J. Héctor Morales
J. Héctor Morales
 

Taller de modelado matemático I

Presentación

Taller de modelado matemático I

 Maestría en Ciencias (Matemáticas Aplicadas e Industriales)

 Trimestre 20-I  Grupo CZ12  Clave: 2137079

Prof. José Héctor Morales Bárcenas

jhmb@xanum.uam.mx

Planeación

taller_I_20I.pdf

 

Tema principal

 Una introducción a la epidemiología matemática.

 

Temario

1. Introducción a la modelación matemática.

2. Epidemiología: infecciones, transmisión y modelos.

3. Dinámica de una infección en poblaciones.

4. Infecciones virales y el sistema inmunitario.

 

Planteamiento del problema matemático

Se presenta una colección de datos observacionales y se requieren determinar características de su tendencia media. De ser posible, determinar o estimar el o los sistemas dinámicos subyacentes que explican, reproducen y son capaces de predecir (interpolar y extrapolar) tendencias. Cabe aclarar que, aunque abordaremos el problema de la estimación estadística, no será a profundidad. Se dará énfasis al problema del planteamiento de modelos deterministas, basados en analogías con la cinética química, pero en todo momento quedarán claramente establecidas las hipótesis bajo las cuales los modelos aproximan al fenómeno en cuestión.

Finalmente, acerca de las simulaciones computacionales se sugiere aprender a programar en cualquier lenguaje, tanto R y R Studio como Python son de licencia libre, así también Octave. En mi opinión, éste último es compatible con Matlab y es mucha más fácil para implementar que otros. Hay varias referencias en la bibliografía (Allesina, Hansen).

 

Texto principal (presionar sobre el título)

 

Forma de evaluación

Tareas semanales, elaborar y entregar un proyecto final. La calificación total del Taller se promedia con la de la primer sección del mismo.

 

Tareas y lecturas (contestar y entregar las respuestas de las preguntas y ejercicios)

  1. tarea1_taller_20I.pdf
  2. Ejercicios 2.1, 2.2 y 2.3 del texto.
  3. Ejercicios 3.1, 3.2 y 3.3 del texto.
  4. Proyecto final Primera Parte del taller.

 

