Publications
| Authors | Title | Journal | Year | Link |
| J. López-de-la-Cruz S. Merchán F. Rivero J. Rodrigo | SIR models with demography, random transmission coefficient and non-autonomous vaccination rate | Computational and Applied Mathematics | 2026 |  |
| J. López-de-la-Cruz A. N. Oliveira-Sousa | SIR models with vital dynamics, reinfection, and randomness to investigate the spread of infectious diseases | Communications in Nonlinear Science and Numerical Simulation | 2025 |  |
| T. Caraballo J. López-de-la-Cruz V. Caraballo-Romero | Effects of real random perturbations on Monod and Haldane consumption functions in the chemostat model | Mathematics and Computers in Simulation | 2024 | |
| T. Caraballo J. López-de-la-Cruz V. Caraballo-Romero | Chemostat models with Monod and Haldane consumption functions and random environmental fluctuations | Mathematical Methods in the Applied Sciences | 2023 |  |
| T. Caraballo J. López-de-la-Cruz V. Caraballo-Romero | Non-autonomous chemostat models with non- monotonic growth | International Journal of Computer Mathematics | 2022 | |
| T. Caraballo J. López-de-la-Cruz A. Rapaport | Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations | Stochastics and Dynamics | 2022 | |
| T. Caraballo J. López-de-la-Cruz | Survey on chemostat models with bounded random input flow | Mathematical Modelling and Control | 2021 | |
| T. Caraballo J. López-de-la-Cruz | Bounded random fluctuations on the input flow in chemostat models with wall growth an non-monotonic kinetics | AIMS Mathematics | 2021 | |
| T. Caraballo R. Colucci J. López-de-la-Cruz A. Rapaport | Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate | Mathematical Biosciences and Engineering | 2020 | |
| J. López-de-la-Cruz et al | Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infection | Communications in Nonlinear Science and Numerical Simulation | 2020 | |
| R. Colucci J. López-de-la-Cruz | Dynamics of fermentation models for the production of dry and sweet wine | Communications in Pure and Applied Analysis | 2020 | |
| T. Caraballo J. López-de-la-Cruz A. Rapaport | Modeling bounded random fluctuations in biological systems: application to the chemostat model with two species | IFAC Papers Online | 2019 | |
| J. López-de-la-Cruz | Random and stochastic disturbances on the input flow in chemostat models with wall growth | Stochastic Analysis and Applications | 2019 | |
| T. Caraballo R. Colucci J. López-de-la-Cruz A. Rapaport | A way to model stochastic perturbations in population dynamics models with bounded realizations | Communications in Nonlinear Science and Numerical Simulation | 2019 | |
| T. Caraballo M. J. Garrido-Atienza J. López-de-la-Cruz A. Rapaport | Modeling and analysis of random and stochastic input flows in the chemostat model | Discrete and Continuous Dynamical Systems – Series B | 2019 | |
| T. Caraballo M. J. Garrido-Atienza J. López-de-la-Cruz | Dynamics of some stochastic chemostat models with multiplicative noise | Communications in Pure and Applied Analysis | 2017 | |
| T. Caraballo M. J. Garrido-Atienza J. López-de-la-Cruz | Some Aspects Concerning the Dynamics of Stochastic Chemostats. Chapter in Advances in Dynamical Systems and Control | Springer International Publishing Switzerland | 2016 | |
Participation in research groups
| Research group | University | Link |
| Análisis Estocástico de Sistemas Diferenciales (Stochastic Analysis of Differential Systems) | Universidad de Sevilla (Spain) |  |
| Modelos Matemáticos No Lineales (Non-linear Mathematical Models) | Universidad Politécnica de Madrid (Spain) | |
Participation in research projects
| Title of the project | Reference | Funder | University |
| Dinámica determinista y estocástica en las ciencias aplicadas | PID2021-122991NB-C21 | Ministerio de Ciencia e Innovación (Spanish government) | Universidad de Sevilla (Spain) |
| Deterministic and stochastic dynamics of models from Neuroscience, Epidemiology, Biology and other branches of the Applied Sciences | US-1254251 | Proyectos I+D+i FEDER Andalucía 2014-2020 (Andalusian government) | Universidad de Sevilla (Spain) |
| Análisis y Aplicaciones de Sistemas Dinámicos no Autónomos y Estocásticos (Analysis and applications of non-autonomous and stochastic dynamical systems) | P12-FQM-1492 | Proyectos de Excelencia Junta de Andalucía (Projects of Excellence Andalusian government) | Universidad de Sevilla (Spain) |
Research stays and visits
| Host | University | City / Country | Dates |
