abstract: Combination therapy has shown to improve success for cancer treatment. Oncolytic virotherapy is cancer treatment that uses engineered viruses to specifically infect and kill cancer cells, without harming healthy cells. Immunotherapy boosts the body's natural defenses towards cancer. The combination of oncolytic virotherapy and immunotherapy is explored through deterministic systems of nonlinear differential equations, constructed to match experimental data for murine melanoma. Mathematical analysis was done in order to gain insight on the relationship between cancer, viruses and immune response. One extension of the model focuses on clinical needs, with the underlying goal to seek optimal treatment regimens; for both frequency and dose quantity. The models in this work were first used to estimate parameters from preclinical experimental data, to identify biologically realistic parameter values. Insight gained from the mathematical analysis in the first model, allowed for numerical analysis to explore optimal treatment regimens of combination oncolytic virotherapy and dendritic vaccinations. Permutations accounting for treatment scheduled were done to find regimens that reduce tumor size. Observations from the produced data lead to in silico exploration of immune-viral interactions. Results suggest under optimal settings, combination treatment works better than monotherapy of either type. The most optimal result suggests treatment over a longer period of time, with fractioned doses, while reducing the total dendritic vaccination quantity, and maintaining the maximum virotherapy used in the experimental work. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2016

Submitted by ÉVERTON DE TOLEDO HANSER null (cebolamat@yahoo.com.br) on 2016-06-29T18:10:55Z No. of bitstreams: 1 dissertacao - Éverton.pdf: 1347372 bytes, checksum: f12e0b124e947f94dfa18b18550ab0ff (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-07-04T12:23:32Z (GMT) No. of bitstreams: 1 hanser_et_me_rcla.pdf: 1347372 bytes, checksum: f12e0b124e947f94dfa18b18550ab0ff (MD5) / Made available in DSpace on 2016-07-04T12:23:33Z (GMT). No. of bitstreams: 1 hanser_et_me_rcla.pdf: 1347372 bytes, checksum: f12e0b124e947f94dfa18b18550ab0ff (MD5) Previous issue date: 2016-06-02 / O objetivo principal deste trabalho é o estudo da teoria de sistemas de equações diferenciais ordinárias autônomas e suas aplicações em modelos matemáticos, enfatizando os sistemas bidimensionais. / The main objective of this work is to study the theory of autonomous ordinary differential equations and their applications in mathematical models, emphasing the two-dimensional systems.

Orientadora: Marta Cilene Gadotti / Banca: Renata Zotin Gomes de Oliveira / Banca: Andréa Cristina Prokopczyk Arita / Resumo: O objetivo principal deste trabalho é o estudo da teoria de sistemas de equações diferenciais ordinárias autônomas e suas aplicações em modelos matemáticos, enfatizando os sistemas bidimensionais / Abstract: The main objective of this work is to study the theory of autonomous ordinary differential equations and their applications in mathematical models, emphasing the two-dimensional systems / Mestre

