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, USA.cesar.munayco@usuhs.edu

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.

¿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

“All models are wrong, but some are useful.”

George Box

“Models should be as simple as possible, but not

simpler”Albert Einsten

Principios del modelamiento matemático

Dym CL. Principles of mathematical modeling. 2nd ed. Amsterdam ; Boston: Elsevier Academic Press; 2004. xviii, 303 p. p.

¿Cómo se crea un modelo?

Kallrath J. Modeling languages in mathematical optimization. Boston: Kluwer Academic Publishers; 2004. xxx, 407 p. p.

¿Cómo se crea un modelo?

Kallrath J. Modeling languages in mathematical optimization. Boston: Kluwer Academic Publishers; 2004. xxx, 407 p. p.

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.

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

Ejemplo SIR model

Keeling MJ, Danon L. Mathematical modelling of infectious diseases. British medical bulletin. 2009;92:33-42

Modelo Complejo

Travis C. Porco, Sally M. Blower. Quantifying the Intrinsic Transmission Dynamics of Tuberculosis. Theoretical Population Biology 54, 117132 (1998)

Fiiting model to the data

Fiiting model to the data

beta=2.4029,gamma=0.9093,delta=0.4123

Conceptos

Ejemplor de R0

Gregory E. Glass. Measuring Disease Dynamics in Populations: Characterizing the Likelihood of Control. On line course. Johns Hopkins University

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

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

Inmundidad de grupo y R0

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

Generaciones de una epidemia

Notes On R0. James Holland Jones. Department of Anthropological Sciences. Stanford University

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.

Análisis de sensibilidad

Análisis de sensibilidad

Análisis de sensibilidad

Análisis de sensibilidad

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.

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.

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.