| Prof. Dr. Renato Colucci | Università Politecnica delle Marche | Ancona / Italy | 15th February – 22nd August 2020 (6 months) |
| Prof. Dr. Renato Colucci | Università degli Studi Niccolò Cusano | Roma / Italy | 22nd November – 5th December 2018 (19 days) |
| Prof. Dr. Alain Rapaport | UMR INRA / SupAgro MISTEA | Montpellier / France | 4th September – 22nd September 2018 (18 days) |
| Prof. Dr. Alain Rapaport | UMR INRA / SupAgro MISTEA | Montpellier / France | 8th May – 10th June 2017 (1 month) |
| Prof. Dr. Alain Rapaport | UMR INRA / SupAgro MISTEA | Montpellier / France | 9th October – 10th December 2016 (2 months) |
Contributions in national and international congresses
| Title of the contribution | Congress | Place | Type | Date |
| Advanced Modeling Techniques in Life Sciences: The Role of Stochastic and Random Differential Equations | International Seminar on PDE Theory and Applications | Lima (Peru) | Invited talk | August 2025 |
| Uncertainty Modeling in Real-World Applications: the Classical Approach versus new Emerging Trends | XXXVIII Coloquio de la Sociedad Matemática Peruana | Lima (Peru) | Invited talk | August 2025 |
| Modelling and analysis of the dynamics of infectious diseases described by differential systems with uncertainties | Mathematical Modelling in Engineering & Human Behaviour 2025 Conference (MME&HB 2025) | Valencia (Spain) | Invited talk | July 2025 |
| Dynamics of biological phenomena described by differential systems with different types of noise | International Workshop on Nonlinear Problems in Partial Differential Equations. Applications and Methods | Madrid (Spain) | Plenary talk | February 2025 |
| Study of the spread of infectious diseases: SIR models incorporating vital dynamics, reinfection, and random transmission coefficient | ICMC Summer Meeting on Differential Equations 2025 | São Carlos (Brazil) | Invited talk | February 2025 |
| A new approach to model randomness in differential systems with real applications | VIII Jornada Internacional de Ecuaciones Diferenciales y Aplicaciones | Lima (Peru) | Invited talk | October 2024 |
| Dynamics of the classical chemostat model with real random kinetics | International Conference on Mathematical Analysis and Applications in Science and Engineering | Porto (Portugal) | Regular talk | June 2024 |
| The chemostat model with real random perturbations on Monod and Haldane consumption functions | ICMC Summer Meeting on Differential Equations 2024 Chapter | São Carlos (Brazil) | Invited talk | January 2024 |
| Comparison between white and real noise to model disturbances on the input flow in chemostats | International Workshop on Deterministic and Stochastic Dynamics and Applications | Elche (Spain) | Invited talk | March 2023 |
| Modeling real noise in population dynamics with applications to the chemostat model | International Conference on Mathematical Analysis and Applications in Science and Engineering | Oporto (Portugal) | Regular talk | June 2022 |
| Modeling bounded random fluctuations in the classical chemostat with non-monotonic consumption function | ICMC Summer Meeting on Differential Equations 2021 Chapter | São Carlos (Brazil) | Invited talk | February 2021 |
| Modeling bounded random disturbances in biological systems: an application to bioreactors | 1st International Congress of Pure and Applied Mathematics | Callao (Peru) | Invited talk | November 2020 |
| Studying the long-time dynamics of fermentation models: production of dry and sweet wine | ICMC Summer Meeting on Differential Equations 2020 Chapter | São Carlos (Brazil) | Regular talk | February 2020 |
| Modeling bounded random fluctuations in biological systems: application to the chemostat model with two species | 8th IFAC Conference on Foundations of Systems Biology in Engineering | Valencia (Spain) | Invited talk | October 2019 |
| Biological systems with bounded random disturbances: the chemostat model with wall growth | Workshop on PDEs for biology systems | Sevilla (Spain) | Regular talk | April 2019 |
| Effects of bounded random disturbances on chemostat models with several species and wall growth | ICMC Summer Meeting on Differential Equations 2019 Chapter | São Carlos (Brazil) | Regular talk | February 2019 |
| Modeling and analyzing the dynamics of random chemostat models with wall growth and Monod kinetics | II Joint Meeting Spain-Brazil in Mathematics | Cádiz (Spain) | Invited talk | December 2018 |
