PUBLICATIONS
González-Parra, G., Arenas, A. J., Chen-Charpentier, B., & Sultana, S. (2023). Mathematical modeling of toxoplasmosis with multiple hosts, vertical transmission and cat vaccination. Computational and Applied Mathematics, 42(2), 88.
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González-Parra, G., Díaz-Rodríguez, M., & Arenas, A. J. (2022). Mathematical modeling to study the impact of immigration on the dynamics of the COVID-19 pandemic: A case study for Venezuela. Spatial and Spatio-temporal Epidemiology, 43, 100532.
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Gilbert Kerr, Gilberto González-Parra, and Michelle Sherman. A new method based on the Laplace transform and Fourier series for solving linear neutral delay differential equations. Applied Mathematics and Computation, 420:126914, 2022.
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Gilbert Kerr and Gilberto González-Parra. Accuracy of the Laplace transform method for linear neutral delay differential equations. Mathematics and Computers in Simulation, 2022.
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Ruth Bowness, Jonathan Karr, Rahuman Sheriff, James Osborne, Gilberto Gonzalez-Parra, Eric Forgoston, Yaling Liu, Robin Thompson, Winston Garira, Jacob Barhak, et al. Model integration in computational biology: the role of reproducibility, credibility and utility. Frontiers in Systems Biology, 2022.
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Gilberto Gonzalez-Parra, Abraham J Arenas, and Myladis R Cogollo. Mathematical modeling to study optimal allocation of vaccines against covid-19 using an agestructured population. Axioms, 2022.
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Gilberto González-Parra, Sharmin Sultana, and Abraham J Arenas. Mathematical modeling of toxoplasmosis considering a time delay in the infectivity of oocysts. Mathematics, 10(3):354, 2022.
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Myladis R Cogollo, Gilberto González-Parra, and Abraham J Arenas. Modeling and forecasting cases of RSV using artificial neural networks. Mathematics, 9(22):2958, 2021.
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Gilberto González-Parra and Abraham J Arenas. Qualitative analysis of a mathematical model with presymptomatic individuals and two SARS-CoV-2 variants. Computational and Applied Mathematics, 40(6):1–25, 2021.
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Gilberto Gonzalez-Parra. Analysis of delayed vaccination regimens: A mathematical modeling approach. Epidemiologia, 2(3):271–293, 2021.
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Gilberto Gonzalez-Parra and Abraham J Arenas. Nonlinear dynamics of the introduction of a new SARS-CoV-2 variant with different infectiousness. Mathematics, 9(13):1564, 2021.
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Gilberto Gonzalez-Parra, David Martínez-Rodríguez, and Rafael J. Villanueva-Micó. Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach. Mathematical and Computational Applications, 26(2), 2021.
David Martínez-Rodríguez, Gilberto Gonzalez-Parra, and Rafael-J Villanueva. Analysis of key factors of a SARS-CoV-2 vaccination program: A mathematical modeling approach. Epidemiologia, 2(2):140–161, 2021.
Abraham J Arenas, Gilberto González-Parra, and Nicolás De La Espriella. Nonlinear dynamics of a new seasonal epidemiological model with age-structure and nonlinear incidence rate. Computational and Applied Mathematics, 40(2):1–27, 2021.
Abraham J Arenas, Gilberto González-Parra, Jhon J Naranjo, Myladis Cogollo, and Nicolás De La Espriella. Mathematical Analysis and numerical solution of a model of HIV with a discrete time delay. Mathematics, 9(3):257, 2021.
Gilberto González-Parra, Miguel Díaz-Rodríguez, and Abraham J Arenas. Optimization of the controls against the spread of Zika virus in populations. Computation, 8(3):76, 2020.
Gilberto Gonzalez-Parra, Miguel Díaz-Rodríguez, and Abraham J Arenas. Mathematical modeling to design public health policies for Chikungunya epidemic using optimal control. Optimal Control Applications and Methods, 2020.
