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A Stochastic Approach for Modeling Treatment and Diagnosis of Attention Deficit Disorder

Attention Deficit Disorder (ADD) is the most common type of mental disorder affecting children. It is estimated that, on the average, 6% of the total United States population is affected by this disorder. The exact causes have not been identified yet, although studies show that there is a genetic component. Our aim is to build an individual based mathematical model that includes the efficiency of the current treatment for ADD. We use a Markov chain approach to model the transitions through different states in a population of children. The asymptotic distribution of the population is computed as a function of the limiting probability of the transition probability matrix. The ratio of children without the disorder to children with disorder as a function of the probability of treatment efficiency is simulated and implications of variations on this ratio as a function of key parameters is described. The importance of early and efficient treatment as well as diagnosis are highlighted through sensitivity analyses performed on the model.

Article Number:
BU-1614-M

Year:
2002

Authors:
Carlos Acevedo-Estefanía, University of Texas-Austin
Carlos Torre, Cornell University
Ariel Cintrón-Arias, Cornell University
Carlos Hernandez-Suárez, Universidad de Colima-México
Sophonie Nashinyabakobeje, Cornell University

stochastic_approach_for_modeling_treatment_and_diagnosis_of_attention_deficit_disorder.pdf