Referencias bibliográficas

  1. M. J. Keeling and P. Rohani, Modeling Infectious Diseases, Princeton University Press, 2008.
  2. H. van den Berg, Mathematical Models of Biology Systems, Oxford, 2011.
  3. David J. D. Earn, Pejman Rohani, Benjamin M. Bolker, Bryan T. Grenfell, ``A Simple Model for Complex Dynamical Transitions in Epidemics'', Science 287, 667-670 earn_rohani_bolker.pdf
  4. Steven L. Peck, ``A Tutorial for Understanding Ecological Modeling Papers for the Nonmodeler'', American Entomologist, Spring 2000 peck_ecological_modeling_2000.pdf
  5. O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases, Wiley, 2000.
  6. Klaus Dietz and J. A. P. Heesterbeek, ``Daniel Bernoulli's epidemiological model revisited'', Math. Biosci. 180 (2002) 1-21 DanielBernoulli.pdf
  7. Ottar N. Bjørnstad, Epidemics: Models and Data Using R, Springer, 2018.
  8. Andrew M. Hein and Benjamin T. Martin, ``Information limitation and the dynamics of coupled ecological systems'', Nature Ecology & Evolution 4, pp 82-90 (2020).
  9. Chun-Houh Chen and Ker-Chau Li, ``Can SIR be as Popular as Multiple Linear Regression?'', Statistica Sinica 8(1998), 289-316 chen_li_sir_linear_regression_ss_1998.pdf 
  10. Luis Tenorio, An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems, SIAM, 2017.
  11. Mark Woodward, Epidemiology: Study Design and Data Analysis, 3rd Ed., Chapman & Hall, 2014.
  12. Greenwood, M., ``The Application of Mathematics to Epidemiology'', Nature 97, pp. 243-244 (1916) greenwood_nature_1916.pdf
  13. Fred Brauer and Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, 2nd Ed., Springer, 2012.
  14. Fred Brauer, ``Review: Mathematical epidemiology is not an oxymoron'', BMC Public Health 2009, 9(Suppl 1):S2 brauer_review.pdf
  15. Gerardo Chowell and Fred Brauer, ``The Basic Reproduction Number of Infectious Diseases: Computation and Estimation Using Compartmental Epidemic Models'', in Mathematical and Statistical Estimation Approaches in Epidemiology, G.~Chowell, et al., Editors, Springer, 2009 chap_chowell_brauer.pdf
  16. A. P. Heesterbeek and M. G. Roberts, ``How mathematical epidemiology became a field of biology: a commentary on Anderson and May (1981) ‘The population dynamics of microparasites and their invertebrate hosts’'', Phil. Trans. R. Soc. B 370: 20140307 heesterbeek_roberts_2015.pdf
  17. Elizabeth S. Allman and John A. Rhodes, Mathematical Models in Biology: An Introduction, Cambridge, 2004.
  18. Clive L. Dym, Principles of Mathematical Modeling, 2nd Ed., Elsevier, 2004.
  19. Charles L. Nunn and Sonia Altizer, Infectious Diseases in Primates: Behavior, Ecology and Evolution, Oxford Series in Ecology and Evolution, Oxford, 2006.
  20. Ulf Dieckmann, Johan A. J. Metz, Maurice W. Sabelis, and Karl Sigmund (Editors), Adaptive Dynamics of Infectious Diseases: In Pursuit of Virulence Management, Cambridge, 2005.
  21. D. J. Daley and J. Gani, Epidemic Modelling: An Introduction, 1st Ed., Cambridge, 2005.
  22. Kenneth J. Rothman, Epidemiology: An Introduction, 2nd Ed., Oxford, 2012.
  23. David D. Celentano and Moyses Szklo, Gordis Epidemiology, 6th Ed., Elsevier, 2019.
  24. Michael Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases, Springer, 2018.
  25. Robert M. May, ``Uses and Abuses of Mathematics in Biology'', Science 303, 6 Feb 2004 may_science_303_2004.pdf 
  26. K. P. Hadeler, ``Parameter identification in epidemic models'', Math. Biosc. 229 (2011) 185-189 hadeler_parameter_identification_epidemic_models.pdf 
  27. D. Calvetti and E. Somersalo, Computational Mathematical Modeling, SIAM, 2013.
  28. Mya Breitbart and Forest Rohwer, ``Here a virus, there a virus, everywhere the same virus?'', TRENDS in Microbiology 13 (6) June 2006 breitbart_rohwer_virus.pdf
  29. Andrew M. Hein, ``Information limitation and the dynamics of coupled ecological systems'', Nature Ecology & Evolution 4, 82-90 (2020).
  30. James P. O'Dwyer, ``Beyond an ecological idela gas law'', Nature Ecology & Evolution 4, 14-15 (2020) odwyer_beyond_gas_law_nature_2019.pdf
  31. Marcelino Cereijido, Por qué no tenemos ciencia, 3a ed., Siglo XXI, 2008.
  32. Luis Villoro, Creer, saber, conocer, 2a ed., Siglo XXI, 1989.
  33. Ruy Pérez Tamayo, ¿Existe el método científico?, La ciencia para todos 161, FCE y El Colegio Nacional, 1990.
  34. León Olivé y Ruy Pérez Tamayo, Temas de ética y epistemología de la ciencia, FCE, 2011.
  35. S. Heinz, Mathematical Modeling, Springer, 2011.
  36. R. C. Aster, B. Borchers and C. H. Thurber. Parameter Estimation and Inverse Problems. Elsevier\Academic Press, 2005.
  37. J. P. Hespanha. Linear System Theory. Princeton University Press, 2009.
  38. A. Halevy, P. Norvig, and F. Pereira, (Google). "The Unreasonable Effectiveness of Data". IEEE Intelligent Systems, March/april 2009 35179.pdf
  39. Tom Siegfried. "Odds Are, It's Wrong". Science News 177 (7) (MARCH 27, 2010), pp. 26-29 25656121.pdf
  40. G. A. Diamond, and S. Kaul. "Prior Convictions: Bayesian Approaches to the Analysis and Interpretation of Clinical Megatrials". State-of-The-Art Paper. J. Am. Coll. Card. 43 (11) 2004 01035.pdf
  41. J. Harte. Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics. Oxford Series in Ecology and Evolution. Oxford University Press, 2011.
  42. Allesina, Stefano & Wilmes, Madlen, Computing Skills for Biologists: A Toolbox, Princeton, 2019.
  43. Hansen, Jesper Schmidt, GNU Octave Beginner's Guide, Packt Publishing Ltd., 2011 hansen_octave.pdf
  44. T. Vicsek. Fluctuations and Scaling in Biology. Oxford University Press, 2001.
  45. N. G. Van Kampen. "Determinism and Predictability". Synthese, Vol. 89, No. 2 (Nov., 1991), pp. 273-281 20116969.pdf
  46. K. S. Brown and J. P. Sethna. "Statistical mechanical approaches to models with many poorly known parameters". Phys. Rev. E 68, 021904 (2003) SloppyPRE.pdf
  47. S. I. Resnick. Adventures in Stochastic Processes. Birkhäuser, 3rd printing, 2002.
  48. H. Haken. Synergetics: Introduction and Advanced Topics. Springer, 2004.
  49. P. Bonacich & P. Lu. Introduction to Mathematical Sociology. Princeton University Press, 2012.