Lubna Pinky, Gilberto Gonzalez-Parra, and Hana M Dobrovolny. Effect of stochasticity on coinfection dynamics of respiratory viruses. BMC bioinformatics, 20(1):191, 2019.
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Gilberto González-Parra, Tommaso Benincasa, et al. Mathematical modeling and numerical simulations of Zika in Colombia considering mutation. Mathematics and Computers in Simulation, 163:1–18, 2019.
Gilberto González-Parra and Hana M Dobrovolny. The rate of viral transfer between upper and lower respiratory tracts determines RSV illness duration. Journal of Mathematical Biology, pages 1–17, 2019.
Lubna Pinky, Gilberto González-Parra, and Hana M Dobrovolny. Superinfection and cell regeneration can lead to chronic viral coinfections. Journal of Theoretical Biology, 466:24–38, 2019.
Gilberto C. González-Parra, Diego F. Aranda, Benito Chen-Charpentier, Miguel Díaz-Rodríguez, and Jaime E. Castellanos. Mathematical modeling and characterization of the spread of Chikungunya in Colombia. Mathematical and Computational Applications, 24(1), 2019.
Gilberto Gonzalez-Parra, Filip De Ridder, Dymphy Huntjens, Dirk Roymans, Gabriela Ispas, and Hana M. Dobrovolny. A comparison of RSV and influenza in vitro kinetic parameters reveals differences in infecting time. PLOS ONE, 13(2):1–24, 02 2018.
[1] Gilberto González-Parra and Hana M Dobrovolny. A quantitative assessment of dynamical differences of RSV infections in vitro and in vivo. Virology, 2018.
[2] Gilberto González-Parra and Hana M Dobrovolny. Modeling of fusion inhibitor treatment of RSV in african green monkeys. Journal of Theoretical Biology, 2018.
[3] Gilberto González-Parra, Benito Chen-Charpentier, and Hristo V Kojouharov. Mathematical modeling of crime as a social epidemic. Journal of Interdisciplinary Mathematics, 21(3):623–643, 2018.
[4] Gilberto González-Parra, Hana M Dobrovolny, Diego F Aranda, Benito Chen-Charpentier, and Rafael Antonio Guerrero Rojas. Quantifying rotavirus kinetics in the reh tumor cell line using in vitro data. Virus research, 244:53–63, 2018.
[5] Gilberto González-Parra, Abraham J Arenas, and Myladis R Cogollo. Positivity and boundedness of solutions for a stochastic seasonal epidemiological model for respiratory syncytial virus (RSV). Ingeniería y Ciencia, 13(25):95–121, 2017.
[6] Gilberto González-Parra, Thalia Rodriguez, and Hana M. Dobrovolny. A comparison of methods for extracting influenza viral titer characteristics. Journal of Virological Methods, 231:14 – 24, 2016.
[7] Gilberto González-Parra, José F Querales, and Diego Aranda. Predicción de la epidemia del virus respiratorio sincitial en Bogotá DC utilizando variables climatológicas. Biomédica, 36(3), 2016.
[8] Benito Chen-Charpentier, Gilberto González-Parra, and Abraham J Arenas. Fractional order financial models for awareness and trial advertising decisions. Computational Economics, pages 1–14, 2015.
[9] Gilberto González-Parra and Hana M Dobrovolny. Assessing Uncertainty in A2 Respiratory Syncytial Virus Viral Dynamics. Computational and Mathematical Methods in Medicine, 2015.
[10] Gilberto González-Parra, Benito M Chen-Charpentier, and Moises Bermúdez. Modeling Chagas disease at population level to explain Venezuela’s real data. Osong Public Health and Research Perspectives, 6(5):288 – 301, 2015.
[11] Abraham J. Arenas, Gilberto González-Parra, and Benito M. Chen-Charpentier. Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order. Mathematics and Computers in Simulation, 121:48–63, 2016.
