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A Numerical Study of Several Species Population Models

Journal of Applied Mathematics and Physics 2023年第12期11卷 3943-3952页

作者： Francisco J. Sánchez-Bernabe maria del rosario escalona-magdaleno Department of Mathematics Universidad Autónoma Metropolitana Iztapalapa Ciudad de México Mexico Instituto de Educación Media Superior de la Ciudad de México Plantel Miravalle Zapote y Mirador Mexico

This work considers a special case of Lotka-Volterra equations, which means that in the system of two ordinary differential equations, we take the four parameters equal to one. The reason is that we want just to illustrate the procedure to reduce that system to only one ordinary differential equation, such that we know its analytical solution. This idea will be applied to study the relations between a system of three ordinary differential equations, and a couple of partial differential equations. Lotka-Volterra equations are solved numerically by a fourth-order predictor-corrector method, which is initialized by an improved Euler method with a rather small time step because it is only a second-order algorithm. Then, it is proposed a model with three species, defined by ordinary differential equations.

关键词： Lotka-Volterra Equations Adams-Bashfort Predictor Adams-Moulton Corrector Improved Euler Method GeoGebra Matlab

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Colorectal Cancer Surgery in Extreme Elderly Population

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Journal of Cancer Therapy 2015年第1期6卷 12-20页

作者： Javier Gallego Plazas Elena Asensio Juan C. Navalon Inmaculada Lozano Jose M. Navarro Guillermo Ricote Montse Olcina Almudena Cotes Henry M. Ore Alejandra magdaleno maria C. Ors maria J. Escudero Miguel A. Morcillo Servicio de Oncología Médica Hospital General Universitario de Elche-Hospital Vega Baja Alicante Espana Servicio de Cirugía General Hospital Vega Baja Alicante Espana

Background: Colorectal cancer surgery in extreme elderly population (380 years) is a growing problem and a subject in question. Experiences and results in this scenario are limited. Methods: Medical records of patients?380 years old hospitalized in General Surgery Department in Vega Baja Hospital between January 1st 2008 and December 31st 2012 were retrospectively reviewed. Patients diagnosed with colorectal cancer (CRC) were selected. Data regarding comorbidities, treatment performed, complications and survival were collected. Results: 95 patients (74 colon, 21 rectum) were identified: median age 83.0 years (80 - 93), 64.2% males. 93.7% of patients were operated on: median hospital and post-operative stay of 11 and 9 days, respectively;curative intention surgery 82.1%. 4.2% of patients were treated with interventionist procedures, and 2.1% of patients in a conservative way. 17.9% and 4.2% of patients came up with early and late complications, respectively. Early and late mortality occurred in 9.5% and 3.2% of patients, respectively. By March 2014, with a median follow up of 43.8 months, median overall survival for colorectal cancer patients was 2.7 years (95%IC, 2.0 - 3.2). Univariaye Cox Regresion analysis revealed the presence of cardiomyopathy (p = 0.024), the presence of chornic kidney disease (p = 0.025), the presence of comorbidities (vs absence) (0.026), the number of comorbidities (0.034), type of admission (p = 0.001), treatment with surgery (p = 0.001) and the incidence of early (p = 0.004) or late complications (p = 0.023) associated to overall survival with statically significance. Multivariate Cox Regression analysis showed number of comorbidities (HR = 1.104;95%CI: 0.851 - 1.431;p = 0.456), treatment with surgery (HR = 4.928;95%CI: 1.815 - 13.385;p = 0.002), programmed admission into hospital (HR = 2.316;95%CI: 1.298 - 4.133;p = 0.004), and the incidence of late complications (HR = 4.629;95%CI: 1.279 - 16.750;p = 0.020) independently associated with o

关键词： Colorectal Cancer Surgery Elderly

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