 


Recursos en línea

 

COVID-19 Math Modelling Seminar

The Fields Institute

July 1, 2019 to June 30, 2020

Location: Online

 

Organización Mundial de la Salud

 Coronavirus disease (COVID-19) Pandemic

https://www.who.int/emergencies/diseases/novel-coronavirus-2019

Sentinel Surveillance

 

International Mathematical Union

 COVID-19 Resource Website

The outbreak of the COVID-19 pandemic has changed modern society worldwide – and in particular, the way we work.

There is an almost universal temporary ban on international travel. As a consequence, numerous congresses, conferences, scientific meetings, and workshops have either been cancelled or postponed. Thus the traditional arena for exchanging ideas has come to a halt. However, many groups are utilizing modern technological solutions to offer online seminars in which we can all participate.

The spread of infectious diseases has also long been studied by mathematicians. Here we provide a few links to both current resources and recent activities in the field.


 

The Society for Industrial and Applied Mathematics

The SIAM Epidemiology Collection has been made freely available in response to the outbreak of the novel coronavirus SARS-CoV-2 and the associated disease COVID-19.  We hope this content on epidemiology, disease modeling, pandemics and vaccines will help in the rapid fight against this global problem https://epubs.siam.org/page/EpidemiologyCollection

 

El Colegio Nacional

Transmisiones en vivo https://colnal.mx

Las fases de la pandemia

Doctor Alejandro Macías

https://youtu.be/UzwbgpmpZsE

(visualizar después del minuto 11:05)

 

Página del Laboratorio de Origen de la Vida, UNAM

https://origendelavidaciencias.org


Molecular explorations through biology and medicine

Protein Data Bank (PDB)

http://pdb101.rcsb.org

PDB-101 helps teachers, students, and the general public explore the 3D world of proteins and nucleic acids. Learning about their diverse shapes and functions helps to understand all aspects of biomedicine and agriculture, from protein synthesis to health and disease to biological energy.

 

Prof. Matt Keeling, Director of Zeeman Institute (SBIDER), University of Warwick

https://warwick.ac.uk/fac/cross_fac/zeeman_institute/staffv2/keeling/

Warwick Infectious Disease Epidemiology Research

https://warwick.ac.uk/fac/cross_fac/wider

 

Comisión Universitaria para la Atención de la Emergencia Coronavirus, UNAM
https://covid19comisionunam.unamglobal.com

 

Worldometer

COVID-19 CORONAVIRUS PANDEMIC

https://www.worldometers.info/coronavirus

 

LA CRISIS DEL CORONAVIRUS

 La magnitud de la epidemia en México

Jorge Galindo y Javier Lafuente

 
Una estimación de EL PAÍS basada en datos oficiales del sistema de salud apunta a que el número de contagiados se sitúa entre 620.000 y 730.000