[12] Gilberto González-Parra, Rafael-J. Villanueva, Javier Ruiz-Baragaño, and Jose-A. Moraño. Modelling influenza A(H1N1) 2009 epidemics using a random network in a distributed computing environment. Acta Tropica, 143:29–35, 2015.
[13] Diego F Aranda-Lozano, Gilberto C González-Parra, and José Querales. Modelling respiratory syncytial virus (RSV) transmission children aged less than five years-old. Revista de Salud Pública, 15(4):689–700, 2013.
[14] Tarek Abdel-Hamid, Felix Ankel, Michele Battle-Fisher, Bryan Gibson, Gilberto Gonzalez-Parra, Mohammad Jalali, Kirsikka Kaipainen, Nishan Kalupahana, Ozge Karanfil, Achla Marathe, Brian Martinson, Karma McKelvey, Suptendra Nath Sarbadhikari, Stephen Pintauro, Patrick Poucheret, Nicolaas Pronk, Ying Qian, Edward Sazonov, Kim Van Oorschot, Akshay Venkitasubramanian, and Philip Murphy. Public
and health professionals misconceptions about the dynamics of body weight gain-loss. System Dynamics Review, 30(1-2):58–74, 2014.
[15] Gilberto González-Parra, Benito Chen-Charpentier, Abraham J Arenas, and Miguel Diaz-Rodriguez. Mathematical modeling of physical capital using the spatial Solow model. arXiv preprint arXiv:1504.04388, 2015.
16] Gilberto González-Parra, Abraham J Arenas, and Myladis Cogollo. Analytical numerical solution of a parabolic diffusion equation under uncertainty conditions using DTM with Monte Carlo simulations. Ingeniería y Ciencia, 11(22):49–72, 2015.
[17] Gilberto González-Parra and Abraham J. Arenas. A mathematical model for social security systems with dynamical systems. Ingeniería y Ciencia, 10(19), 2014.
[18] Gilberto González-Parra, Benito Chen-Charpentier, and Abraham J. Arenas. Polynomial chaos for random fractional order differential equations. Applied Mathematics and Computation, 226(1):123–130, 2014.
[19] G. González, Abraham J. Arenas, and Myladis Cogollo. Numerical-analytical solutions of predator-prey models. Wseas Transactions on Biology and Biomedicine, 10(2):79– 87, 2013.
[20] Gilberto González-Parra, Luis Acedo, and Abraham J Arenas. A novel approach to obtain analytical-numerical solutions of nonlinear Lorenz system. Numerical Algorithms, pages 1–15, 2013.
[21] Gilberto González-Parra, Abraham J Arenas, and Benito M Chen-Charpentier. A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1). Mathematical Methods in the Applied Sciences, 2013.
[22] Gilberto González-Parra, Abraham J. Arenas, and Benito M. Chen-Charpentier. Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes. Numerical Methods for Partial Differential Equations, 30(1):210– 221, 2014.
[23] M. Díaz-Rodríguez, Walter Ocando, and Gilberto González-Parra. Desarrollo tecnológico de robots de bajo costo para aplicaciones de rehabilitación del cuerpo humano: prototipo virtual para la extremidad inferior. Observador del Conocimiento,
[24] Jorge Cayama and Gilberto C. González-Parra. Aplicación del caos polinomial a ecuaciones diferenciales parciales aleatorias. Revista Ciencia e Ingeniería, 34(2), 2013.
[25] F. Guerrero, Gilberto González-Parra, and A. Arenas. A nonstandard finite difference numerical scheme applied to a mathematical model of the prevalence of smoking in Spain. A case study. Computational & Applied Mathematics, 33(1):13–25, 2014.
[26] Jorge Cayama and Gilberto C. González-Parra. Comparación de Caos polinomial y Monte Carlo para ecuaciones diferenciales ordinarias aleatorias. Revista Ciencia e Ingeniería, 33(1), 2012.
