# Jose D. FloresUniversity of South Dakota | USD · Department of Mathematical Sciences

Jose D. Flores

Numerical Analysis, Ph.D.

My research interest is in mathematical models for population ecology.

## About

52

Publications

13,522

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,013

Citations

Introduction

My research interest is population dynamics: Population models, predator-prey type with dispersion. Ecological Networks.

Additional affiliations

Education

August 1982 - May 1989

## Publications

Publications (52)

In this manuscript, we study a Leslie–Gower predator-prey model with a hyperbolic functional response and weak Allee effect. The results reveal that the model supports coexistence and oscillation of both predator and prey populations. We also identify regions in the parameter space in which different kinds of bifurcations, such as saddle-node bifur...

Anticipating the number of hospital beds needed for patients with COVID-19 remains a challenge. Early efforts to predict hospital bed needs focused on deriving predictions from SIR models, largely at the level of countries, provinces, or states. In the USA, these models rely on data reported by state health agencies. However, predicting disease and...

A predator–prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium points in the first quadrant, one is always a saddle point and the other exhibits multi-stability phenomenon since the equilibrium...

We study the Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response and show the existence and stability of two interior equilibrium points. We prove that the model displays a wide range of different bifur-cations, such as saddle-node bifurcations, Hopf bifurcations, homoclinic bifurcations and...

In this manuscript, we consider temporal and spatio-temporal modified Holling–Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator. From our result of the temporal model, we identify regions in parameter space in which Turing instability in t...

In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least-weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from...

In the present study, we have modified the traditional May-Holling-Tanner predator-prey model used to represent the interaction between least weasel and field-vole population by adding an Allee effect (strong and weak) on the field-vole population and alternative food source for the weasel population. It is shown that the dynamic is different from...

In this manuscript, we study a Leslie–Gower predator-prey model with a hyperbolic functional response and weak Allee effect on the prey. The results reveal that the model supports coexistence and oscillation of both
predator and prey populations. We also identify regions in the parameter space in which different kinds of bifurcations, such as saddl...

Anticipating the number of hospital beds needed for patients with COVID-19 remains a challenge. Early efforts to predict hospital bed needs focused on deriving predictions from SIR models, largely at the level of countries, provinces, or states. In the United States, these models rely on data reported by state health agencies. However, predictive d...

In this manuscript, we consider temporal and spatio-temporal modified Holling-Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator. From our result of the temporal model, we identify regions in parameter space in which Turing instability in t...

We analyze a modified Holling–Tanner predator–prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements the results of previous articles by Saez and González-Olivares [1999] and Arancibia-Ibarra and González-Olivares [2015]...

We study a predator-prey model with predator intra-specific interactions and ratio-dependent functional response. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, we show that when the parameters are varied the model displays a...

We study a predator-prey model with predator intra-specific interactions and ratio-dependent functional response. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, we show that when the parameters are varied the model displays a...

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stab...

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stab...

We analyse a modified Holling-Tanner predator-prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements results of previous articles by Saez and Gonzalez-Olivares (SIAM J. Appl. Math. 59 1867-1878, 1999) and Arancibia-Ibarra...

In this work, a modified Leslie–Gower predator–prey model is analyzed, considering an alternative food for the predator and a ratio-dependent functional response to express the species interaction. The system is well defined in the entire first quadrant except at the origin (0,0). Given the importance of the origin (0,0) as it represents the extinc...

We study a predator-prey model with Holling type I functional response, an alternative food source for the predator, and multiple Allee effects on the prey. We show that the model has at most two equilibrium points in the first quadrant, one is always a saddle point while the other can be a repeller or an attractor. Moreover, there is always a stab...

Introduction:
Epidemiological studies of the 1957 influenza pandemic are scarce, particularly from lower income settings.
Methods:
We analyzed the spatial-temporal mortality patterns of the 1957 influenza pandemic in Chile including detailed age-specific mortality data from a large city and investigated risk factors for severe mortality impact a...