Este trabalho, ao apresentar os conceitos básicos da Epidemiologia Matemática e da modelagem de populações por classes etárias, tem por objetivo desenvolver e implementar três modelos epidemiológicos de transmissão do dengue, a fim de avaliar teoricamente os efeitos da aplicação de inseticidas em populações de Aedes aegypti, em relação às epidemias de dengue. Uma variedade de métodos têm sido empregados no controle do vetor, sendo o Aedes aegypti a principal espécie envolvida na transmissão do dengue. A· aplicação de inseticidas de ultrabaixo volume (UL V) é uma das técnicas amplamente utilizada, particularmente durante epidemias. Tal técnica tem como objetivo matar os mosquitos adultos (adulticida). Há muita controvérsia em tomo destas aplicações, no que diz respeito ao impacto no controle da transmissão do dengue. Desta forma, através deste trabalho, procuramos observar a influência do uso de inseticida na dinâmica populacional do vetor transmissor e na dinâmica da epidemia, e analisar as circunstâncias em que o inseticida pode ser utilizado a fim de agir eficientemente no controle da transmissão do dengue. O emprego de larvicidas também é abordado, a fim de que se possa observar a influência deste na dinâmica populacional do vetor transmissor e na dinâmica da epidemia. Neste trabalho são detalhadas as hipóteses utilizadas na construção de cada modelo de transmissão do dengue apresentado. Apresentados os modelos, são considerados os aspectos relativos à implementação. Assim, mediante os aspectos teóricos envolvidos na modelagem e implementação, resultados numéricos são obtidos, através das simulações, as quais nos auxiliam a avaliar os efeitos da aplicação de inseticidas em populações de Aedes aegypti no controle da transmissão do dengue. / In this work the basic Mathematical Epidemiology ideas are presented and three models of Dengue Fever transrnission are developed in order to measure the effects of the use o f insecticides on the populations o f the mosquito Aedes aegypti that are related to the dengue epidemics. There is a good variety of control methods on the Aedes aegypti populations. The use of ultra-low volume (UL V) insecticides is widely employed specially during epidemics. The goal of such method is to eliminate a fraction of the adult mosquito population. There is a great deal o f controversy on the effectiveness o f insecticide use during a dengue epidemic. In this way we propose to investigate the impact o f UL V on the mosquito dynarnics and on the epidemics dynarnics as well in order to determine in which circumstances the use o f UL V can truly effective on the course o f a epidemic. On the same line, we also propose a study on the use of larvicides as a control method. In this study we detail the hypotheses that are used to construct the dynarnic models. Once the models are presented we consider the implementation details. The numerical results are obtained after various simulations which provide the data that allow us to measure the impact ofthe control technique on the dengue epidemics.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-09-28T11:43:16Z No. of bitstreams: 2 Dissertação - Celso Faria de Souza - 2018.pdf: 2806613 bytes, checksum: aa7e4cd9f40fee3c977c41da37a2e86e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-09-28T14:12:15Z (GMT) No. of bitstreams: 2 Dissertação - Celso Faria de Souza - 2018.pdf: 2806613 bytes, checksum: aa7e4cd9f40fee3c977c41da37a2e86e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-09-28T14:12:15Z (GMT). No. of bitstreams: 2 Dissertação - Celso Faria de Souza - 2018.pdf: 2806613 bytes, checksum: aa7e4cd9f40fee3c977c41da37a2e86e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-08-31 / In this work, we present an innovative approach at Ordinary Di erential Equations (ODE) for engineers. We show how to address ODEs without the characteristic formalism that exists in universities, but maintaining the feeling required to model classic problems in physics and engineering. We discuss a new methodology to introduce the concepts and techniques used to solve many kinds of ODEs / Neste trabalho, apresentamos uma nova abordagem no ensino de Equações Diferenciais Ordinárias (EDOs) para engenheiros. Mostramos como apresentar as EDO sem o formalismo característico com que é tratado o assunto nas universidades, mas sem perder o feeling necessário para a modelagem de problemas clássicos de física e engenharia. Discutimos uma nova metodologia para a introdução dos conceitos e técnicas de solução para diversos tipos de EDOs.

