Mayra Núñez López

Instituto Tecnológico Autónomo de México (ITAM) · Department of Mathematics

The objective of this paper is to explain through the ecological hypothesis superinfection and competitive interaction between two viral populations and niche (host) availability, the alternating patterns of RSV and influenza observed in a regional hospital in San Luis Potosí State, México using a mathematical model as a methodological tool. The da...

Diffusive predator–prey systems are well known to exhibit spatial patterns obtained by using the Turing instability mechanism. reaction–diffusion systems were already studied by replacing the time derivative with a fractional order derivative, finding the conditions under which spatial patterns could be formed in such systems. The recent interest i...

We present a model that explicitly links the epidemiological Ross-Macdonald model with a simple immunological model through a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the relationship between the reproductive numbers at the population (between-host) and individual level (within-host), in particular the...

Human trafficking is a heartless crime that represents the second most profitable crime in the world. Mexico's geographical position makes it a country with high levels of human trafficking. Using the snowball sampling method, the major contribution of this paper is the abstraction of the human trafficking network on the southern border of Mexico....

En este trabajo estudiamos la influencia de la curvatura del medio sobre la formaci´on de patrones mediante el mecanismo de inestabilidad de Turing generada por difusi´on. Para analizar el efecto de la curvatura consideramos la variedad curva cerrada m´as simple, una circunferencia. Presentamos el operador de Laplace-Beltrami, que es la generalizac...

In this work, we present a diffusive predator–prey model with a finite interaction scale between species and an external flow. The system is confined to a two-dimensional domain with one coordinate larger than another, which allows us to use the one-dimensional projection of the diffusion operator, known as the Fick-Jacobs projection, here with an...

Modeling the interplay between immune system components and cancer cells via immunotherapy is the purpose of this work. We present a simple mathematical model of interaction between tumor cells and the immune system’s effector cells. With rigorous mathematical analysis and numerical continuation, we study the generalized Hopf bifurcations (GH), kno...

In this paper, we explore the interplay between tumor cells and the human immune system, based on a deterministic mathematical model of minimal interactions by transforming it to stochastic model using a continuous-time Markov chain, where time is continuous but the state space is discrete. Furthermore, we simulate the stochastic basin of attractio...

The interaction and possibly interference between viruses infecting a common host population is the problem addressed in this work. We model two viral diseases both of the SIRS type that have similar mechanism of transmission and for which a vaccine exists. The vaccine is characterized by its coverage, induced temporal immunity and efficacy. The po...

Highlights: • We address the migration of the human population and its effect on pathogen reinfection. • We use a Markov-chain SIS metapopulation model over a network. • The contact rate is based on the infected hosts and the incidence of their neighboring locations. • We estimate from Dengue data in Mexico the dynamics of migration incorporating...

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metap...

We study a reaction-diffusion system within a long channel in the regime in which the projected Fick-Jacobs-Zwanzig operator for confined diffusion can be used. We found that under this approximation, Turing instability conditions can be modified due to the channel geometry. The dispersion relation, range of unstable modes where pattern formation o...

The objective of this study was to investigate the effect of four levels of molasses on chemical composition, in vitro digestibility, methane production and fatty acid profile of canola silages. A canola (Brassica napus var. Monty) crop was established in a small-scale agricultural farm and harvested 148 days after sowing. Four levels of molasses w...

In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and volume of adsorbent particles, which are well-represented by their fractal dimensions. The method of lines was u...

Most of the recent epidemic outbreaks in the world have a strong immigration component as a trigger rather than the dynamics implied by the basic reproduction number. In this work we present and discuss an approach to the problem of pathogen reinfections in a given area that associates people mobility and transmission of dengue, using a Markov-chai...

In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and volume of adsorbent particles, which are well-represented by their fractal dimensions. The method of lines was u...

In this paper, we explore the interplay of virus contact rate, virus production rates, and initial viral load during early HIV infection. First, we consider an early HIV infection model formulated as a bivariate branching process and provide conditions for its criticality R0 > 1. Using dimensionless rates, we show that the criticality condition R0...

We present a mathematical model for competition between species that includes variable carrying capacity within the framework of niche construction. We make use the classical Lotka-Volterra system for species competition and introduce a new variable which contains the dynamics of the constructed niche. The paper illustrates that the total available...

In this work we present a mathematical model that incorporates two Dengue serotypes. The model has been constructed to study both the epidemiological trends of the disease and conditions that allow coexistence in competing strains under vaccination. We consider two viral strains and temporary cross-immunity with one vector mosquito population. Resu...

In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with mixtures of rotational symmetries not reported before. The type of anomalous diffusion discussed in this work, e...

In this work, we present a methodological procedure to validate the numerical solution of the diffusive part in a reaction-diffusion model. Uniform explicit finite differences method is used to generate the solution in a confined circular domain with boundary condition of zero flux. For the validation of the numerical solution, we consider three di...

In this manuscript, we review the reaction-diffusion systems when these processes occur on curved surfaces. We show a general overview, from the original manuscripts by Turing, to the most recent developments with thick curved surfaces. We use the classical Schnakenberg model to present in a self-contained way the instability conditions of pattern...

In this work we present the two-dimensional motion of a viscoelastic membrane immersed in incompressible inviscid and viscous fluids. The motion of the fluid is modelled by two-dimensional Navier-Stokes equations, and a constitutive equation is considered for the membrane which captures along with the fluid equations the essential features of the v...

We present a mathematical model for a technology cycle model that centers its attention on the coexistence mechanism of competing technologies. We use a biologically analogy to couple the adoption of a technology with the supply of financial resources. In our model financial resources are limited but provided at a constant rate. There are two varia...

The objective of this paper is to explain through the ecological hypothesis superinfection and competitive interaction between two viral populations and niche (host) availability, the alternating patterns of Respiratory Syncytial Virus (RSV) and influenza observed in a regional hospital in San Luis Potosí State, México using a mathematical model as...

We present a general phenomenological formalism for the modeling of hydraulic head behaviour in naturally fractured aquifers. A non local in time version of the double porosity model is developed for Euclidean and fractal reservoirs. In the fractal case, time non-locality allows to find the geometric and topological factors responsible for subdiffu...

The Galton’s board is a periodic lattice made with fixed nails at its nodes, spherical grains travel through them due to gravity. We show the convenience of this system to present the main concepts of Markovian-stochastic trajectories during the motion of only one particle. In a special case, the Galton board was modified, a set of nails (20%) were r...

In this work we present a brief review of specific models that have been used for pressure-transient modeling in fractal reservoirs, and propose some alternatives with particular emphasis on the description of pressure-tests on naturally fractured reservoir with fractal geometry. The model equations can be classified as local or differential models...

The Galton´s board is a periodic lattice with fixed nails at its nodes, spherical grains travel through them due to gravity. This system is commonly used to show the central limit theorem when a big quantity of grains fall down from the upper edge. We show the convenience of this system to present the main concepts of Markovian-stochastic motion of...

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals’ interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one, showing how spatial patterns can emerge for some values of the interaction range and of the diffusion parameter.

We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that patterns can emerge in some regions of the parameters space where the instability is driven by the range of the i...