Background. Quantitative estimates of the global burden of the 1957 influenza pandemic are lacking. Here we fill this gap by modeling historical mortality statistics.
Methods. We used annual rates of age- and cause-specific deaths to estimate pandemic-related mortality in excess of background levels in 39 countries in Europe, the Asia-Pacific regio...

This work deals with the dynamics of a bioeconomic continuous time model, where the combined action of the fishing effort exerted by men (as a predator) and multiple Allee effect or depensation on the growth rate of a self-regenerating resource (the prey) are considered.
It has been recently established that a depensation phenomenon appears by dive...

Scarce information about the epidemiology of historical influenza pandemics in South America prevents complete understanding of pandemic patterns throughout the continent and across different climatic zones. To fill gaps with regard to spatiotemporal patterns of deaths associated with the 1918 influenza pandemic in Chile, we reviewed archival recor...

The social dynamics of residential solar panel use within a theoretical
population are studied using a compartmental model. In this study we consider
three solar power options commonly available to consumers: the community block,
leasing, and buying. In particular we are interested in studying how social
influence affects the dynamics within these...

We analyze a ratio-dependent predator–prey model with Allee effect on the prey by making a parametric analysis of the stability properties of the dynamics of the system in which the functional response is a function of the ratio of prey to predator abundance. An important mathematical feature of these type of models is that while the functional res...

We extend a previous study of a predator–prey model with strong Allee effect on the prey in which the functional response is a function of the ratio of prey to predator. We prove that the solutions are always bounded and non-negative, and that the species can always tend to long-term extinction. By means of bifurcation analysis and advanced numeric...

Pollution represents a major threat to biodiversity. A wide class of pollutants tends to accumulate within organisms and propagate within communities via trophic interactions. Thus the final effects of accumulable pollutants may be determined by the structure of food webs and not only by the susceptibility of their constituent species. Species with...

Human activities have led to massive influxes of pollutants, degrading the habitat of species and simplifying their biodiversity. However, the interaction between food web complexity, pollution and stability is still poorly understood. In this study we evaluate the effect exerted by accumulable pollutants on the relationship between complexity and...

In this work, a predator-prey model considering a ratio-dependent functional response
and the influence of a simple Allee effect on prey is analyzed.
Main properties of model are established using a topological equivalent system for
which we proved the existence of a separatrix curve determined by the non-hyperbolic
equilibrium point (0; 0).
We als...

The main purpose of this work is to analyze a Gause type predator-prey model in which two ecological phenomena are considered: the Allee effect affecting the prey growth function and the formation of group defence by prey in order to avoid the predation. We prove the existence of a separatrix curves in the phase plane, determined by the stable mani...

The purpose of this study is to analyze the population dynamics of loggerhead sea turtles (Caretta caretta) affected by localized oil spills. Methods include development of a spatial, stage-classified matrix model parameterized for the following primary loggerhead populations: Gulf of Mexico, western North Atlantic Ocean, and Florida peninsula. Oil...

1. Earlier studies used static models to evaluate the responses of mutualistic networks to external perturbations. Two classes of dynamics can be distinguished in ecological networks; population dynamics, represented mainly by changes in species abundances, and topological dynamics, represented by changes in the architecture of the web.
2. In this...

The aim of this paper is to correct two mistakes in [Appl. Math. Modell. (2011) 366–381], which are: the function defining the time rescaling given and the inclusion of a parameter outside of model.For a modified Leslie–Gower type predator–prey model considering the Allee effect on prey, a change of variables and a new time rescaling generating a d...

A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a paramet-
ric analysis of stability properties of dynamics on the system in which the functional response is a function of the ratio of prey to predator. It is shown that incorporating of Allee effect on prey equation significantly modifies the dynamics of...

