Examinando por Materia "Epidemic threshold"

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    Ítem
    Basic reproductive rate of a spatial epidemic model using computer algebra software
    (2005-01-01) Doracelly Hincapié, P.; Juan Ospina, G.; Doracelly Hincapié, P.; Juan Ospina, G.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    Using computer algebra software we obtain the basic reproductive rate corresponding to the propagation of a directly transmitted disease in a circular habitat when the disease is endemic at the boundary. The method used is the Laplace Transform Technique and calculus of residues. The results that were obtained include both the explicit form of the R0 for the boundary condition that was considered, as the explicit symbolic solution of the model equation. The method that was used can be extended to other more complex problems such as indirectly transmitted diseases with one or more intermediary hosts or effects of genetic, immunological, geographical or social heterogeneity in the human population. This application indicates that the computer algebra software for symbolic computation has a very promissory future in mathematical epidemiology.
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    Ítem
    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.