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Doctoral Thesis
DOI
10.11606/T.59.2012.tde-01082012-110701
Document
Author
Full name
Brenno Caetano Troca Cabella
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Ribeirão Preto, 2012
Supervisor
Committee
Martinez, Alexandre Souto (President)
Silva Filho, Antonio Carlos Roque da
Felicio, Jose Roberto Drugowich de
Kraenkel, Roberto Andre
Silva, Marco Antonio Alves da
Title in Portuguese
Modelos aplicados ao crescimento e tratamento de tumores e à disseminação da dengue e tuberculose
Keywords in Portuguese
modelos baseados em agentes.
Modelos de crescimento
modelos epidemiologicos
Abstract in Portuguese
A generalização de modelos de crescimento por meio de um parâmetro de controle foi primeiramente proposta por Richards, em 1959. Em nosso trabalho, propomos uma forma alternativa de generalização obtendo uma interpretação emp rica e outra microscopica do parâmetro de controle. Mais especificamente, quando consideramos a proliferacão de c elulas, o parâmetro est a relacionado ao alcance da interação e a dimensão fractal da estrutura celular. Obtemos a solucão anal ítica para esta equação diferencial. Mostramos que, atrav és da escolha apropriada da escala conseguimos o colapso de dados representando a independência em relacão aos parâmetros e as condições iniciais. Al ém disso, ao considerarmos a taxa de esforco como a retirada de indiví duos de uma população, podemos associ á-la ao tratamento visando extinguir uma populacãoo de c élulas cancerosas. Em modelos epidemiol ogicos, propomos modelar a dinâmica de transmissão da dengue utilizando equacões diferenciais ordin árias. Em nosso modelo, levamos em conta tanto a dinâmica do hospedeiro quanto a do vetor, assim temos o controle da dinâmica de ambas as populações. Inclu ímos tamb ém no modelo o efeito "enhancing" com intuito de verificar sua influência na dinâmica de disseminacão da doença. O efeito "enhancing" é considerado uma das principais hipóteses para explicar a dengue hemorr ágica que pode levar a morte. Fizemos o estudo de um modelo epidemiol ógico da dengue com o objetivo de revelar quais são os fatores que levam a disseminação desse caso mais severo da doenca e, possivelmente, sugerir polí ticas p úblicas de sa úde para evit á-lo. Implementamos tamb ém um modelo de transmissão da tuberculose fazendo uso da modelagem computacional baseada em agentes, que oferece a possibilidade de representar explicitamente heterogeneidades em nível individual.
Title in English
Models applied to tumors growth and treatment and the spread of dengue and tuberculosis.
Keywords in English
agent-based models.
epidemiological models
Growth models
Abstract in English
The generalization of growth models by means of a control parameter was first proposed by Richards in 1959. In our work, we propose an alternative way to obtainin an empirical and microscopic interpretation of control parameter. More specically, when considering the proliferation of cells, the parameter is related to the range of interaction and the fractal dimension of the cell structure. We obtain the analytical solution for this dierential equation. We show that, by appropriate choice of scale we have data collapse, representing the independence on parameters and initial conditions. Furthermore, when considering the e ffort as rate the removal of individuals from a population, we can associate it with the treatment to extinguish cancer cells population. In epidemiological models, we propose to model the dynamics of dengue transmission using ordinary dierential equations. In our model, we take into account both the dynamics of the host and the vector, so we have control of the dynamics of both populations. We also included in the model the effect of enhancing in order to verify their inuence on the dynamics of disease spread. The effect of enhancing is considered one of the main hypotheses to explain the hemorrhagic fever that can lead to death. We study a model of epidemiology of dengue in order to reveal what are the factors that lead to the dissemination of this more severe case of the disease and, possibly suggesting public health policies to prevent it. We also implemented a model of tuberculosis transmission making use of agent-based computational modeling, which o ffers the possibility to explicitly represent heterogeneity at the individual level. This approach allows us to deal with each individual in particular, unlike the model of dierential equations, in which all individuals are in the same compartment interact in a similar way as in a mean field interaction.
 
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BrennoCabella.pdf (4.59 Mbytes)
Publishing Date
2012-08-20
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • CABELLA, B. C. T., MARTINEZ, A. S., and RIBEIRO, F. Data collapse, scaling functions, and analytical solutions of generalized growth models [doi:10.1103/PhysRevE.83.061902]. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics [online], 2011, vol. 83, p. 061902.
  • CABELLA, Brenno Caetano Troca, RIBEIRO, Fabiano, and MARTINEZ, Alexandre Souto. Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model [doi:10.1016/j.physa.2011.11.018]. Physica A: Statistical Mechanics and its Applications [online], 2012, vol. 391, n. 4, p. 1281-1286.
  • CABELLA, Brenno, MARTINEZ, Alexandre, and RIBEIRO, Fabiano. Data collapse, scaling functions, and analytical solutions of generalized growth models [doi:10.1103/PhysRevE.83.061902]. Physical Review E [online], 2011, vol. 83, n. 6.
  • DE ESPíNDOLA, Aquino L, et al. An agent-based computational model of the spread of tuberculosis [doi:10.1088/1742-5468/2011/05/P05003]. Journal of Statistical Mechanics: Theory and Experiment [online], 2011, vol. 2011, n. 5, p. P05003.
  • ESPINDOLA, AQUINO L., et al. Exploration of the parameter space in na agent-based model of tuberculosis spread : emergence of drug resistancein developing vs developedcountries [doi:10.1142/S0129183112500465]. International Journal of Modern Physics C [online], 2012, vol. 23, n. 6, p. 1250046.
  • CABELLA, B. C. T., RIBEIRO, F., and MARTINEZ, A. S. Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model [doi:10.1016/j.physa.2011.11.018]. Physica. A [online], 2012, vol. 391, p. 1281-1286.
  • ESPÍNDOLA, A. L., et al. An agent-based computational model of the spread of tuberculosis [doi:10.1088/1742-5468/2011/05/P05003]. Journal of Statistical Mechanics [online], 2011, vol. 2011, p. P05003.
  • ESPÍNDOLA, A. L., et al. Exploration of the parameter space in an agent-based model of tuberculosis spread: emergence of drug resistance in developing versus developed countries [doi:10.1142/S0129183112500465]. International Journal of Modern Physics C [online], 2012, vol. 23, p. 1250046.
  • CABELLA, B. C. T., e MARTINEZ, A. S. Generalized Population Dynamics. In 10th International Symposium on Mathematical Biology, Rio de Janeiro, RJ,Brazil, 2010. Proceedings of 10th International Symposium on Mathematical Biology., 2010. Resumo.
  • CABELLA, B. C. T., RIBEIRO, F., and MARTINEZ, A. S. Data collapse, scaling functions, and analytical solutions of generalized growth models. In International Conference on Statistical Physics, Larnaca, 2011. Abstracts Booklet., 2011. Abstract.
  • MARTINEZ, A. S., CABELLA, B. C. T., and RIBEIRO, F. Data collapse, scaling functions, and analytical solutions of generalized growth models. In Workshop on Complex Systems: Social and Biological Applications, São Paulo/SP, 2011. Abstracts.São Paulo : Instituto de Física USP, 2011. Abstract. Available from: http://web.if.usp.br/fge/node/283.
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