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Importancia de los Modelos Matemáticos en
Salud Pública
César V. Munayco, MD, MSc, MPHDoctoral Student
Department of Preventive Medicine and BiometricsUniformed Services University of Health Sciences
Bethesda, Maryland, [email protected]
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Usos de los modelos matemáticos en Salud Pública
Informar sobre políticas de Salud Pública
Simulación teórica de la patogénesis de una enfermedad
Estimar el impacto de intervenciones sanitarias para controlar enfermedades epidémicas como influenza, VIH, etc.
Determianr el impacto en la salud y estudios de costo-efectividad de intervenciones
Basu S, Andrews J. Complexity in mathematical models of public health policies: a guide for consumers of models. PLoS Med. 2013 Oct;10(10):e1001540.
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¿Qué es un modelo matemático?
A mathematical model is an abstract model that uses
mathematical language to describe the behaviour of a system.
http://www.sciencedaily.com/articles/m/mathematical_model.htm
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“All models are wrong, but some are useful.”
George Box
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“Models should be as simple as possible, but not
simpler”Albert Einsten
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Principios del modelamiento matemático
Dym CL. Principles of mathematical modeling. 2nd ed. Amsterdam ; Boston: Elsevier Academic Press; 2004. xviii, 303 p. p.
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¿Cómo se crea un modelo?
Kallrath J. Modeling languages in mathematical optimization. Boston: Kluwer Academic Publishers; 2004. xxx, 407 p. p.
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¿Cómo se crea un modelo?
Kallrath J. Modeling languages in mathematical optimization. Boston: Kluwer Academic Publishers; 2004. xxx, 407 p. p.
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Tipo de modelos matemáticos
• Deterministic models: the same input will produce the same output. The only uncertainty in a deterministic model is generated by input variation.
• Stochastic models: model involves some randomness and will not produce the same output given the same input.
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Modelos determinísticos• Input factors: parameter values, initial conditions
• The input factors are uncertain due to• natural variation• error in measurements• lack of current measurement techniques
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Ejemplo SIR model
Keeling MJ, Danon L. Mathematical modelling of infectious diseases. British medical bulletin. 2009;92:33-42
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Modelo Complejo
Travis C. Porco, Sally M. Blower. Quantifying the Intrinsic Transmission Dynamics of Tuberculosis. Theoretical Population Biology 54, 117132 (1998)
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Fiiting model to the data
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Fiiting model to the data
beta=2.4029,gamma=0.9093,delta=0.4123
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Ejemplor de R0
Gregory E. Glass. Measuring Disease Dynamics in Populations: Characterizing the Likelihood of Control. On line course. Johns Hopkins University
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Relación entre la tasa de ataque y el R0
Gregory E. Glass. Measuring Disease Dynamics in Populations: Characterizing the Likelihood of Control. On line course. Johns Hopkins University
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Relación entre la inmunidad de grupo y el
R0
Gregory E. Glass. Measuring Disease Dynamics in Populations: Characterizing the Likelihood of Control. On line course. Johns Hopkins University
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Inmundidad de grupo y R0
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Inmunidad de grupo
*4 doses† Modified from Epid Rev 1993;15: 265-302, Am J Prev Med 2001; 20 (4S): 88-153, MMWR 2000; 49 (SS-9); 27-38
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Generaciones de una epidemia
Notes On R0. James Holland Jones. Department of Anthropological Sciences. Stanford University
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Análisis de sensibilidad• The objective of SA is to identify critical inputs
(parameters and initial conditions) of a model and quantifying how input uncertainty impacts model outcome(s).
• Local sensitivity analysis (LSA): examine change in output values based only on changes in one input factor.
• Global sensitivity analysis (GSA): examine change in output values when all parameter values change.
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Análisis de sensibilidad
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Análisis de sensibilidad
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Análisis de sensibilidad
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Análisis de sensibilidad
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Implicancias de dos parámetros diferentes
Basu S, Andrews J. Complexity in mathematical models of public health policies: a guide for consumers of models. PLoS Med. 2013 Oct;10(10):e1001540.
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Un ejemplo de sobreajuste de un
modelo
Basu S, Andrews J. Complexity in mathematical models of public health policies: a guide for consumers of models. PLoS Med. 2013 Oct;10(10):e1001540.
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Un ejemplo de sobreajuste de un modelo
Basu S, Andrews J. Complexity in mathematical models of public health policies: a guide for consumers of models. PLoS Med. 2013 Oct;10(10):e1001540.