Operator approach to epidemic systems in networks

ilustraciones

Autores:: Rojas Venegas, José Alejandro

Tipo de recurso:

Fecha de publicación:: 2022

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

id	UNACIONAL2_769460d1296f1ea95133a861481640e7
oai_identifier_str	oai:repositorio.unal.edu.co:unal/82980
network_acronym_str	UNACIONAL2
network_name_str	Universidad Nacional de Colombia
repository_id_str
dc.title.eng.fl_str_mv	Operator approach to epidemic systems in networks
dc.title.translated.spa.fl_str_mv	Aproximación de operadores a los sistemas epidémicos en redes
title	Operator approach to epidemic systems in networks
spellingShingle	Operator approach to epidemic systems in networks 530 - Física::539 - Física moderna 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 620 - Ingeniería y operaciones afines::621 - Física aplicada Análisis de redes Análisis de sistemas Network analysis System analysis Stochastic epidemic models Doi-Peliti operator formalism Metapopulation network modelling Modelos epidémicos estocásticos Formalismo de operadores de Doi- Peliti Modelamiento de redes de metapoblaciones
title_short	Operator approach to epidemic systems in networks
title_full	Operator approach to epidemic systems in networks
title_fullStr	Operator approach to epidemic systems in networks
title_full_unstemmed	Operator approach to epidemic systems in networks
title_sort	Operator approach to epidemic systems in networks
dc.creator.fl_str_mv	Rojas Venegas, José Alejandro
dc.contributor.advisor.none.fl_str_mv	Hurtado Heredia, Rafael Germán
dc.contributor.author.none.fl_str_mv	Rojas Venegas, José Alejandro
dc.contributor.educationalvalidator.none.fl_str_mv	Jesús Gómez-Gardeñes Zulma Cucunubá
dc.contributor.researchgroup.spa.fl_str_mv	Econofisica y Sociofisica
dc.subject.ddc.spa.fl_str_mv	530 - Física::539 - Física moderna 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 620 - Ingeniería y operaciones afines::621 - Física aplicada
topic	530 - Física::539 - Física moderna 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas 620 - Ingeniería y operaciones afines::621 - Física aplicada Análisis de redes Análisis de sistemas Network analysis System analysis Stochastic epidemic models Doi-Peliti operator formalism Metapopulation network modelling Modelos epidémicos estocásticos Formalismo de operadores de Doi- Peliti Modelamiento de redes de metapoblaciones
dc.subject.lemb.spa.fl_str_mv	Análisis de redes Análisis de sistemas
dc.subject.lemb.eng.fl_str_mv	Network analysis System analysis
dc.subject.proposal.eng.fl_str_mv	Stochastic epidemic models Doi-Peliti operator formalism Metapopulation network modelling
dc.subject.proposal.spa.fl_str_mv	Modelos epidémicos estocásticos Formalismo de operadores de Doi- Peliti Modelamiento de redes de metapoblaciones
description	ilustraciones
publishDate	2022
dc.date.issued.none.fl_str_mv	2022
dc.date.accessioned.none.fl_str_mv	2023-01-17T16:09:13Z
dc.date.available.none.fl_str_mv	2023-01-17T16:09:13Z
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv	Text
dc.type.redcol.spa.fl_str_mv	http://purl.org/redcol/resource_type/TM
status_str	acceptedVersion
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/82980
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/82980 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.references.spa.fl_str_mv	Aadrita, N. (2019). Stochastic Models of Emerging or Re-emerging Infectious Diseases: Probability of Outbreak, Epidemic Duration and Final Size. PhD thesis, Texas Tech University. Al-Mohy, A. H. and Higham, N. J. (2010). A new scaling and squaring algorithm for the matrix exponential. SIAM Journal on Matrix Analysis and Applications, 31(3):970–989. Al-Mohy, A. H. and Higham, N. J. (2010). A new scaling and squaring algorithm for the matrix exponential. SIAM Journal on Matrix Analysis and Applications, 31(3):970–989. Allen, L. J. (2017). A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis. Infectious Disease Modelling, 2(2):128–142. Arai, T. (2015). Path integral representation for stochastic jump processes with boundaries. Biswas, M. H. A., , Paiva, L. T., and de Pinho, M. (2014). A SEIR model for control of infectious diseases with constraints. Mathematical Biosciences and Engineering, 11(4):761–784. Brauer, F., van den Driessche, P., and Wu, J., editors (2008). Compartmental Models in Epidemiology, pages 19–79. Springer Berlin Heidelberg, Berlin, Heidelberg. Byrne, A. W., McEvoy, D., Collins, A. B., Hunt, K., Casey, M., Barber, A., Butler, F., Griffin, J., Lane, E. A., McAloon, C., Brien, K. O., Wall, P., Walsh, K. A., and More, S. J. (2020). Inferred duration of infectious period of SARS-CoV-2: rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases. BMJ Open, 10(8):e039856. Caicedo-Ochoa, Y., Rebell´on-S´anchez, D. E., Pe˜naloza-Rall´on, M., Cort´es-Motta, H. F., and M´endez-Fandi˜no, Y. R. (2020). Effective reproductive number estimation for initial stage of COVID-19 pandemic in latin american countries. International Journal of Infectious Diseases, 95:316–318. Cardy, J. (2006). Reaction-diffusion processes. Oxford, 1 edition. CDC (2021). Sars-cov-2 variant classifications and definitions. Colizza, V. and Vespignani, A. (2008). Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations. Journal of Theoretical Biology, 251(3):450–467. Cooper, I., Mondal, A., and Antonopoulos, C. G. (2020). A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons & Fractals, 139:110057. Dadlani, A., Afolabi, R. O., Jung, H., Sohraby, K., and Kim, K. (2020). Deterministic models in epidemiology: From modeling to implementation De, P., Singh, A. E., Wong, T., and Kaida, A. (2007). Predictors of gonorrhea reinfection in a cohort of sexually transmitted disease patients in alberta, canada, 1991–2003. Sexually Transmitted Diseases, 34(1):30–36. Dicker, R. C., Coronado, F., Koo, D., and Parrish, R. G. (2012). Principles of Epidemiology in Public Health Practice: An introduction to applied epidemiology and biostatistics. U.S. Departmentt of Health and Human Services, Centers for Disease Control and Prevention (CDC), Office of Workforce and Career Development, third edition. Dodd, P. J. and Ferguson, N. M. (2009). A many-body field theory approach to stochastic models in population biology. PLoS ONE, 4(9):e6855. Doi, M. (1976). Second quantization representation for classical many-particle system. Journal of Physics A: Mathematical and General, 9(9):1465–1477. El-Hay, T., Friedman, N., Koller, D., and Kupferman, R. (2012). Continuous time markov networks. Erten, E., Lizier, J., Piraveenan, M., and Prokopenko, M. (2017). Criticality and information dynamics in epidemiological models. Entropy, 19(5):194. Estrada, E. and Hatano, N. (2008). Communicability in complex networks. Physical Review E, 77(3). Ferraz de Arruda, G., Petri, G., Martin Rodriguez, P., and Moreno, Y. (2021). Multistability, intermittency and hybrid transitions in social contagion models on hypergraphs. arXiv e-prints, page arXiv:2112.04273. Gardiner, C. W. (2004). Handbook of stochastic methods for physics, chemistry and the natural sciences, volume 13 of Springer Series in Synergetics. Springer- Verlag, Berlin, third edition. Ghosh, I., Tiwari, P. K., Samanta, S., Elmojtaba, I. M., Al-Salti, N., and Chattopadhyay, J. (2018). A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear. Mathematical Biosciences, 306:160–169. Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25):2340–2361 Gillespie, D. T. (2007). Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 58(1):35–55. Haag, G. (2017). Modelling with the Master Equation. Springer International Publishing. Hammer, W. (1906). The milroy lectures on epidemic disease in england—the evidence of variability and of persistency of type. The Lancet, 167(4305):569– 574. Originally published as Volume 1, Issue 4305. Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4):599–653. Hunter, E., Namee, B. M., and Kelleher, J. D. (2017). A taxonomy for agentbased models in human infectious disease epidemiology. Journal of Artificial Societies and Social Simulation, 20(3). Institute, N. C. (2022). Nci dictionary of genetics terms. Keeling, M. and Ross, J. (2007). On methods for studying stochastic disease dynamics. Journal of The Royal Society Interface, 5(19):171–181. Keeling, M. J. and Eames, K. T. (2005). Networks and epidemic models. Journal of The Royal Society Interface, 2(4):295–307. Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772):700– 721. Manrique-Abril, F. G., Agudelo-Calderon, C. A., Gonzalez-Chorda, V. M., Gutierrez Lesmes, O., Tellez Pi˜neres, C. F., and Herrera-Amaya, G. (2020). Modelo SIR de la pandemia de COVID-19 en Colombia. Revista de Salud Publica, 22. Masuda, N. and Rocha, L. E. C. (2018). A gillespie algorithm for non-markovian stochastic processes. SIAM Review, 60(1):95–115. Mehdaoui, M. (2021). A review of commonly used compartmental models in epidemiology. Moein, S., Nickaeen, N., Roointan, A., Borhani, N., Heidary, Z., Javanmard, S. H., Ghaisari, J., and Gheisari, Y. (2021). Inefficiency of SIR models in forecasting COVID-19 epidemic: a case study of isfahan. Scientific Reports, 11(1). Moler, C. and Loan, C. V. (2003). Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49. Mondaini, L. (2015). Second quantization approach to stochastic epidemic models. Noyola-Martinez, J. C. (2008). Investigation of the tau-leap method for stochastic simulation. PhD thesis, Rice University. Pastor-Satorras, R., Castellano, C., Mieghem, P. V., and Vespignani, A. (2015). Epidemic processes in complex networks. Reviews of Modern Physics, 87(3):925–979. Pastor-Satorras, R. and Sol´e, R. V. (2001). Field theory for a reaction-diffusion model of quasispecies dynamics. Physical Review E, 64(5). Peliti, L. (1985). Path integral approach to birth-death processes on a lattice. J. Phys. France, 46(9):1469–1483 Rojas-Venegas, J. A., Hurtado, R., and Gomez-Garde˜nes, J. (2022). The consequences of locality and initial conditions in the operator approach to epidemic models. In process. Ross, R. (1916). An application of the theory of probabilities to the study of a priori pathometry.—part i. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 92(638):204– 230. Schiøler, H., Knudsen, T., Brøndum, R. F., Stoustrup, J., and Bøgsted, M. (2021). Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction. Scientific Reports, 11(1). Soriano-Pa˜nos, D., Lotero, L., Arenas, A., and G´omez-Garde˜nes, J. (2018). Spreading processes in multiplex metapopulations containing different mobility networks. Physical Review X, 8(3). Thanh, V. H. and Priami, C. (2015). Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm. The Journal of Chemical Physics, 143(5):054104. Treibert, S., , Brunner, H., Ehrhardt, M., , and and (2019). Compartment models for vaccine effectiveness and non-specific effects for tuberculosis. Mathematical Biosciences and Engineering, 16(6):7250–7298. van Wijland, F., Oerding, K., and Hilhorst, H. (1998). Wilson renormalization of a reaction–diffusion process. Physica A: Statistical Mechanics and its Applications, 251(1-2):179–201. Vargas-De-Le´on, C. (2011). On the global stability of SIS, SIR and SIRS epidemic models with standard incidence. Chaos, Solitons & Fractals, 44(12):1106–1110. Vastola, J. J. (2019). Solving the chemical master equation for monomolecular reaction systems analytically: a doi-peliti path integral view. Wasserman, S. and Faust, K. (1994). Social Network Analysis. Cambridge University Press. Weidlich, W. and Haag, G. (1982). Concepts and models of a quantitative sociology. Springer Series in Synergetics. Springer, Berlin, Germany. Whittle, P. (1955). The outcome of a stochastic epidemic- a note on bailey’s paper. Biometrika, 42(1-2):116–122. Willem, L., Verelst, F., Bilcke, J., Hens, N., and Beutels, P. (2017). Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015). BMC Infectious Diseases, 17(1).