Pollination systems are recognized as critical for the maintenance of biodiversity in terrestrial ecosystems. Therefore, the understanding of mechanisms that promote the integrity of those mutualistic assemblages is an important issue for the conservation of biodiversity and ecosystem function. In this study we present a new population dynamics mod...

The main goal of this work is to show a comparative analysis of simple continuous time predator–prey models considering the Allee effect affecting the prey population, also known as depensation in fisheries sciences.This phenomenon may be expressed by different mathematical forms, yielding a distinct number of limit cycles surrounding a positive eq...

Background/Question/Methods
Mutualistic systems composed by flowering plants and their pollinators are fundamental for the maintenance of biodiversity in terrestrial ecosystems. Nevertheless, our understanding of the factors affecting their dynamic responses to environmental disruption is still poor. In this study we analyze the effect of adaptiv...

This work deals with the analysis of a predator–prey model derived from the Leslie–Gower type model, where the most common mathematical form to express the Allee effect in the prey growth function is considered.It is well-known that the Leslie–Gower model has a unique globally asymptotically stable equilibrium point. However, it is shown here the A...

Research on ecological communities, and plant–pollinator mutualistic networks in particular, has increasingly benefited from the theory and tools of complexity science. Nevertheless, up to now there have been few attempts to investigate the interplay between the structure of real pollination networks and their dynamics. This study is one of the fir...

Inducible defenses are a form of phenotypic plasticity that potentially modify direct interactions between various members of an ecological community, generating traitmediated indirect effects. In this work, the hypothesis that inducible defenses increase the stability of tritrophic chains is tested, through the numerical analysis of a continuousti...

In the fragmented Maulino forest (in Central Chile), differences in the relative frequencies of species between seedlings and mature trees are strong indicators of a changing replacement dynamics in the community. Stationary Markov chain models predict that the future tree composition such Maulino forest fragments will differ from that of continuou...

In this work we analyze a predator-prey model proposed by A. Kent et al. in Ecol. Model.162, 233 (2003), in which two aspect of the model are considered: an effect of emigration or immigration on prey population to constant rate and a prey threshold level for predators. We prove that the system when the immigration effect is introduced in the model...

In this work we analyze the consequences of incorporating the phenomenon of depensation, also known as Allee effect, into the bioeconomic model proposed by Smith in [20]. The Smith's model is one of the simplest bioeconomic models used in the management of renewable resources, which related the biomass of the exploited resources and the nominal fis...

A boundary integral equation reformulation of the exterior Dirichlet problem for Laplace's equation yields an integral equation of the first kind, in which the unknown is the normal derivative on the boundary of the unknown harmonic function. The integral equation is solved with a collocation method based on piecewise quadratic interpolation. The d...

We consider the interior Dirichlet problem for Laplace’s equation on a non-simply connected two-dimensional regions with smooth boundaries. The solution is sought as the real part of a holomorphic function on the region, given as Cauchy-type integral. The approximate double layer density function is found by solving a system of Fredholm integral eq...

We consider the interior Dirichlet problem for Laplace's equation on a non-simply connected two-dimensional regions with smooth boundaries. The solution is sought as the real part of a holomorphic function on the region, given as Cauchy-type integral. The approximate double layer density function is found by solving a system of Fredholm integral eq...

We present the conjugate gradient method, CG method, to solve large dense linear systems whose associated matrix has clustered eigenvalues, and we give the implementation of the algorithm using MATLAB, an interactive programming language for scientific computing.

The collocation method for solving linear and nonlinear integral equations results in many integrals which must be evaluated numerically. In this paper, we give a general framework for discrete collocation methods, in which all integrals are replaced by numerical integrals. In some cases, the collocation method leads to solutions which are supercon...

The conjugate gradient method (CG method) is applied to linear integral equations of the second kind. Based on a result from Winther [23] rate of convergence is given for several integral operators considering the smoothness of the kernel function. Numerical examples are included.

## Projects

Project (1)