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A new class of differential equations with impulses at instants dependent on preceding pulses. Applications to management of renewable resources
In this paper, a new type of mathematical model to represent certain processes with impulsive dynamic behavior is introduced. The main assumption is that the next impulse time is determined by three fundamental elements: ...
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A non-Newtonian gradient for contour detection in images with multiplicative noise
In this paper, a new operator for contour detection in images with multiplicative noise is presented. Traditional methods of edge detection, as those based in gradient operator or measures of variance, follow a logic and ...
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A pulse fishery model with closures as function of the catch: Conditions for sustainability
We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the remaining stock size after the last capture. The ...
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An impulsive fishery model with environmental stochasticity. Feasibility
An environmental random-effect over a deterministic population model of a resource (e.g., a fish stock) is introduced. It is assumed that the harvest activity is concentrated at a non-predetermined sequence of instants, ...
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An index to quantify individual social responsibility in the decision to be vaccinated
In the context of generic infectious disease studies, the aim of this paper is to quantify and represent the individual social responsibility based on whether or not a single individual is vaccinated. Although the objective ...
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An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors
Cabrera-Hernández, Maritza; Cordova-Lepe, Fernando ; Gutiérrez-Jara, Juan P.; Vogt-Geisse, Katia (2021)Modeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible–Infectious–Removed to ...
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Competition among predators and allee effect on prey, their influence on a gause-type predation model
González-Olivares, Eduardo; Cabrera-Villegas, Javier; Cordova-Lepe, Fernando ; Rojas, Alejandro (2019)Interference or competition among predators (CAP) has often been ruled out in depredation models, although there are varied mathematical forms to describe and incorporate it into this interaction. In this work, we present ...
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Distribution model of toxic agents and runoff phenomenon in flat aquatic regions
The study presents a model of distribution of toxic agents in flat aquatic regions such as lakes, lagoons, and coastal seas, two sources of pollution are modeled, one from the waste of industrial plants and another one, a ...
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Introductory elements for the development of a multiplicative statistic
Indicators such as the arithmetic mean and the variance have a construction based on the additive character of the real numbers field. Here we explored the analogues of some measures of central tendency and dispersion data, ...
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Linearity and its algebra in the bi-geometrical context
The multiplicative arithmetic is the base of the Biogeometric Calculus. In this work, we present the fundamental elements to construct a multiplicative linear algebra. Some important concepts and examples are given to ...
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Mathematical approach to the prevention-immigration causality of outbreaks of sexually transmitted diseases in Chile using HIV as a model
Cordova-Lepe, Fernando ; Cabrera-Hernández, Maritza; Gutiérrez-Jara, Juan P.; Gutiérrez, Rodrigo I. (2019)In Chile, in the contingent public debate about the alarming indicators of the prevalence of infectious diseases (such sexually transmitted ones), two factors stand out as determinants: inefficient or scarce preventive ...
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Mathematical model for predicting the biomass growth of Mytilus chilensis (Hupe 1954) in suspension cultures
A growth mathematical model (individual-population) of biomass for Mytilus chilensis is introduced. This incorporates the energy variable when assuming a predation component by means of the filtering. We will assume that ...
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Mathematical model of the spread of hantavirus infection
Gutiérrez-Jara, Juan Pablo; Muñoz-Quezada, María Teresa; Cordova-Lepe, Fernando ; Silva-Guzmán, Alex (2023)A mathematical epidemiological model incorporating the mobility of rodents and human groups among zones of less or major contact between them is presented. The hantavirus infection dynamics is expressed using a model type ...
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Modeling pulse infectious events irrupting into a controlled context: A SIS disease with almost periodic parameters
A new epidemic model of seasonal/cyclical pulse contagions of an infectious disease is introduced: a population with a controlled infectious disease is perturbed by a sequence of pulse infectious events arising from the ...
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Modelización del impacto epidemiológico de la existencia de un grupo conductual preventivo
En lo que concierne a salud, la experiencia indica que en toda población humana existe un porcentaje de individuos que se comporta en forma consciente ante la presencia de enfermedades infectocontagiosas. Esto implica que ...
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Modelo de umbral de reducción de tasa diaria de casos COVID-19 para evitar el colapso hospitalario en Chile
Gutiérrez Aguilar, Rodrigo; Cordova-Lepe, Fernando ; Muñoz-Quezada, María Teresa; Gutiérrez-Jara, Juan P. (2020)Mediante un modelo matemático este trabajo explora la problemática de la disponibilidad versus sobredemanda de procesos críticos hospitalarias (por ejemplo, camas críticas) ante una fuerte expansión epidémica como la que ...
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Number of COVID-19 cases in Chile at 120 days with data at 21/03/2020 and threshold of daily effort to flatten the epi-curve
Realizamos una prospectiva básica, con datos al 21/03/2020 de la evolución del número de casos COVID-19 diarios en Chile con datos del Ministerio de Salud. Asumiendo un crecimiento aritmético en la segunda variación de los ...
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Pesticide application, educational treatment and infectious respiratory diseases. A mechanistic model with two impulsive controls
In this paper, we develop and analyze an SIS-type epidemiological-mathematical model of the interaction between pesticide use and infectious respiratory disease transmission for investigating the impact of pesticide ...
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Population growth modeling with boom and bust patterns: The impulsive differential equation formalism
This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time–scales with Malthusian ...
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Pulse hospitalization to control sis diseases on farms: Economics effects
This paper introduces a mathematical model of control for an animal epidemic outbreak in an ideal farm. What has been considered for this is poultry, aquaculture or livestock affected by an infectious disease (without ...