Documentos de conferencia

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Examinando Documentos de conferencia por Autor "Hincapie, D."

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    Mathematical model for dengue with three states of infection
    (SPIE-INT SOC OPTICAL ENGINEERING, 2012-01-01) Hincapie, D.; Ospina, J.; Hincapie, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases. © 2012 SPIE.
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    Ítem
    Solving stochastic epidemiological models using computer algebra
    (SPIE-INT SOC OPTICAL ENGINEERING, 2011-01-01) Hincapie, D.; Ospina, J.; Hincapie, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).