[27] Gilberto C. González-Parra and J.C.Cortes and R.J. Villanueva and F.J. Santonja . Modeling population dynamics with random initial conditions by means of statistical
moments. Boletín de Estadística e Investigacíon Operativa, 28(3):204–219, 2012.
[28] Gilberto C. González-Parra and R.J. Villanueva and Lupe Segovia . Dinámica del virus
pandémico AH1N1/09 en la población de Venezuela. Revista Interciencia, 37(4),
2012.
[29] Jose Luis Herrera and Gilberto C. González-Parra. Modelado de enfermedades contagiosas
mediante una clase de redes sociales dinámicas. Revista de la Facultad de
Ingeniería de la UCV, 27(2), 2012.
[30] A. Arenas, Gilberto González-Parra, and Blas Melendez Caraballo. A nonstandard
finite difference scheme for a nonlinear Black-Scholes equation. Mathematical and
Computer Modelling, 57(7-8):1633–1670, 2011.
[31] Gilberto González-Parra, A. Arenas, and Lupe Segovia Diego F. Aranda. Modeling
the epidemic waves of AH1N1/09 influenza around the world. Spatial and Spatiotemporal
Epidemiology, 2:219–226, 2011.
[32] Gilberto González-Parra, R.J. Villanueva, and A. Arenas. Matrix nonstandard numerical
schemes for epidemic models. WSEAS Transactions on Mathematics, 9(11),
2010.
[33] Gilberto González-Parra, L. Acedo, and A. Arenas. Accuracy of analytical-numerical
solutions of the Michaelis-Menten equation. Journal of Computational and Applied
Mathematics, 30(2):445–461, 2011.
[34] Gilberto González-Parra, R.J. Villanueva, and A. Arenas. An age structured model for
obesity prevalence dynamics in populations. Rev.MVZ Córdoba, 15(2):2051–2059,
2010.
[35] Gilberto González-Parra, L. Acedo, R.J. Villanueva, and A. Arenas. Modeling social
obesity epidemic with stochastic networks. Physica A, 389(17):3692–3701, 2010.
[36] A. Arenas, Gilberto González-Parra, and Benito M. Chen-Charpentier. A nonstandard
numerical scheme of predictor-corrector type for epidemic models. Computers and
Mathematics with Applications, 59(12):3740–3749, 2010.
[37] Gilberto González-Parra, Abraham J. Arenas, and Benito M. Chen-Charpentier. Combination
of nonstandard schemes and Richardson’s extrapolation to improve the numerical
solution of population models. Mathematical and Computer Modelling,
52(7-8):1030–1036, 2010.
[38] Abraham J. Arenas, Gilberto González-Parra, and Rafael J. Villanueva. Modeling
toxoplasmosis spread in cat populations under vaccination. Theoretical Population
Biology, 77:227–237, 2010.
[39] M. Díaz-Rodríguez, Gilberto González-Parra, and Abraham J. Arenas. Nonstandard
numerical schemes for modeling a 2-DOF serial robot with rotational spring-damperactuators.
Communications in numerical methods in engineering, 4(1):69–71,
2009.
[40] Abraham J. Arenas, Gilberto González-Parra, and Lucas Jódar. Randomness in a
mathematical model for the transmission of respiratory syncytial virus (RSV). Mathematics
and Computers in Simulation, 80:971–981, 2010.
[41] F.J. Santonja, R.-J. Villanueva, L. Jódar, and Gilberto González-Parra. Mathematical
modeling of social obesity epidemic in the Region of Valencia, Spain. Mathematical
and Computer Modelling of Dynamical Systems, 16:23–34, 2010.
[42] L. Acedo, Gilberto González-Parra, and Abraham J. Arenas. Modal series solution for
a epidemic model. Physica A, 389:1151–1157, 2010.
[43] Abraham J. Arenas, Gilberto González-Parra, and Benito M. Chen-Charpentier. Dynamical
analysis of the transmission of seasonal diseases using the differential transformation
method. Mathematical and Computer Modelling, 50(5-6):765–776,
2009.
