Exploring the effects of competition and predation on the success of biological invasion through mathematical modeling.

Biological invasions are a major cause of species extinction and biodiversity loss. Exotic predators are the type of introduced species that have the greatest negative impact, causing the extinction of hundreds of native species. Despite this, they continue to be intentionally introduced by humans. Understanding the causes that determine the success of these invasions is a challenge within the field of invasion biology. Mathematical models play a crucial role in understanding and predicting the behavior of exotic species in different ecosystems. This study examines the effect of predation and competition on the invasion success of an exotic generalist predator in a native predator-prey system. Considering that the exotic predator both consumes the native prey and competes with the native predator, it is necessary to study the interplay between predation and competition, as one of these interspecific interactions may either counteract or contribute to the impact of the other on the success of a biological invasion. Through a mathematical model, represented by a system of ordinary differential equations, it is possible to describe four different scenarios upon the arrival of the exotic predator in a native predator-prey system. The conditions for each of these scenarios are described analytically and numerically. The numerical simulations are performed considering the American mink (Mustela vison), an invasive generalist predator. The results highlight the importance of considering the interplay between interspecific interactions for understanding biological invasion success.

Mathematical Model of the Spread of Hantavirus Infection.

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 SEIR (Susceptible-Exposed-Infectious-Removed), which incorporates the displacement of the rodent and the human, between the urban and rural sector, the latter being subdivided in populated and non-populated. The results show the impact that rodent or human displacement may have on the propagation of hantavirus infection. Human mobility is more significant than rodents in increasing the number of hantavirus infection cases. The results found may be used as a reference by the health authorities to develop more specific campaigns on the territorial dynamics of the rodent, attend to the mobility of humans in these territories, mainly agricultural and forestry workers, and strengthen control-prevention actions in the community, to prevent future outbreaks that are fatal.

Concurrent dilution and amplification effects in an intraguild predation eco-epidemiological model.

The dilution and amplification effects are important concepts in the field of zoonotic diseases. While the dilution effect predicts that pathogen prevalence is negatively correlated with increased species diversity, the opposite trend is observed when the amplification effect occurs. Understanding how interspecific interactions such as predation and competition within a community influence disease transmission is highly relevant. We explore the conditions under which the dilution and amplification effects arise, using compartmental models that integrate ecological and epidemiological interactions. We formulate an intraguild predation model where each species is divided into two compartments: susceptible and infected individuals. We obtained that increasing predation increases the disease transmission potential of the predator and the density of infected individuals, but decreases the disease transmission potential of the prey, as well as their density. Also, we found that interspecific competition always helps to decrease the number of infected individuals in the population of the two species. Therefore, dilution and amplification effects can be observed simultaneously but depending on different types of cological interactions.

A description of the epidemiological dynamics of Chagas disease via mathematical modeling.

Chagas disease is caused by the protozoan Trypanosoma cruzi, which parasitizes many mammals, including humans. Its vectors are blood-feeding hematophagous triatomine insects of different species, which vary according to the geographical area. One of the 17 neglected diseases targeted by the World Health Organization, Chagas disease is endemic to the Americas, but has spread to other countries due to human migratory movements. In this study, we describe the epidemiological dynamics of Chagas disease in an endemic area, considering the main transmission mechanisms and the demographic effects of birth, mortality, and human migration in this phenomenon. We apply mathematical models as a methodological approach to simulate the interactions between reservoirs, vectors, and humans using a system of ordinary differential equations. The results show that the Chagas disease control measures currently in place cannot be relaxed without endangering the progress achieved to date.

Análisis de modelos tipo SEIR utilizados en los inicios de la pandemia COVID-19 reportados en revistas de alto impacto / Analysis of SEIR-type models used at the beginning of COVID-19 pandemic reported in high-impact journals

