
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
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)
- Emilia Vynnycky and Richard G. White, An Introduction to Infectious Disease Modelling, Oxford University Press, 2010.
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)
- tarea1_taller_20I.pdf
- Ejercicios 2.1, 2.2 y 2.3 del texto.
- Ejercicios 3.1, 3.2 y 3.3 del texto.
- Proyecto final Primera Parte del taller.
Referencias bibliográficas
- M. J. Keeling and P. Rohani, Modeling Infectious Diseases, Princeton University Press, 2008.
- H. van den Berg, Mathematical Models of Biology Systems, Oxford, 2011.
- 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
- Steven L. Peck, ``A Tutorial for Understanding Ecological Modeling Papers for the Nonmodeler'', American Entomologist, Spring 2000 peck_ecological_modeling_2000.pdf
- O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases, Wiley, 2000.
- Klaus Dietz and J. A. P. Heesterbeek, ``Daniel Bernoulli's epidemiological model revisited'', Math. Biosci. 180 (2002) 1-21 DanielBernoulli.pdf
- Ottar N. Bjørnstad, Epidemics: Models and Data Using R, Springer, 2018.
- Andrew M. Hein and Benjamin T. Martin, ``Information limitation and the dynamics of coupled ecological systems'', Nature Ecology & Evolution 4, pp 82-90 (2020).
- 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
- Luis Tenorio, An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems, SIAM, 2017.
- Mark Woodward, Epidemiology: Study Design and Data Analysis, 3rd Ed., Chapman & Hall, 2014.
- Greenwood, M., ``The Application of Mathematics to Epidemiology'', Nature 97, pp. 243-244 (1916) greenwood_nature_1916.pdf
- Fred Brauer and Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, 2nd Ed., Springer, 2012.
- Fred Brauer, ``Review: Mathematical epidemiology is not an oxymoron'', BMC Public Health 2009, 9(Suppl 1):S2 brauer_review.pdf
- 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
- 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
- Elizabeth S. Allman and John A. Rhodes, Mathematical Models in Biology: An Introduction, Cambridge, 2004.
- Clive L. Dym, Principles of Mathematical Modeling, 2nd Ed., Elsevier, 2004.
- Charles L. Nunn and Sonia Altizer, Infectious Diseases in Primates: Behavior, Ecology and Evolution, Oxford Series in Ecology and Evolution, Oxford, 2006.
- 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.
- D. J. Daley and J. Gani, Epidemic Modelling: An Introduction, 1st Ed., Cambridge, 2005.
- Kenneth J. Rothman, Epidemiology: An Introduction, 2nd Ed., Oxford, 2012.
- David D. Celentano and Moyses Szklo, Gordis Epidemiology, 6th Ed., Elsevier, 2019.
- Michael Y. Li, An Introduction to Mathematical Modeling of Infectious Diseases, Springer, 2018.
- Robert M. May, ``Uses and Abuses of Mathematics in Biology'', Science 303, 6 Feb 2004 may_science_303_2004.pdf
- K. P. Hadeler, ``Parameter identification in epidemic models'', Math. Biosc. 229 (2011) 185-189 hadeler_parameter_identification_epidemic_models.pdf
- D. Calvetti and E. Somersalo, Computational Mathematical Modeling, SIAM, 2013.
- 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
- Andrew M. Hein, ``Information limitation and the dynamics of coupled ecological systems'', Nature Ecology & Evolution 4, 82-90 (2020).
- James P. O'Dwyer, ``Beyond an ecological idela gas law'', Nature Ecology & Evolution 4, 14-15 (2020) odwyer_beyond_gas_law_nature_2019.pdf
- Marcelino Cereijido, Por qué no tenemos ciencia, 3a ed., Siglo XXI, 2008.
- Luis Villoro, Creer, saber, conocer, 2a ed., Siglo XXI, 1989.
- Ruy Pérez Tamayo, ¿Existe el método científico?, La ciencia para todos 161, FCE y El Colegio Nacional, 1990.
- León Olivé y Ruy Pérez Tamayo, Temas de ética y epistemología de la ciencia, FCE, 2011.
- S. Heinz, Mathematical Modeling, Springer, 2011.
- R. C. Aster, B. Borchers and C. H. Thurber. Parameter Estimation and Inverse Problems. Elsevier\Academic Press, 2005.
- J. P. Hespanha. Linear System Theory. Princeton University Press, 2009.
- A. Halevy, P. Norvig, and F. Pereira, (Google). "The Unreasonable Effectiveness of Data". IEEE Intelligent Systems, March/april 2009 35179.pdf
- Tom Siegfried. "Odds Are, It's Wrong". Science News 177 (7) (MARCH 27, 2010), pp. 26-29 25656121.pdf
- 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
- J. Harte. Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics. Oxford Series in Ecology and Evolution. Oxford University Press, 2011.
- Allesina, Stefano & Wilmes, Madlen, Computing Skills for Biologists: A Toolbox, Princeton, 2019.
- Hansen, Jesper Schmidt, GNU Octave Beginner's Guide, Packt Publishing Ltd., 2011 hansen_octave.pdf
- T. Vicsek. Fluctuations and Scaling in Biology. Oxford University Press, 2001.
- N. G. Van Kampen. "Determinism and Predictability". Synthese, Vol. 89, No. 2 (Nov., 1991), pp. 273-281 20116969.pdf
- 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
- S. I. Resnick. Adventures in Stochastic Processes. Birkhäuser, 3rd printing, 2002.
- H. Haken. Synergetics: Introduction and Advanced Topics. Springer, 2004.
- 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
International Mathematical Union
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
(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)
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