arXiv subjects

Javier López-de-la-Cruz

Publications and source records attributed to Javier López-de-la-Cruz.

8 recordsLinked to original sources

arXiv2026

SIR model with random diffusion, reinfection, and random transmission: exponential attractors and spread of the disease

We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence of both random and exponential attractors. We construct a non-stationary, random disease-free global solution, which serves to localize the random attractor. Furthermore, we analyze the mean value of the random transmission coefficient to establish conditions under which the disease may either be eradicated or persist in an endemic state, depending on the system's parameters.

math.DS↗

arXiv2026

Random chemostats with competition and different kinetics to investigate the growth of the gut microbiome

We investigate some chemostat models incorporating wall growth, competition, random fluctuations on the dilution rate, and different consumption functions (Monod and Haldane). We analyze the asymptotic behavior of the solutions of the corresponding random differential systems to establish conditions on the model parameters under which the microbes persist in the gut or disappear. Moreover, several numerical simulations are presented to support the theoretical results and illustrate their biological interpretation.

math.DS↗

arXiv2025

SIR models with demography, random transmission coefficient and non-autonomous vaccination rate

In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we establish the existence and uniqueness of non-negative global solution of the models and derive conditions under which either the disease is eradicated or becomes endemic. In addition, the theoretical results are further illustrated by several numerical simulations.

q-bio.PE↗

arXiv2024

SIR models with vital dynamics, reinfection and randomness to investigate the spread of infectious diseases

We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and global well-posedness, the existence and internal structure of attractors, and the presence of gradient dynamics. Subsequently, we explore the implications of small nonautonomous random perturbations, establishing the continuity of attractors and ensuring their topological structural stability. Additionally, we study scenarios in which both the transmission coefficient and the recruitment rate exhibit time-dependent or random behavior. For each scenario, we establish the existence of attractors and delineate conditions that determine whether the disease is eradicated or reaches an endemic state. Finally, we depict numerical simulations to illustrate the theoretical results.

math.DS↗

arXiv2024

A way to model stochastic perturbations in population dynamics models with bounded realizations

In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some basic models in population dynamics such as the logistic equations and competitive Lotka-Volterra systems. The key is the fact that these perturbations can be ensured to keep inside some interval that can be previously fixed, for instance, by practitioners, even though the resulting model does not generate a random dynamical system. However, one can still analyze the forwards asymptotic behavior of these random differential systems. Moreover, to illustrate the advantages of this type of modeling, we exhibit an example testing the theoretical results with real data, and consequently one can see this method as a realistic one, which can be very useful and helpful for scientists.

math.DS↗

arXiv2024

Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infection

This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas aeruginosa. This dangerous pathogen is one of the leading causes of multi-resistant infections and can be transmitted from dogs to humans. Numerical simulations and appropriated codes were developed using Matlab software to gather information concerning long-time dynamics of the susceptible, infected and recovered individuals. All data compiled from the mathematical model was used to provide an appropriated antibiotic sensitivity panel for this specific infection. In this study, several variables have been included in this model to predict which treatment should be prescribed in emergency cases, when there is no time to perform an antibiogram or the cost of it could not be assumed. In particular, we highlight the use of this model aiming to become part of the convenient toolbox of Public Health research and decision-making in the design of the mitigation strategy of bacterial pathogens.

q-bio.PE↗

arXiv2024

Random and stochastic disturbances on the input flow in chemostat models with wall growth

In this paper we analyze a chemostat model with wall growth where the input flow is affected by two different stochastic processes: the well-known standard Wiener process, which leads into several drawbacks from the biological point of view, and a suitable Orsntein-Uhlenbeck process depending on some parameters which allow us to control the noise to be bounded inside some interval that can be fixed previously by practitioners. Thanks to this last approach, which has already proved to be very realistic when modeling other simplest chemostat models, it will be possible to prove the persistence and coexistence of the species in the model without needing the theory of random dynamical systems and pullback attractors needed when dealing with the Wiener process which, moreover, does not provide much information about the long-time behavior of the systems in many situations.

math.DS↗

arXiv2017

Corrigendum to the chapter "Some aspects concerning the dynamics of stochastic chemostats"

In this paper we correct an error made in a previous work, where a misleading stochastic system was obtained due to a lapse concerning a sign in one of the equations at the beginning of the work such that the results obtained are quite different to the ones developed throughout this paper since the required conditions, and also the results, substantially change. Then, in this work we repair the analysis carried out there, where we studied a simple chemostat model influenced by white noise by making use of the theory of random attractors. Even though the changes are minor, we have chosen to provide a new version of the entire paper instead of a list of changes, for sake of readability. We first perform a change of variable using the Ornstein-Uhlenbeck process, transforming our stochastic model into a system of differential equations with random coefficients. After proving that this random system possesses a unique solution for any initial value, we analyze the existence of random attractors. Finally we illustrate our results with some numerical simulations.

math.DS↗