dc.rights.coar.fl_str_mv	http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv	Atribución-CompartirIgual 4.0 Internacional
dc.rights.uri.spa.fl_str_mv	http://creativecommons.org/licenses/by-sa/4.0/
dc.rights.accessrights.spa.fl_str_mv	info:eu-repo/semantics/openAccess
rights_invalid_str_mv	Atribución-CompartirIgual 4.0 Internacional http://creativecommons.org/licenses/by-sa/4.0/ http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv	openAccess
dc.format.extent.spa.fl_str_mv	x, 80 páginas
dc.format.mimetype.spa.fl_str_mv	application/pdf
dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Maestría en Ciencias - Física
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
bitstream.url.fl_str_mv	https://repositorio.unal.edu.co/bitstream/unal/82980/1/license.txt https://repositorio.unal.edu.co/bitstream/unal/82980/3/1020814002-2022.pdf
bitstream.checksum.fl_str_mv	eb34b1cf90b7e1103fc9dfd26be24b4a 1295e99509b0c892a9ea6cc646c88546
bitstream.checksumAlgorithm.fl_str_mv	MD5 MD5
repository.name.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv	repositorio_nal@unal.edu.co
_version_	1806886412416450560
spelling	Atribución-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Hurtado Heredia, Rafael Germán1f7913fe245db1b00e2d9dfcfcb6cc0aRojas Venegas, José Alejandro2a30c7ecaab23055e0485e1f383e976bJesús Gómez-GardeñesZulma CucunubáEconofisica y Sociofisica2023-01-17T16:09:13Z2023-01-17T16:09:13Z2022https://repositorio.unal.edu.co/handle/unal/82980Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustracionesEpidemic models are a precious tool for public health and epidemiology as they can simulate the outcome of outbreaks based on assumptions and data. In particular, Stochastic epidemic models are an exciting tool that is based on the jump process theory; these models can be simulated with a field-like description called the “Doi-Peliti formalism”. This thesis aims to describe epidemic models in this formalism and exploit the structure and properties of the formalism and the models. Here I present a variety of results based on an operator representation of the Markovian Master Equation that is useful to simulate small systems, I also present a result that allows calculating the probability of no-outbreak even if the basic reproductive number is greater than one. At the end of the thesis, I present some results based on a τ -leap sampling algorithm for a metapopulation consisting of two subpopulations where migration plays a fundamental role, adding more stable states and creating interesting differential dynamics, especially in the case of slow migrations. (Texto tomado de la fuente)Los modelos epidémicos son una herramienta muy valiosa para la salud pública y la epidemiología dado que son capaces de simular el resultado de un brote basándose en asunciones y datos. En particular, los modelos epidémicos estocásticos son una herramienta interesante que está basada en la teoría de procesos de salto, estos modelos pueden ser simulados con una descripción similar a la teoría de campos llamada “Formalismo de Doi-Peliti”. El objetivo de esta tesis es describir modelos epidémicos en dicho formalismo utilizando propiedades del formalismo y de los modelos. Acá presento una variedad de resultados basado en una representación de operadores de la ecuación maestra Markoviana que son útiles para simular sistemas pequeños, también presento un resultado que permite calcular la probabilidad de que no exista un brote aún cuando el número reproductivo básico es mayor a uno. Al final de esta tesis presento algunos resultados basados en un algoritmo de muestreo llamado τ leap, este procedimiento