Examinando por Autor "Hincapié-Palacio, D."
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Ítem Approximated analytical solution to an Ebola optimal control problem(Board Members, 2016-01-01) Hincapié-Palacio, D.; Ospina, J.; Torres, D.F.M.; Hincapié-Palacio, D.; Ospina, J.; Torres, D.F.M.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónAn analytical expression for the optimal control of an Ebola problem is obtained. The analytical solution is found as a first-order approximation to the Pontryagin Maximum Principle via the Euler-Lagrange equation. An implementation of the method is given using the computer algebra system Maple. Our analytical solutions confirm the results recently reported in the literature using numerical methods.Ítem The Critical Proportion of Immune Individuals needed to Control Hepatitis B(SPIE-INT SOC OPTICAL ENGINEERING, 2016-05-13) Ospina, J.; Hincapié-Palacio, D.; Ospina, J.; Hincapié-Palacio, D.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónWe estimate the critical proportion of immunity (Pc) to control hepatitis B in Medellin - Colombia, based on a random population survey of 2077 individuals of 6-64 years of age. The force of infection (Fi) was estimated according to empirical data of susceptibility by age S(a), assuming a quadratic expression. Parameters were estimated by adjusting data to a nonlinear regression. Fi was defined by -(ds(a)/da)/s(a) and according to the form of the empirical curve S(a) we assume a quadratic expression given by S(a)= Ea2+Ba+C. Then we have the explicit expression for the accumulated Fi by age given by F(a) = -a(Ea+B)/c. The expression of average infection age A is obtained as A = L + EL3/(3C)+BL2/(2C) and the basic reproductive number R-0 is obtained as R-0 = 1 + 6C/(6C+2EL2+3BL). From the las result we obtain the Pc given by Pc=6C/(12C+2EL2+3BL). Numerical simulations were performed with the age-susceptibility proportion and initial values (a=0.02, b=20, c=100), obtaining an adjusted coefficient of multiple determination of 64.83%. According to the best estimate, the algebraic expressions for S(a) and the Fi were derived. Using the result of Fi, we obtain A = 30, L = 85; R-0 CI 95%: 1.42 - 1.64 and Pc: 0-0.29. These results indicate that at the worst case, to maintain control of the disease should be immunes at least 30% of susceptible individuals. Similar results were obtained by sex and residential area.Ítem Simulación del nivel de eliminación de sarampión y rubéola según la estratificación e interacción social(Universidad Nacional de Colombia, 2010-01-01) Hincapié-Palacio, D.; Ospina-Giraldo, J.; Gómez-Arias, R.D.; Uyi-Afuwape, A.; Chowell-Puente, G.; Hincapié-Palacio, D.; Ospina-Giraldo, J.; Gómez-Arias, R.D.; Uyi-Afuwape, A.; Chowell-Puente, G.; Universidad EAFIT. Departamento de Ciencias; Lógica y ComputaciónObjective The study was aimed at comparing measles and rubella disease elimination levels in a homogeneous and heterogeneous population according to socioeconomic status with interactions amongst low- and high-income individuals and diversity in the average number of contacts amongst them. Methods Effective reproductive rate simulations were deduced from a susceptibleinfected-recovered (SIR) mathematical model according to different immunization rates using measles (1980 and 2005) and rubella (1998 and 2005) incidence data from Latin-America and the Caribbean. Low- and high-income individuals' social interaction and their average number of contacts were analysed by bipartite random network analysis. MAPLE 12 (Maplesoft Inc, Ontario Canada) software was used for making the simulations. Results The progress made in eliminating both diseases between both periods of time was reproduced in the socially-homogeneous population. Measles (2005) would be eliminated in high- and low-income groups; however, it would only be achieved in rubella (2005) if there were a high immunity rate amongst the low-income group. If the average number of contacts were varied, then rubella would not be eliminated, even with a 95 % immunity rate. Conclusion Monitoring the elimination level in diseases like measles and rubella requires that socio-economic status be considered as well as the population's interaction pattern. Special attention should be paid to communities having diversity in their average number of contacts occurring in confined spaces such as displaced communities, prisons, educational establishments, or hospitals.