Este trabalho, ao apresentar os conceitos básicos da Epidemiologia Matemática e da modelagem de populações por classes etárias, tem por objetivo desenvolver e implementar três modelos epidemiológicos de transmissão do dengue, a fim de avaliar teoricamente os efeitos da aplicação de inseticidas em populações de Aedes aegypti, em relação às epidemias de dengue. Uma variedade de métodos têm sido empregados no controle do vetor, sendo o Aedes aegypti a principal espécie envolvida na transmissão do dengue. A· aplicação de inseticidas de ultrabaixo volume (UL V) é uma das técnicas amplamente utilizada, particularmente durante epidemias. Tal técnica tem como objetivo matar os mosquitos adultos (adulticida). Há muita controvérsia em tomo destas aplicações, no que diz respeito ao impacto no controle da transmissão do dengue. Desta forma, através deste trabalho, procuramos observar a influência do uso de inseticida na dinâmica populacional do vetor transmissor e na dinâmica da epidemia, e analisar as circunstâncias em que o inseticida pode ser utilizado a fim de agir eficientemente no controle da transmissão do dengue. O emprego de larvicidas também é abordado, a fim de que se possa observar a influência deste na dinâmica populacional do vetor transmissor e na dinâmica da epidemia. Neste trabalho são detalhadas as hipóteses utilizadas na construção de cada modelo de transmissão do dengue apresentado. Apresentados os modelos, são considerados os aspectos relativos à implementação. Assim, mediante os aspectos teóricos envolvidos na modelagem e implementação, resultados numéricos são obtidos, através das simulações, as quais nos auxiliam a avaliar os efeitos da aplicação de inseticidas em populações de Aedes aegypti no controle da transmissão do dengue. / In this work the basic Mathematical Epidemiology ideas are presented and three models of Dengue Fever transrnission are developed in order to measure the effects of the use o f insecticides on the populations o f the mosquito Aedes aegypti that are related to the dengue epidemics. There is a good variety of control methods on the Aedes aegypti populations. The use of ultra-low volume (UL V) insecticides is widely employed specially during epidemics. The goal of such method is to eliminate a fraction of the adult mosquito population. There is a great deal o f controversy on the effectiveness o f insecticide use during a dengue epidemic. In this way we propose to investigate the impact o f UL V on the mosquito dynarnics and on the epidemics dynarnics as well in order to determine in which circumstances the use o f UL V can truly effective on the course o f a epidemic. On the same line, we also propose a study on the use of larvicides as a control method. In this study we detail the hypotheses that are used to construct the dynarnic models. Once the models are presented we consider the implementation details. The numerical results are obtained after various simulations which provide the data that allow us to measure the impact ofthe control technique on the dengue epidemics.

Orientador: Laecio Carvalho de Barros / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-06T13:08:35Z (GMT). No. of bitstreams: 1 Dias_MarinaRibeiroBarros_M.pdf: 1045465 bytes, checksum: 2e062089a387fb46a8cc2bcf51f082f4 (MD5) Previous issue date: 2006 / Resumo: Nesse trabalho propomos uma metodologia para o estudo de Equações Diferenciais Ordinárias cujo campo de direções é apenas parcialmente conhecido. Para isto, aliamos a teoria de controladores fuzzy com métodos numéricos tradicionais. A partir de teoremas clássicos de continuidade e estudos sobre aproximação, vimos que, para alguns casos, as soluções aqui produzidas aproximam-se das teóricas. Fazemos uso da metodologia aqui proposta para analisar modelos de crescimento populacional de espécie isolada e também modelos que envolvem várias espécies. Finalmente, indicamos essa metodologia como uma ferramenta auxiliar para obtenção de parâmetros de equações diferenciais determinísticas / Abstract: In this work we propose a metodology to study Ordinary Differential Equations supposing the direction field is partially known. We join theory of Fuzzy Controlers and traditional numerical methods to develop this study. Using classical theorems of continuity and aproximation theory we saw that, for some cases, the solutions we present here estimate the theorical ones. We'll use the metodology proposed here to analyse unidimensional models of populational growth and models that envolves many species. Finally, we point out our metodology like an auxiliar tool to obtain parameters of deterministic differential equations / Mestrado / Mestre em Matemática Aplicada

Orientador: João Frederico da Costa Azevedo Meyer / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T23:09:37Z (GMT). No. of bitstreams: 1 Alves_LourimaraFariasBarros_M.pdf: 3434748 bytes, checksum: 47ffff091840f19264eeb59a290d59d5 (MD5) Previous issue date: 2009 / Resumo: Em todo mundo, a preocupação com problemas ambientais vem crescendo de maneira muito rápida, com especial destaque aos recursos hídricos, pois a humanidade parecia acreditar que tais recursos seriam inesgotáveis, e hoje se depara com uma realidade totalmente diferente. Neste contexto, este trabalho buscou por meio de dois sistemas: um de Equações de Diferenças e o outro de Equações Diferenciais obter em primeira aproximação a modelagem matemática do comportamento evolutivo de manchas de materiais poluentes de superfície no Rio Balsas ao sul do estado do Maranhão. Com estudo e análise dessa modelagem, construímos algoritmos computacionais (em ambiente MATLAB) que permitem a criação de instrumental para simulação de acidentes, de estratégias de prevenção, de contenção além de também servir de apoio no combate a práticas que possam levar à presença de materiais tóxicos prejudiciais à biota fuvial / Abstract: Worldwide, the growing concern with environmental problems has happened quite rapidly, with special emphasis, in many cases, as regards sweet water resources; humanity has acted as if such resources were endless, and today the situation has changed into a very diferent reality. In this general picture, this work proposes the modelling of the evolutive behavior of pollutants on the water surface of rivers, focusing upon the Rio Balsas, in southern Maranhão State. A analysis of the chosen modelling process, led to the defnition computational algorithms, obtained in a MATLAB environment creating numerical tools for the simulation of accidents and processes, for theoretically testing prevention and protection strategies, as well as serving a general purpose of challenging choices and procedures that may lead to the presence of toxic material at levels which negatively affect local biota / Mestrado / Biomatematica / Mestre em Matemática

The cell cycle is an essential process in all living organisms that must be carefully regulated to ensure successful cell growth and division. Disregulation of the cell cycle is a key contributing factor towards the formation of cancerous cells. Understanding events at a cellular level is the first step towards comprehending how cancer manifests at an organismal level. Mathematical modelling can be used as a means of formalising and predicting the behaviour of the biological systems involved in cancer. In response, cell cycle models have been constructed to simulate and predict what happens to the mammalian cell over a time course in response to variable parameters.Current cell cycle models rarely account for certain precursors of cell growth such as energy usage and the need for non-essential amino acids as fundamental building blocks of macromolecules. Normal and cancer cell metabolism differ in the way they derive energy from glucose. In addition, normal and cancer cells also demonstrate different levels of gene expression. Two versions of a mammalian cell cycle and metabolism model, based on ordinary differential equations (ODEs) that respond to fluctuations in glucose concentration levels, have been developed here for the normal and cancer cell scenarios. Sensitivity analysis is performed for both normal and cancer cells using these cell cycle and metabolism models to investigate which kinetic reaction steps have a greater effect over the cell cycle period. Detailed analysis of the models and quantitatively assessing metabolite levels at various stages of the cell cycle may offer novel insights into how the glycolytic rate varies during the cell cycle for both normal and cancer cells.The results of the sensitivity analysis are used to identify potential drug targets in cancer therapy. Combinations of these individual targets are also investigated to compare the different effects of single and multiple drug compounds on the time it takes to complete a cell division cycle.

Vaccination has been used to control the spread of infectious diseases for centuries with widespread success. Deterministic models studying the spread of infectious disease often use the assumption of mass vaccination; however, these models do not allow for the inclusion of human behaviour. Since current vaccination campaigns are voluntary in nature, it is important to extend the study of infectious disease models to include the effects of human behaviour. To model the effects of vaccination behaviour on the spread of influenza, we examine a series of models in which individuals vaccinate according to memory or individual decision-making processes based upon self-interest. Allowing individuals to vaccinate proportionally to an exponentially decaying memory function of disease prevalence, we demonstrate the existence of a Hopf bifurcation for short memory spans. Using a game-theoretic influenza model, we determine that lowering the perceived vaccine risk may be insufficient to increase coverage to established target levels. Utilizing evolutionary game theory, we examine models with imitation dynamics both with and without a decaying memory function and show that, under certain conditions, periodic dynamics occur without seasonal forcing. Our results suggest that maintaining diseases at low prevalence with voluntary vaccination campaigns could lead to subsequent epidemics following the free-rider dilemma and that future research in disease control reliant on individual-based decision-making need to include the effects of human behaviour.