lo aplico a metapoblaciones que consisten de dos subpoblaciones en las que la migración juega un rol fundamental, añadiendo más estados estables al sistema y creando una dinámica diferencial, especialmente en el caso de migraciones lentas.MaestríaMagíster en Ciencias - Físicax, 80 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - FísicaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá530 - Física::539 - Física moderna510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas620 - Ingeniería y operaciones afines::621 - Física aplicadaAnálisis de redesAnálisis de sistemasNetwork analysisSystem analysisStochastic epidemic modelsDoi-Peliti operator formalismMetapopulation network modellingModelos epidémicos estocásticosFormalismo de operadores de Doi- PelitiModelamiento de redes de metapoblacionesOperator approach to epidemic systems in networksAproximación de operadores a los sistemas epidémicos en redesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAadrita, N. (2019). Stochastic Models of Emerging or Re-emerging Infectious Diseases: Probability of Outbreak, Epidemic Duration and Final Size. PhD thesis, Texas Tech University.Al-Mohy, A. H. and Higham, N. J. (2010). A new scaling and squaring algorithm for the matrix exponential. SIAM Journal on Matrix Analysis and Applications, 31(3):970–989.Al-Mohy, A. H. and Higham, N. J. (2010). A new scaling and squaring algorithm for the matrix exponential. SIAM Journal on Matrix Analysis and Applications, 31(3):970–989.Allen, L. J. (2017). A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis. Infectious Disease Modelling, 2(2):128–142.Arai, T. (2015). Path integral representation for stochastic jump processes with boundaries.Biswas, M. H. A., , Paiva, L. T., and de Pinho, M. (2014). A SEIR model for control of infectious diseases with constraints. Mathematical Biosciences and Engineering, 11(4):761–784.Brauer, F., van den Driessche, P., and Wu, J., editors (2008). Compartmental Models in Epidemiology, pages 19–79. Springer Berlin Heidelberg, Berlin, Heidelberg.Byrne, A. W., McEvoy, D., Collins, A. B., Hunt, K., Casey, M., Barber, A., Butler, F., Griffin, J., Lane, E. A., McAloon, C., Brien, K. O., Wall, P., Walsh, K. A., and More, S. J. (2020). Inferred duration of infectious period of SARS-CoV-2: rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases. BMJ Open, 10(8):e039856.Caicedo-Ochoa, Y., Rebell´on-S´anchez, D. E., Pe˜naloza-Rall´on, M., Cort´es-Motta, H. F., and M´endez-Fandi˜no, Y. R. (2020). Effective reproductive number estimation for initial stage of COVID-19 pandemic in latin american countries. International Journal of Infectious Diseases, 95:316–318.Cardy, J. (2006). Reaction-diffusion processes. Oxford, 1 edition.CDC (2021). Sars-cov-2 variant classifications and definitions.Colizza, V. and Vespignani, A. (2008). Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations. Journal of Theoretical Biology, 251(3):450–467.Cooper, I., Mondal, A., and Antonopoulos, C. G. (2020). A SIR model assumption for the spread of COVID-19 in different communities. Chaos, Solitons & Fractals, 139:110057.Dadlani, A., Afolabi, R. O., Jung, H., Sohraby, K., and Kim, K. (2020). Deterministic models in epidemiology: From modeling to implementationDe, P., Singh, A. E., Wong, T., and Kaida, A. (2007). Predictors of gonorrhea reinfection in a cohort of sexually transmitted disease patients in alberta, canada, 1991–2003. Sexually Transmitted Diseases, 34(1):30–36.Dicker, R. C., Coronado, F., Koo, D., and Parrish, R. G. (2012). Principles of Epidemiology in Public Health Practice: An introduction to applied epidemiology