[44] Gilberto González-Parra, Abraham J. Arenas, and F. Santonja. Stochastic modeling
with Monte Carlo of obesity population. Journal of Biological Systems, 18(1):93–
108, 2010.
[45] Gilberto González-Parra, L. Jódar, F. Santonja, and R.J Villanueva. An age-structured
model for childhood obesity. Mathematical Population Studies, 17:1–11, 2010.
[46] L. Acedo, Gilberto González-Parra, and Abraham J. Arenas. An exact global solution
for the classical SIRS epidemic model. Nonlinear Analysis: Real World Applications,
11(3):1819–1825, 2010.
[47] Abraham J. Arenas, Gilberto González-Parra, and Lucas Jódar. Periodic solutions of
nonautonomous differential systems modeling obesity population. Chaos, Solitons &
Fractals, 42(2):1234–1244, 2009.
[48] Gilberto González, Abraham J. Arenas, and Lucas Jódar. Piecewise finite series
solutions of seasonal diseases models using multistage Adomian method. Communications
in Nonlinear Science and Numerical Simulation, 14:3967–3977, 2009.
[49] Abraham J. Arenas, Gilberto González-Parra, Lucas Jódar, and Rafael-J. Villanueva.
Piecewise finite series solution of nonlinear initial value differential problem. Applied
Mathematics and Computation, 212(1):209–215, 2009.
[50] Abraham J. Arenas, Gilberto González-Parra, and José Antonio Moraˆno. Stochastic
modeling of the transmission of respiratory syncytial virus (RSV) in the region of
Valencia, Spain. BioSystems, 96(3):206–212, 2009.
[51] Rafael J. Villanueva, Abraham J. Arenas, and Gilberto González-Parra. A nonstandard
dynamically consistent numerical scheme applied to obesity dynamics. Journal of
Applied Mathematics, 2008, 2008.
[52] Gilberto C. González-Parra, Abraham J. Arenas, Diego F. Aranda, Rafael J. Villanueva,
and Lucas Jódar. Dynamics of a model of Toxoplasmosis disease in human and cat
populations. Computers & Mathematics with Applications, 57(10):1692–1700,
2009.
[53] Lucas Jódar, Rafael J. Villanueva, Abraham J. Arenas, and Gilberto C. González. Nonstandard
numerical methods for a mathematical model for influenza disease. Mathematics
Computers in Simulation, 79:622–633, 2008.
[54] Diego F. Aranda, Rafael J. Villanueva, Abraham J. Arenas, and Gilberto González-
Parra. Mathematical modeling of Toxoplasmosis disease in varying size populations.
Computers & Mathematics with Applications, 56:690–696, 2008.
[55] Abraham J. Arenas, Gilberto González, and Lucas Jódar. Existence of periodic solutions
in a model of respiratory syncytial virus RSV. Journal of Mathematical
Analysis and Applications, 344:969–980, 2008.
[56] G. González, L. Jódar, R. Villanueva, and F. Santonja. Random modeling of population
dynamics with uncertainty. Wseas Transactions on Biology and Biomedicine,
5(2):34–45, 2008.
[57] L. Jódar, F. Santonja, and G. González-Parra. Modeling dynamics of infant obesity
in the region of Valencia, Spain. Computers & Mathematics with Applications,
56(3):679–689, 2008.
[58] A. Morales, L. Jódar, G. González, F.J. Santonja, R.J. Villanueva, and C. Rubio. Childhood
Obesity in the Region of Valencia, Spain: Evolution and Prevention Strategies.
Journal of Medical Sciences, 8(8):715–721, 2008.
[59] Gilberto C. González-Parra, Abraham J. Arenas, Diego F. Aranda, Rafael J. Villanueva,
and Lucas Jódar. Dinámica y modelo matemático de la toxoplasmosis en una población
de humanos y gatos. Revista Biomédica, 29(Suplemento 1):314–315, 2009.