahlblom, O. (2003). On Latin hypercube sampling for structural reliability analysis. Structural Safety, 25(1), 47-68. doi:10.1016/s0167-4730(02)00039-5Santonja, F. J., Tarazona, A. C., & Villanueva, R. J. (2008). A mathematical model of the pressure of an extreme ideology on a society. Computers & Mathematics with Applications, 56(3), 836-846. doi:10.1016/j.camwa.2008.01.001Schmitz, J. M., Stotts, A. L., Rhoades, H. M., & Grabowski, J. (2001). Naltrexone and relapse prevention treatment for cocaine-dependent patients. Addictive Behaviors, 26(2), 167-180. doi:10.1016/s0306-4603(00)00098-8Sharomi, O., & Gumel, A. B. (2008). Curtailing smoking dynamics: A mathematical modeling approach. Applied Mathematics and Computation, 195(2), 475-499. doi:10.1016/j.amc.2007.05.012Stotts, A. L., Mooney, M. E., Sayre, S. L., Novy, M., Schmitz, J. M., & Grabowski, J. (2007). Illusory predictors: Generalizability of findings in cocaine treatment retention research. Addictive Behaviors, 32(12), 2819-2836. doi:10.1016/j.addbeh.2007.04.020White, E., & Comiskey, C. (2007). Heroin epidemics, treatment and ODE modelling. Mathematical Biosciences, 208(1), 312-324. doi:10.1016/j.mbs.2006.10.00

Modeling the obesity epidemic: Social contagion and its implications for control

published_or_final_versio

Forward Bifurcation with Hysteresis Phenomena from Atherosclerosis Mathematical Model

Atherosclerosis is a non-communicable disease (NCDs) which appears when the blood vessels in the human body become thick and stiff. The symptoms range from chest pain, sudden numbness in the arms or legs, temporary loss of vision in one eye, or even kidney failure, which may lead to death. Treatment in cases with severe symptoms requires surgery, in which the number of doctors or hospitals is limited in some countries, especially countries with low health levels. This article aims to propose a mathematical model to understand the impact of limited hospital resources on the success of the control program of atherosclerosis spreads. The model was constructed based on a deterministic model, where the hospitalization rate is defined as a time-dependent saturated function concerning the number of infected individuals. The existence and stability of all possible equilibrium points were shown analytically and numerically, along with the basic reproduction number. Our analysis indicates that our model may exhibit various types of bifurcation phenomena, such as forward bifurcation, backward bifurcation, or a forward bifurcation with hysteresis depending on the value of hospitalization saturation parameter and the infection rate for treated infected individuals. These phenomenon triggers a complex and tricky control program of atherosclerosis. A forward bifurcation with hysteresis auses a possible condition of having more than one stable endemic equilibrium when the basic reproduction number is larger than one, but close to one. The more significant value of hospitalization saturation rate or the infection rate for treated infected individuals increases the possibility of the stable endemic equilibrium point even though the disease-free equilibrium is stable. Furthermore, the Pontryagin Maximum Principle was used to characterize the optimal control problem for our model. Based on the results of our analysis, we conclude that atherosclerosis control interventions should prioritize prevention efforts over endemic reduction scenarios to avoid high intervention costs. In addition, the government also needs to pay great attention to the availability of hospital services for this disease to avoid the dynamic complexity of the spread of atherosclerosis in the field

Uncertainty quantification in dynamical models. An application to cocaine consumption in Spain

[EN] The present Ph.D. Thesis considers epidemiological mathematical models based on ordinary differential equations and shows its application to understand the cocaine consumption epidemic in Spain. Three mathematical models are presented to predict the evolution of the epidemic in the near future in order to select the model that best reflects the data. By the results obtained for the selected model, if there are not changes in cocaine consumption policies or in the economic environment, the cocaine consumption will increase in Spain over the next few years. Furthermore, we use different techniques to estimate 95% confidence intervals and, consequently, quantify the uncertainty in the predictions. In addition, using several techniques, we conducted a model sensitivity analysis to determine which parameters are those that most influence the cocaine consumption in Spain. These analysis reveal that prevention actions on cocaine consumer population can be the most effective strategy to control this trend.[ES] La presente Tesis considera modelos matemáticos epidemiológicos basados en ecuaciones diferenciales ordinarias y muestra su aplicación para entender la epidemia del consumo de cocaína en España. Se presentan tres modelos matemáticos para predecir la evolución de dicha epidemia en un futuro próximo, con el objetivo de seleccionar el modelo que mejor refleja los datos. Por los resultados obtenidos para el modelo seleccionado, si no hay cambios en las políticas del consumo de cocaína ni en el ámbito económico, el consumo de cocaína aumentará en los próximos años. Además, utilizamos diferentes técnicas para estimar los intervalos de confianza al 95% y, de esta forma, cuantificar la incertidumbre en las predicciones. Finalmente, utilizando diferentes técnicas, hemos realizado un análisis de sensibilidad para determinar qué parámetros son los que más influyen en el consumo de cocaína. Estos análisis revelan que las acciones de prevención sobre la población de consumidores de cocaína pueden ser la estrategia más efectiva para controlar esta tendencia.[CA] La present Tesi considera models matemàtics epidemiològics basats en equacions diferencials ordinàries i mostra la seua aplicació per a entendre l'epidèmia del consum de cocaïna en Espanya. Es presenten tres models matemàtics per a predir l'evolució d'aquesta epidèmia en un futur pròxim, amb l'objectiu de seleccionar el model que millor reflecteix les dades. Pels resultats obtinguts per al model seleccionat, si no hi ha canvis en les polítiques de consum de cocaïna ni en l'àmbit econòmic, el consum de cocaïna augmentarà en els pròxims anys. A més, utilitzem diferents tècniques per a estimar els intervals de confiança al 95% i, d'aquesta manera, quantificar la incertesa en les prediccions. Finalment, utilitzant diferents tècniques, hem realitzat un anàlisi de sensibilitat per a determinar quins paràmetres són els que més influencien el consum de cocaïna. Aquestos anàlisis revelen que les accions de prevenció en la població de consumidors de cocaïna poden ser l'estratègia més efectiva per a controlar aquesta tendència.Rubio Monzó, M. (2015). Uncertainty quantification in dynamical models. An application to cocaine consumption in Spain [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/55844TESI

Contract and Grant Awards Fiscal Year 2005

I invite you to read this report Contract & Grant Awards, fiscal year 2005, which lists contract and grant (C&G) awards received by the University of New Mexico (UNM) during the period from July 1, 2004 - June 30, 2005 (FY05). These awards represent new funds that were acquired during FY05 by the main campus, branch campuses and education centers, and the Health Sciences Center (HSC). The HSC includes the School of Medicine, College of Nursing, and College of Pharmacy. The awards received for FY05 total $295.4M, of which$167.6M is attributed to the main campus and $127.8M to HSC. These awards assist in providing resources that are necessary to support and enhance the quality of research and teaching at UNM, as well as the opportunities for students to be trained in state-of-the-art laboratories in a variety of disciplines

Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion

We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering R0 (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when R0<1 and unstable when R0>1, whereas the two endemic equilibria appear from R0⁎ (a specific positive value reached by R0 and less than unity), one being asymptotically stable and the other unstable, but for R0>1 values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable