Population Growth Modeling With Boom and Bust Patterns: The Impulsive Differential Equation Formalism

Córdova–Lepe, Fernando; Robledo, Gonzalo; Cabrera-Villegas, Javier

doi:10.1142/s0218339015400112

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…Our goal was to study the trade-off dynamics between the removal of waste containers and the cleaning of illegal micro-dumps. This dynamics was represented using a mathematical model described by an impulsive differential system at both fixed and variable times (Cordova-Lepe et al, 2015). The findings establish two scenarios in the long term, the containers are full or not, and whose differentiation depends on a threshold that is a function of all model parameters.…”

Section: Discussionmentioning

confidence: 90%

Un modelo matemático estratégico de la disposición de residuos

Gutiérrez,

Córdova-Lepe,

Acuña-Rodríguez

2023

Rev. model. mat. sist. biol.

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El impacto de las acciones humanas sobre el medio ambiente plantea varios desafíos a nivel global con soluciones que merecen la participación conjunta de los sectores productivos, políticos y de la sociedad civil. La escasez de recursos, la degradación de los ecosistemas y el cambio climático deben ser abordados con urgencia, siendo necesario un cambio de paradigma en las formas de producción y consumo. Sin embargo, a pesar de los notables avances en el reciclaje y el suprareciclaje, los rellenos sanitarios y vertederos siguen siendo la principal forma de eliminación de residuos en todo el mundo. Es más, una cantidad importante de residuos se elimina de manera ilegal afectando la calidad de vida de las comunidades que viven en zonas cercanas. Este trabajo estudia la compensación entre el retiro de contenedores de residuos y la limpieza de micro-vertederos ilegales mediante el control impulsivo. Se formula un modelo matemático de tipo estratégico, aquel que capta aspectos mínimos pero relevantes del fenómeno, para describir la dinámica de la basura.

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Section: Discussionmentioning

confidence: 90%

Un modelo matemático estratégico de la disposición de residuos

Gutiérrez,

Córdova-Lepe,

Acuña-Rodríguez

2023

Rev. model. mat. sist. biol.

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“…To show the effects of allergen immunotherapy and its results when the patient is exposed to high concentrations of pollen in the environment, the dynamics are described on two time scales, continuous and discrete, typical of the formalism of impulsive differential equations. [18,19]. The first describes the response of the immune system in the absence of the allergen either by therapy or by exposure t = {t k , t m } phenomenon described by cell interaction, where the naive lymphocytes or T h 0 change their concentration due to their differentiation processes, both for T reg lymphocytes and T h 2 lymphocytes, with rates α 2 , α 3 respectively.…”

Section: Mathematical Modelingmentioning

confidence: 99%

Impulsive simulation model for the dynamics of allergen immunotherapy

Vergaño-Salazar

Córdova–Lepe

Pastenes

et al. 2022

J. Phys.: Conf. Ser.

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This study aims to analyze the effects of allergen immunotherapy, used to treat allergic symptoms such as pollen allergy. Mathematical models are used as a methodological approach to simulate from a system of impulsive differential equations the dynamics of the model. Immunotherapy is based of supplying small amounts of pollen to the patient, which leads to minimizing severe allergic symptoms when patients are subsequently exposed to higher amounts of pollen in the environment. Lymphocyte concentrations are considered state variables, allowing the behavior and efficacy of allergen immunotherapy to be identified. The manuscript proposes a method that allows to model mixed systems. Phenomena that present continuous times in some instants and discrete times in others, these are phenomena that are frequently found in the field of physics. Allergen immunotherapy is most effective when a treatment is created with pollen dose increments in a linear form.

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“…To address our objective, we use semi-discrete models, due to the division of the annual cycle into two seasons (namely, reproductive and non-reproductive) acting on two different time scales (namely, continuous and discrete). These models have a common mathematical formalism in terms of impulsive differential equations 33,34 , which are widely used to address topics of interest in epidemiology and population ecology [35][36][37][38][39] . Our consumer-resource model has a "bottom-up" mechanistic formulation [40][41][42] to obtain a better understanding of the dynamic behaviors of the populations by incorporating the individual allocation of energetic resources towards reproduction.…”

mentioning

confidence: 99%

Persistence and size of seasonal populations on a consumer–resource relationship depends on the allocation strategy toward life-history functions

Gutiérrez

Córdova–Lepe

Moreno‐Gómez

et al. 2020

Sci Rep

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The long-term ecological dynamics of a population inhabiting a seasonal environment is analyzed using a semi-discrete or impulsive system to represent the consumer–resource interaction. The resource corresponds to an incoming energy flow for consumers that is allocated to reproduction as well as to maintenance in each non-reproductive season. The energy invested in these life-history functions is used in reproductive events, determining the size of the offspring in each reproductive season. Two long-term dynamic patterns are found, resulting in either the persistence or the extinction of the population of consumers. In addition, our model indicates that only one energy allocation strategy provides an optimal combination between individual consumption and long-term population size. The current study contributes to the understanding of how the individual-level and the population-level are interrelated, exhibiting the importance of incorporating phenotypic traits in population dynamics.

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Population Growth Modeling With Boom and Bust Patterns: The Impulsive Differential Equation Formalism

Cited by 7 publications

References 26 publications

Un modelo matemático estratégico de la disposición de residuos

Un modelo matemático estratégico de la disposición de residuos

Impulsive simulation model for the dynamics of allergen immunotherapy

Persistence and size of seasonal populations on a consumer–resource relationship depends on the allocation strategy toward life-history functions

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