| Modeling and analyzing the long-time behavior of random chemostat models | 9th Vienna International Conference on Mathematical Modelling | Vienna (Austria) | Poster | February 2018 |
| Pullback attractors to analyze the effect of random and stochastic disturbances in the chemostat model | ICMC Summer Meeting on Differential Equations 2018 Chapter | São Carlos (Brazil) | Regular talk | February 2018 |
| Random dynamical systems to analyze different ways of modeling stochastic chemostats | Conferencia Española de Biometría 2017 | Sevilla (Spain) | Regular talk | September 2017 |
| Dynamics of some stochastic chemostat models with multiplicative noise | Congreso de Ecuaciones Diferenciales y Aplicaciones/Congreso de Matemática Aplicada 2017 | Cartagena (Spain) | Invited talk | June 2017 |
Conferences given in seminars, workshops and visits
| Title of the contribution | Event – University | Place | Date |
| Modeling Biological Phenomena Subject to Randomness: Differential Equations to Understand Real Life | Conferencias Magistrales – Facultad de Ciencias Naturales y Matemática – Universidad Nacional del Callao | Lima (Peru) | August 2025 |
| A walk through stochastic and random differential equations and uncertainty modeling in the life sciences | Seminario Doctorado – Instituto de Matemáticas de la Universidad de Sevilla | Sevilla (Spain) | June 2025 |
| Stochastic versus random differential equations to model real phenomena in life sciences | XXVI Summer School of the Graduate Program in Pure and Applied Mathematics – Universidade Federal de Santa Catarina | Florianópolis (Brazil) | February 2025 |
| Modelización y estudio de fenómenos reales descritos mediante sistemas diferenciales sometidos a perturbaciones aleatorias | Curso doctorado “Modelos No Lineales en Ingeniería Matemática” – Universidad Politécnica de Madrid | Madrid (Spain) | January 2025 |
| An introduction to modeling random and stochastic perturbations in differential systems with real applications | Seminário em Dinâmica não-linear – Instituto de Ciências Matemáticas e de Computação – Universidade de São Paulo | São Carlos (Brazil) | May 2024 |
| Modeling and analysis of random and stochastic disturbances in chemostat devices | Seminario de Análisis Matemático y Matemática Aplicada – Universidad Complutense de Madrid | Madrid (Spain) | March 2024 |
| Modelización y estudio de biorreactores sometidos a perturbaciones aleatorias. | Curso doctorado “Modelos No Lineales en Ingeniería Matemática” – Universidad Politécnica de Madrid | Madrid (Spain) | January 2024 |
| Modelización y estudio de biorreactores sometidos a perturbaciones aleatorias. | Curso doctorado “Modelos No Lineales en Ingeniería Matemática” – Universidad Politécnica de Madrid | Madrid (Spain) | January 2023 |
| Stochastic and random fluctuations in biological systems | Seminário em Dinâmica não-linear – Instituto de Ciências Matemáticas e de Computação – Universidade de São Paulo | São Carlos (Brazil) | December 2022 |
| Perturbaciones aleatorias en modelos de quimiostato | Acto Homenaje a la Profesora María José Garrido Atienza – Facultad de Matemáticas – Universidad de Sevilla | Sevilla (Spain) | May 2022 |
| Sistemas dinámicos autónomos y estudio de modelos epidemiológicos | Seminario de investigación Antonio Giraldo y Sonia Sastre – Universidad Politécnica de Madrid | Madrid (Spain) | October 2021 |
| How to maximize the bio-gas production? An optimization problem with different geometrical configurations | Instructor in ECMI Postgraduate / VI Iberian / NeEDS Modeling week – Instituto de Matemáticas de la Universidad de Sevilla | Sevilla (Spain) | July 2019 |
| A new way of modeling random input flows in chemostat models | MOCAS seminar of MISTEA lab – INRA Montpellier SupAgro | Montpellier (France) | September 2018 |
| Analysis of some stochastic chemostat models by means of random dynamical systems | Journée des doctorants et postdoctorants en modelisation et commande des bioprocedes – Laboratory of Environmental Biotechnology | Narbonne (France) | May 2017 |
| Dynamics of some stochastic chemostat models with multiplicative noise | Seminario PHD – Instituto de Matemáticas de la Universidad de Sevilla | Sevilla (Spain) | January 2017 |
| Dynamics of a non-autonomous chemostat | Seminario PHD – Instituto de Matemáticas de la Universidad de Sevilla | Sevilla (Spain) | November 2015 |
| Dynamics of a non-autonomous chemostat | Curso Física y Matemáticas: dos caras de una misma moneda – Instituto de Matemáticas de la Universidad de Sevilla | Sevilla (Spain) | July 2015 |