Introducción El modelo matemático-epidemiológico Susceptible-Expuesto-Infectado-Recuperado (SEIR) ha sido empleado exhaustivamente en el contexto actual de la pandemia COVID-19. En sus inicios de una manera prevalente, donde se buscaba predecir la carga hospitalaria y evaluar las medidas sanitarias para contener su propagación. En este sentido, se han evidenciado fallas en las predicciones de los primeros modelos publicados. Se considera necesario evaluar las diferencias en el planteamiento y verificación de los modelos. Objetivos Categorizar las publicaciones científicas de revistas de alto impacto que propusieron modelos tipo SEIR para modelar la pandemia COVID-19 en sus inicios. Métodos Realizamos una revisión sistemática de los artículos publicados en revistas indexadas en , de primer cuartil y con factor de impacto mayor que dos, que cumplían con los criterios de selección e inclusión siguiendo los estándares PRISMA-ScR. Incluimos un total de 32 artículos que fueron evaluados según características demográficas como el mes de recepción y publicación, el país de origen de la información, la materia temática de la revista, y las características del modelamiento como la presencia de compartimentos adicionales, análisis gráfico, planteamiento de modelo conceptual, interpretación del número reproductivo básico y estimación de los parámetros empleados. Resultados Los artículos publicados en revistas del área médica y salud fueron predominantes en los meses de febrero a julio de 2020. Estos artículos emplearon con mayor frecuencia datos procedentes de China y se centraron mayoritariamente en modelos SEIR o con compartimento de cuarentena completa. Los artículos publicados en revistas del área matemática fueron predominantes en el período de agosto a diciembre de 2020, y emplearon datos procedentes de diversas regiones del mundo, considerando mayor diversidad de compartimentos como pacientes asintomáticos o en cuarentena parcial o completa. Conclusiones Los artículos analizados en su mayoría emplean modelos tipo SEIR ampliados con compartimentos adicionales. Existen discrepancias en la amplitud y calidad metodológica de los artículos publicados, según la materia temática de la revista. Se recomienda la unificación de criterios de calidad para la descripción de los modelos en cualquier revista.

Introduction The Susceptible-Exposed-Infected-Recovered (SEIR) mathematical-epidemiological model has been exhaustively used since de beggining of the COVID-19 pandemic. These models intended to predict hospital burden and evaluate health measures to contain its spread. In this sense, flaws have been evidenced in the predictions of the first published models. It is considered necessary to evaluate the differences in the approach and verification of the models. Objectives We carried out a systematic review of the articles published in journals indexed in the Web of Science, of the first quartile and with an impact factor greater than two, that met the selection and inclusion criteria following the PRISMA-ScR standards. We included a total of 32 articles, which were evaluated according to demographic characteristics such as the month of receipt and publication, the country of origin of the information, the subject matter of the journal, and the characteristics of the modeling such as the presence of additional compartments, graphical analysis, conceptual model approach, interpretation of the basic reproductive number, and estimation of parameters. Methods Articles published in medical and health journals were predominant from February to July 2020. These articles most frequently used data from China and mostly focused on SEIR or full quarantine compartment models. The articles published in journals in mathematics were predominant from August to December 2020. Models used data from different world regions, considering a greater diversity of compartments such as asymptomatic patients or partial or complete quarantine. Results The articles analyzed mostly use SEIR-type models expanded with additional compartments. There are discrepancies in the breadth and methodological quality of the articles published according to the journal's subject matter. The unification of quality criteria for describing the models in any journal is recommended. Conclusions The articles analyzed mostly use SEIR-type models expanded with additional compartments. There are discrepancies in the breadth and methodological quality of the articles published according to the journal's subject matter. The unification of quality criteria for describing the models in any journal is recommended.

Adding a reaction-restoration type transmission rate dynamic-law to the basic SEIR COVID-19 model.

The classical SEIR model, being an autonomous system of differential equations, has important limitations when representing a pandemic situation. Particularly, the geometric unimodal shape of the epidemic curve is not what is generally observed. This work introduces the ßSEIR model, which adds to the classical SEIR model a differential law to model the variation in the transmission rate. It considers two opposite thrives generally found in a population: first, reaction to disease presence that may be linked to mitigation strategies, which tends to decrease transmission, and second, the urge to return to normal conditions that pulls to restore the initial value of the transmission rate. Our results open a wide spectrum of dynamic variabilities in the curve of new infected, which are justified by reaction and restoration thrives that affect disease transmission over time. Some of these dynamics have been observed in the existing COVID-19 disease data. In particular and to further exemplify the potential of the model proposed in this article, we show its capability of capturing the evolution of the number of new confirmed cases of Chile and Italy for several months after epidemic onset, while incorporating a reaction to disease presence with decreasing adherence to mitigation strategies, as well as a seasonal effect on the restoration of the initial transmissibility conditions.

Effects of human mobility and behavior on disease transmission in a COVID-19 mathematical model.