and biostatistics. U.S. Departmentt of Health and Human Services, Centers for Disease Control and Prevention (CDC), Office of Workforce and Career Development, third edition.Dodd, P. J. and Ferguson, N. M. (2009). A many-body field theory approach to stochastic models in population biology. PLoS ONE, 4(9):e6855.Doi, M. (1976). Second quantization representation for classical many-particle system. Journal of Physics A: Mathematical and General, 9(9):1465–1477.El-Hay, T., Friedman, N., Koller, D., and Kupferman, R. (2012). Continuous time markov networks.Erten, E., Lizier, J., Piraveenan, M., and Prokopenko, M. (2017). Criticality and information dynamics in epidemiological models. Entropy, 19(5):194.Estrada, E. and Hatano, N. (2008). Communicability in complex networks. Physical Review E, 77(3).Ferraz de Arruda, G., Petri, G., Martin Rodriguez, P., and Moreno, Y. (2021). Multistability, intermittency and hybrid transitions in social contagion models on hypergraphs. arXiv e-prints, page arXiv:2112.04273.Gardiner, C. W. (2004). Handbook of stochastic methods for physics, chemistry and the natural sciences, volume 13 of Springer Series in Synergetics. Springer- Verlag, Berlin, third edition.Ghosh, I., Tiwari, P. K., Samanta, S., Elmojtaba, I. M., Al-Salti, N., and Chattopadhyay, J. (2018). A simple SI-type model for HIV/AIDS with media and self-imposed psychological fear. Mathematical Biosciences, 306:160–169.Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25):2340–2361Gillespie, D. T. (2007). Stochastic simulation of chemical kinetics. Annual Review of Physical Chemistry, 58(1):35–55.Haag, G. (2017). Modelling with the Master Equation. Springer International Publishing.Hammer, W. (1906). The milroy lectures on epidemic disease in england—the evidence of variability and of persistency of type. The Lancet, 167(4305):569– 574. Originally published as Volume 1, Issue 4305.Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42(4):599–653.Hunter, E., Namee, B. M., and Kelleher, J. D. (2017). A taxonomy for agentbased models in human infectious disease epidemiology. Journal of Artificial Societies and Social Simulation, 20(3).Institute, N. C. (2022). Nci dictionary of genetics terms.Keeling, M. and Ross, J. (2007). On methods for studying stochastic disease dynamics. Journal of The Royal Society Interface, 5(19):171–181.Keeling, M. J. and Eames, K. T. (2005). Networks and epidemic models. Journal of The Royal Society Interface, 2(4):295–307.Kermack, W. O. and McKendrick, A. G. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 115(772):700– 721.Manrique-Abril, F. G., Agudelo-Calderon, C. A., Gonzalez-Chorda, V. M., Gutierrez Lesmes, O., Tellez Pi˜neres, C. F., and Herrera-Amaya, G. (2020). Modelo SIR de la pandemia de COVID-19 en Colombia. Revista de Salud Publica, 22.Masuda, N. and Rocha, L. E. C. (2018). A gillespie algorithm for non-markovian stochastic processes. SIAM Review, 60(1):95–115.Mehdaoui, M. (2021). A review of commonly used compartmental models in epidemiology.Moein, S., Nickaeen, N., Roointan, A., Borhani, N., Heidary, Z., Javanmard, S. H., Ghaisari, J., and Gheisari, Y. (2021). Inefficiency of SIR models in forecasting COVID-19 epidemic: a case study of isfahan. Scientific Reports, 11(1).Moler, C. and Loan, C. V. (2003). Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49.Mondaini, L. (2015). Second quantization approach to stochastic epidemic models.Noyola-Martinez, J. C. (2008). Investigation of the tau-leap method for stochastic simulation. PhD thesis, Rice University.Pastor-Satorras, R., Castellano, C., Mieghem, P. V., and Vespignani, A. (2015). Epidemic processes in complex networks. Reviews of Modern Physics, 87(3):925–979.Pastor-Satorras, R. and Sol´e, R. V. (2001). Field theory for a reaction-diffusion model of quasispecies dynamics. Physical Review E, 64(5).Peliti, L. (1985). Path integral approach to birth-death processes on a lattice. J. Phys. France, 46(9):1469–1483Rojas-Venegas, J. A., Hurtado, R., and Gomez-Garde˜nes, J. (2022). The consequences of locality and initial conditions in the operator approach to epidemic models. In process.Ross, R. (1916). An application of the theory of probabilities to the study of a priori pathometry.—part i. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 92(638):204– 230.Schiøler, H., Knudsen, T., Brøndum, R. F., Stoustrup, J., and Bøgsted, M. (2021). Mathematical modelling of SARS-CoV-2 variant outbreaks reveals their probability of extinction. Scientific Reports, 11(1).Soriano-Pa˜nos, D., Lotero, L., Arenas, A., and G´omez-Garde˜nes, J. (2018). Spreading processes in multiplex metapopulations containing different mobility networks. Physical Review X, 8(3).Thanh, V. H. and Priami, C. (2015). Simulation of biochemical reactions with time-dependent rates by the rejection-based algorithm. The Journal of Chemical Physics, 143(5):054104.Treibert, S., , Brunner, H., Ehrhardt, M., , and and (2019). Compartment models for vaccine effectiveness and non-specific effects for tuberculosis. Mathematical Biosciences and Engineering, 16(6):7250–7298.van Wijland, F., Oerding, K., and Hilhorst, H. (1998). Wilson renormalization of a reaction–diffusion process. Physica A: Statistical Mechanics and its Applications, 251(1-2):179–201.Vargas-De-Le´on, C. (2011). On the global stability of SIS, SIR and SIRS epidemic models with standard incidence. Chaos, Solitons & Fractals, 44(12):1106–1110.Vastola, J. J. (2019). Solving the chemical master equation for monomolecular reaction systems analytically: a doi-peliti path integral view.Wasserman, S. and Faust, K. (1994). Social Network Analysis. Cambridge University Press.Weidlich, W. and Haag, G. (1982). Concepts and models of a quantitative sociology. Springer Series in Synergetics. Springer, Berlin, Germany.Whittle, P. (1955). The outcome of a stochastic epidemic- a note on bailey’s paper. Biometrika, 42(1-2):116–122.Willem, L., Verelst, F., Bilcke, J., Hens, N., and Beutels, P. (2017). Lessons from a decade of individual-based models for infectious disease transmission: a systematic review (2006-2015). BMC Infectious Diseases, 17(1).InvestigadoresLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/82980/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1020814002-2022.pdf1020814002-2022.pdfTesis de Maestría en Ciencias - Físicaapplication/pdf6257957https://repositorio.unal.edu.co/bitstream/unal/82980/3/1020814002-2022.pdf1295e99509b0c892a9ea6cc646c88546MD53unal/82980oai:repositorio.unal.edu.co:unal/829802023-01-17 11:11:16.592Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.coUEFSVEUgMS4gVMOJUk1JTk9TIERFIExBIExJQ0VOQ0lBIFBBUkEgUFVCTElDQUNJw5NOIERFIE9CUkFTIEVOIEVMIFJFUE9TSVRPUklPIElOU1RJVFVDSU9OQUwgVU5BTC4KCkxvcyBhdXRvcmVzIHkvbyB0aXR1bGFyZXMgZGUgbG9zIGRlcmVjaG9zIHBhdHJpbW9uaWFsZXMgZGUgYXV0b3IsIGNvbmZpZXJlbiBhIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHVuYSBsaWNlbmNpYSBubyBleGNsdXNpdmEsIGxpbWl0YWRhIHkgZ3JhdHVpdGEgc29icmUgbGEgb2JyYSBxdWUgc2UgaW50ZWdyYSBlbiBlbCBSZXBvc2l0b3JpbyBJbnN0aXR1Y2lvbmFsLCBiYWpvIGxvcyBzaWd1aWVudGVzIHTDqXJtaW5vczoKCgphKQlMb3MgYXV0b3JlcyB5L28gbG9zIHRpdHVsYXJlcyBkZSBsb3MgZGVyZWNob3MgcGF0cmltb25pYWxlcyBkZSBhdXRvciBzb2JyZSBsYSBvYnJhIGNvbmZpZXJlbiBhIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHVuYSBsaWNlbmNpYSBubyBleGNsdXNpdmEgcGFyYSByZWFsaXphciBsb3Mgc2lndWllbnRlcyBhY3RvcyBzb2JyZSBsYSBvYnJhOiBpKSByZXByb2R1Y2lyIGxhIG9icmEgZGUgbWFuZXJhIGRpZ2l0YWwsIHBlcm1hbmVudGUgbyB0ZW1wb3JhbCwgaW5jbHV5ZW5kbyBlbCBhbG1hY2VuYW1pZW50byBlbGVjdHLDs25pY28sIGFzw60gY29tbyBjb252ZXJ0aXIgZWwgZG9jdW1lbnRvIGVuIGVsIGN1YWwgc2UgZW5jdWVudHJhIGNvbnRlbmlkYSBsYSBvYnJhIGEgY3VhbHF1aWVyIG1lZGlvIG8gZm9ybWF0byBleGlzdGVudGUgYSBsYSBmZWNoYSBkZSBsYSBzdXNjcmlwY2nDs24gZGUgbGEgcHJlc2VudGUgbGljZW5jaWEsIHkgaWkpIGNvbXVuaWNhciBhbCBww7pibGljbyBsYSBvYnJhIHBvciBjdWFscXVpZXIgbWVkaW8gbyBwcm9jZWRpbWllbnRvLCBlbiBtZWRpb3MgYWzDoW1icmljb3MgbyBpbmFsw6FtYnJpY29zLCBpbmNsdXllbmRvIGxhIHB1ZXN0YSBhIGRpc3Bvc2ljacOzbiBlbiBhY2Nlc28gYWJpZXJ0by4gQWRpY2lvbmFsIGEgbG8gYW50ZXJpb3IsIGVsIGF1dG9yIHkvbyB0aXR1bGFyIGF1dG9yaXphIGEgbGEgVW5pdmVyc2lkYWQgTmFjaW9uYWwgZGUgQ29sb21iaWEgcGFyYSBxdWUsIGVuIGxhIHJlcHJvZHVjY2nDs24geSBjb211bmljYWNpw7NuIGFsIHDDumJsaWNvIHF1ZSBsYSBVbml2ZXJzaWRhZCByZWFsaWNlIHNvYnJlIGxhIG9icmEsIGhhZ2EgbWVuY2nDs24gZGUgbWFuZXJhIGV4cHJlc2EgYWwgdGlwbyBkZSBsaWNlbmNpYSBDcmVhdGl2ZSBDb21tb25zIGJham8gbGEgY3VhbCBlbCBhdXRvciB5L28gdGl0dWxhciBkZXNlYSBvZnJlY2VyIHN1IG9icmEgYSBsb3MgdGVyY2Vyb3MgcXVlIGFjY2VkYW4gYSBkaWNoYSBvYnJhIGEgdHJhdsOpcyBkZWwgUmVwb3NpdG9yaW8gSW5zdGl0dWNpb25hbCwgY3VhbmRvIHNlYSBlbCBjYXNvLiBFbCBhdXRvciB5L28gdGl0dWxhciBkZSBsb3MgZGVyZWNob3MgcGF0cmltb25pYWxlcyBkZSBhdXRvciBwb2Ryw6EgZGFyIHBvciB0ZXJtaW5hZGEgbGEgcHJlc2VudGUgbGljZW5jaWEgbWVkaWFudGUgc29saWNpdHVkIGVsZXZhZGEgYSBsYSBEaXJlY2Npw7NuIE5hY2lvbmFsIGRlIEJpYmxpb3RlY2FzIGRlIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhLiAKCmIpIAlMb3MgYXV0b3JlcyB5L28gdGl0dWxhcmVzIGRlIGxvcyBkZXJlY2hvcyBwYXRyaW1vbmlhbGVzIGRlIGF1dG9yIHNvYnJlIGxhIG9icmEgY29uZmllcmVuIGxhIGxpY2VuY2lhIHNlw7FhbGFkYSBlbiBlbCBsaXRlcmFsIGEpIGRlbCBwcmVzZW50ZSBkb2N1bWVudG8gcG9yIGVsIHRpZW1wbyBkZSBwcm90ZWNjacOzbiBkZSBsYSBvYnJhIGVuIHRvZG9zIGxvcyBwYcOtc2VzIGRlbCBtdW5kbywgZXN0byBlcywgc2luIGxpbWl0YWNpw7NuIHRlcnJpdG9yaWFsIGFsZ3VuYS4KCmMpCUxvcyBhdXRvcmVzIHkvbyB0aXR1bGFyZXMgZGUgZGVyZWNob3MgcGF0cmltb25pYWxlcyBkZSBhdXRvciBtYW5pZmllc3RhbiBlc3RhciBkZSBhY3VlcmRvIGNvbiBxdWUgbGEgcHJlc2VudGUgbGljZW5jaWEgc2Ugb3RvcmdhIGEgdMOtdHVsbyBncmF0dWl0bywgcG9yIGxvIHRhbnRvLCByZW51bmNpYW4gYSByZWNpYmlyIGN1YWxxdWllciByZXRyaWJ1Y2nDs24gZWNvbsOzbWljYSBvIGVtb2x1bWVudG8gYWxndW5vIHBvciBsYSBwdWJsaWNhY2nDs24sIGRpc3RyaWJ1Y2nDs24sIGNvbXVuaWNhY2nDs24gcMO6YmxpY2EgeSBjdWFscXVpZXIgb3RybyB1c28gcXVlIHNlIGhhZ2EgZW4gbG9zIHTDqXJtaW5vcyBkZSBsYSBwcmVzZW50ZSBsaWNlbmNpYSB5IGRlIGxhIGxpY2VuY2lhIENyZWF0aXZlIENvbW1vbnMgY29uIHF1ZSBzZSBwdWJsaWNhLgoKZCkJUXVpZW5lcyBmaXJtYW4gZWwgcHJlc2VudGUgZG9jdW1lbnRvIGRlY2xhcmFuIHF1ZSBwYXJhIGxhIGNyZWFjacOzbiBkZSBsYSBvYnJhLCBubyBzZSBoYW4gdnVsbmVyYWRvIGxvcyBkZXJlY2hvcyBkZSBwcm9waWVkYWQgaW50ZWxlY3R1YWwsIGluZHVzdHJpYWwsIG1vcmFsZXMgeSBwYXRyaW1vbmlhbGVzIGRlIHRlcmNlcm9zLiBEZSBvdHJhIHBhcnRlLCAgcmVjb25vY2VuIHF1ZSBsYSBVbml2ZXJzaWRhZCBOYWNpb25hbCBkZSBDb2xvbWJpYSBhY3TDumEgY29tbyB1biB0ZXJjZXJvIGRlIGJ1ZW5hIGZlIHkgc2UgZW5jdWVudHJhIGV4ZW50YSBkZSBjdWxwYSBlbiBjYXNvIGRlIHByZXNlbnRhcnNlIGFsZ8O6biB0aXBvIGRlIHJlY2xhbWFjacOzbiBlbiBtYXRlcmlhIGRlIGRlcmVjaG9zIGRlIGF1dG9yIG8gcHJvcGllZGFkIGludGVsZWN0dWFsIGVuIGdlbmVyYWwuIFBvciBsbyB0YW50bywgbG9zIGZpcm1hbnRlcyAgYWNlcHRhbiBxdWUgY29tbyB0aXR1bGFyZXMgw7puaWNvcyBkZSBsb3MgZGVyZWNob3MgcGF0cmltb25pYWxlcyBkZSBhdXRvciwgYXN1bWlyw6FuIHRvZGEgbGEgcmVzcG9uc2FiaWxpZGFkIGNpdmlsLCBhZG1pbmlzdHJhdGl2YSB5L28gcGVuYWwgcXVlIHB1ZWRhIGRlcml2YXJzZSBkZSBsYSBwdWJsaWNhY2nDs24gZGUgbGEgb2JyYS4gIAoKZikJQXV0b3JpemFuIGEgbGEgVW5pdmVyc2lkYWQgTmFjaW9uYWwgZGUgQ29sb21iaWEgaW5jbHVpciBsYSBvYnJhIGVuIGxvcyBhZ3JlZ2Fkb3JlcyBkZSBjb250ZW5pZG9zLCBidXNjYWRvcmVzIGFjYWTDqW1pY29zLCBtZXRhYnVzY2Fkb3Jlcywgw61uZGljZXMgeSBkZW3DoXMgbWVkaW9zIHF1ZSBzZSBlc3RpbWVuIG5lY2VzYXJpb3MgcGFyYSBwcm9tb3ZlciBlbCBhY2Nlc28geSBjb25zdWx0YSBkZSBsYSBtaXNtYS4gCgpnKQlFbiBlbCBjYXNvIGRlIGxhcyB0ZXNpcyBjcmVhZGFzIHBhcmEgb3B0YXIgZG9ibGUgdGl0dWxhY2nDs24sIGxvcyBmaXJtYW50ZXMgc2Vyw6FuIGxvcyByZXNwb25zYWJsZXMgZGUgY29tdW5pY2FyIGEgbGFzIGluc3RpdHVjaW9uZXMgbmFjaW9uYWxlcyBvIGV4dHJhbmplcmFzIGVuIGNvbnZlbmlvLCBsYXMgbGljZW5jaWFzIGRlIGFjY2VzbyBhYmllcnRvIENyZWF0aXZlIENvbW1vbnMgeSBhdXRvcml6YWNpb25lcyBhc2lnbmFkYXMgYSBzdSBvYnJhIHBhcmEgbGEgcHVibGljYWNpw7NuIGVuIGVsIFJlcG9zaXRvcmlvIEluc3RpdHVjaW9uYWwgVU5BTCBkZSBhY3VlcmRvIGNvbiBsYXMgZGlyZWN0cmljZXMgZGUgbGEgUG9sw610aWNhIEdlbmVyYWwgZGUgbGEgQmlibGlvdGVjYSBEaWdpdGFsLgoKCmgpCVNlIGF1dG9yaXphIGEgbGEgVW5pdmVyc2lkYWQgTmFjaW9uYWwgZGUgQ29sb21iaWEgY29tbyByZXNwb25zYWJsZSBkZWwgdHJhdGFtaWVudG8gZGUgZGF0b3MgcGVyc29uYWxlcywgZGUgYWN1ZXJkbyBjb24gbGEgbGV5IDE1ODEgZGUgMjAxMiBlbnRlbmRpZW5kbyBxdWUgc2UgZW5jdWVudHJhbiBiYWpvIG1lZGlkYXMgcXVlIGdhcmFudGl6YW4gbGEgc2VndXJpZGFkLCBjb25maWRlbmNpYWxpZGFkIGUgaW50ZWdyaWRhZCwgeSBzdSB0cmF0YW1pZW50byB0aWVuZSB1bmEgZmluYWxpZGFkIGhpc3TDs3JpY2EsIGVzdGFkw61zdGljYSBvIGNpZW50w61maWNhIHNlZ8O6biBsbyBkaXNwdWVzdG8gZW4gbGEgUG9sw610aWNhIGRlIFRyYXRhbWllbnRvIGRlIERhdG9zIFBlcnNvbmFsZXMuCgoKClBBUlRFIDIuIEFVVE9SSVpBQ0nDk04gUEFSQSBQVUJMSUNBUiBZIFBFUk1JVElSIExBIENPTlNVTFRBIFkgVVNPIERFIE9CUkFTIEVOIEVMIFJFUE9TSVRPUklPIElOU1RJVFVDSU9OQUwgVU5BTC4KClNlIGF1dG9yaXphIGxhIHB1YmxpY2FjacOzbiBlbGVjdHLDs25pY2EsIGNvbnN1bHRhIHkgdXNvIGRlIGxhIG9icmEgcG9yIHBhcnRlIGRlIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHkgZGUgc3VzIHVzdWFyaW9zIGRlIGxhIHNpZ3VpZW50ZSBtYW5lcmE6CgphLglDb25jZWRvIGxpY2VuY2lhIGVuIGxvcyB0w6lybWlub3Mgc2XDsWFsYWRvcyBlbiBsYSBwYXJ0ZSAxIGRlbCBwcmVzZW50ZSBkb2N1bWVudG8sIGNvbiBlbCBvYmpldGl2byBkZSBxdWUgbGEgb2JyYSBlbnRyZWdhZGEgc2VhIHB1YmxpY2FkYSBlbiBlbCBSZXBvc2l0b3JpbyBJbnN0aXR1Y2lvbmFsIGRlIGxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhIHkgcHVlc3RhIGEgZGlzcG9zaWNpw7NuIGVuIGFjY2VzbyBhYmllcnRvIHBhcmEgc3UgY29uc3VsdGEgcG9yIGxvcyB1c3VhcmlvcyBkZSBsYSBVbml2ZXJzaWRhZCBOYWNpb25hbCBkZSBDb2xvbWJpYSAgYSB0cmF2w6lzIGRlIGludGVybmV0LgoKCgpQQVJURSAzIEFVVE9SSVpBQ0nDk04gREUgVFJBVEFNSUVOVE8gREUgREFUT1MgUEVSU09OQUxFUy4KCkxhIFVuaXZlcnNpZGFkIE5hY2lvbmFsIGRlIENvbG9tYmlhLCBjb21vIHJlc3BvbnNhYmxlIGRlbCBUcmF0YW1pZW50byBkZSBEYXRvcyBQZXJzb25hbGVzLCBpbmZvcm1hIHF1ZSBsb3MgZGF0b3MgZGUgY2Fyw6FjdGVyIHBlcnNvbmFsIHJlY29sZWN0YWRvcyBtZWRpYW50ZSBlc3RlIGZvcm11bGFyaW8sIHNlIGVuY3VlbnRyYW4gYmFqbyBtZWRpZGFzIHF1ZSBnYXJhbnRpemFuIGxhIHNlZ3VyaWRhZCwgY29uZmlkZW5jaWFsaWRhZCBlIGludGVncmlkYWQgeSBzdSB0cmF0YW1pZW50byBzZSByZWFsaXphIGRlIGFjdWVyZG8gYWwgY3VtcGxpbWllbnRvIG5vcm1hdGl2byBkZSBsYSBMZXkgMTU4MSBkZSAyMDEyIHkgZGUgbGEgUG9sw610aWNhIGRlIFRyYXRhbWllbnRvIGRlIERhdG9zIFBlcnNvbmFsZXMgZGUgbGEgVW5pdmVyc2lkYWQgTmFjaW9uYWwgZGUgQ29sb21iaWEuIFB1ZWRlIGVqZXJjZXIgc3VzIGRlcmVjaG9zIGNvbW8gdGl0dWxhciBhIGNvbm9jZXIsIGFjdHVhbGl6YXIsIHJlY3RpZmljYXIgeSByZXZvY2FyIGxhcyBhdXRvcml6YWNpb25lcyBkYWRhcyBhIGxhcyBmaW5hbGlkYWRlcyBhcGxpY2FibGVzIGEgdHJhdsOpcyBkZSBsb3MgY2FuYWxlcyBkaXNwdWVzdG9zIHkgZGlzcG9uaWJsZXMgZW4gd3d3LnVuYWwuZWR1LmNvIG8gZS1tYWlsOiBwcm90ZWNkYXRvc19uYUB1bmFsLmVkdS5jbyIKClRlbmllbmRvIGVuIGN1ZW50YSBsbyBhbnRlcmlvciwgYXV0b3Jpem8gZGUgbWFuZXJhIHZvbHVudGFyaWEsIHByZXZpYSwgZXhwbMOtY2l0YSwgaW5mb3JtYWRhIGUgaW5lcXXDrXZvY2EgYSBsYSBVbml2ZXJzaWRhZCBOYWNpb25hbCBkZSBDb2xvbWJpYSBhIHRyYXRhciBsb3MgZGF0b3MgcGVyc29uYWxlcyBkZSBhY3VlcmRvIGNvbiBsYXMgZmluYWxpZGFkZXMgZXNwZWPDrWZpY2FzIHBhcmEgZWwgZGVzYXJyb2xsbyB5IGVqZXJjaWNpbyBkZSBsYXMgZnVuY2lvbmVzIG1pc2lvbmFsZXMgZGUgZG9jZW5jaWEsIGludmVzdGlnYWNpw7NuIHkgZXh0ZW5zacOzbiwgYXPDrSBjb21vIGxhcyByZWxhY2lvbmVzIGFjYWTDqW1pY2FzLCBsYWJvcmFsZXMsIGNvbnRyYWN0dWFsZXMgeSB0b2RhcyBsYXMgZGVtw6FzIHJlbGFjaW9uYWRhcyBjb24gZWwgb2JqZXRvIHNvY2lhbCBkZSBsYSBVbml2ZXJzaWRhZC4gCgo=

Operator approach to epidemic systems in networks

Publicaciones similares