Human interactions and perceptions about health risk are essential to understand the evolution over the course of a pandemic. We present a Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Susceptible mathematical model with quarantine and social-distance-dependent transmission rates, to study COVID-19 dynamics. Human activities are split across different location settings: home, work, school, and elsewhere. Individuals move from home to the other locations at rates dependent on their epidemiological conditions and maintain a social distancing behavior, which varies with their location. We perform simulations and analyze how distinct social behaviors and restrictive measures affect the dynamic of the disease within a population. The model proposed in this study revealed that the main focus on the transmission of COVID-19 is attributed to the "home" location setting, which is understood as family gatherings including relatives and close friends. Limiting encounters at work, school and other locations will only be effective if COVID-19 restrictions occur simultaneously at all those locations and/or contact tracing or social distancing measures are effectively and strictly implemented, especially at the home setting.

An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors.

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 compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

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

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.

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 intoxication on the spread of these types of diseases. We further investigate the role of educational treatment for appropriate pesticide use on the transmission dynamics. Two impulsive control events are proposed: pesticide use and educational treatment. From the proposed model, it was obtained that the rate of forgetfulness towards educational treatment is a determining factor for the reduction of intoxicated people, as well as for the reduction of costs associated with educational interventions. To get reduced intoxications, the population's fraction to which is necessary to apply the educational treatment depends on its individual effectiveness level and the educational treatments' forgetfulness rate. In addition, the turnover of agricultural workers plays a fundamental role in the dynamics of agrotoxic use, particularly in the application of educational treatment. For illustration, a flu-like disease with a basic reproductive number below the epidemic threshold of 1.0 is shown can acquire epidemic potential in a population at risk of pesticide exposure. Hence, our findings suggest that educational treatment targeting pesticide exposure is an effective tool to reduce the transmission rate of an infectious respiratory disease in a population exposed to the toxic substance.

[Model for a threshold of daily rate reduction of COVID-19 cases to avoid hospital collapse in Chile]. / Modelo de umbral de reducción de tasa diaria de casos COVID-19 para evitar el colapso hospitalario en Chile.

Using a mathematical model, we explore the problem of availability versus overdemand of critical hospital processes (e.g., critical beds) in the face of a steady epidemic expansion such as is occurring from the COVID-19 pandemic. In connection with the statistics of new cases per day, and the assumption of maximum quota, the dynamics associated with the variables number of hospitalized persons (critical occupants) and mortality in the system are explored. A parametric threshold condition is obtained, which involves a parameter associated with the minimum daily effort for not collapsing the system. To exemplify, we include some simulations for the case of Chile, based on a parameter of effort to be sustained with the purpose of lowering the daily infection rate.

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 está ocurriendo como consecuencia de la pandemia de COVID-19. En conexión con la estadística de nuevos casos diarios y el supuesto de cupo máximo, exploramos la dinámica asociada a las variables número de hospitalizados (ocupantes críticos) y mortalidad en el sistema. Obtenemos una condición paramétrica umbral que involucra un parámetro asociado al esfuerzo mínimo diario para el no colapso del sistema. En orden a ejemplificar, incluimos algunas simulaciones para el caso de Chile, en función de un parámetro de esfuerzo a sostener para bajar la tasa de infección diaria.

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. / Número de casos COVID-19 en Chile a 120 días con datos al 21/03/2020 y umbral del esfuerzo diario para aplanar la epi-curva.

We present a straightforward projection with data up to 21/03/2020 of the evolution of the number of COVID-19 cases per day in Chile using data from the Ministry of Health. Assuming an arithmetical growth in the second variation of the data, we present a cubic adjustment model in which we estimate over 100 000 cases at 120 days consistent with the data recorded to date. Furthermore, we use an exponential total case model to represent (using a parameter) the daily effort to reduce a high initial daily growth rate. We simulate this model with different numerical scenarios of feasibility and desired future prevalence.

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 datos, se presenta un modelo de ajuste cúbico que estima en más de 100 mil casos a 120 días y que es consistente con los datos registrados a la fecha. Además, se interviene un modelo de casos totales exponencial, para representar en él (mediante un parámetro) el esfuerzo diario por rebajar una elevada primera tasa de crecimiento diario. Este modelo se simula con distinto escenarios numéricos de factibilidad y prevalencia futura deseada.

An index to quantify individual social responsibility in the decision to be vaccinated. / Índice para cuantificar la responsabilidad social individual en la decisión de vacunarse.

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 of this study is merely educational the approach implemented is based on a classical mathematical model named S.I.R. (Susceptible-Infected-Recovered) using an impulsive vaccination strategy. Dates of vaccination and fraction of individuals vaccinated are used as parameters. In addition, numerical simulations are conducted to represent the outcomes regarding the reduction of infected cases through tables and graphs.

En el contexto de estudios de enfermedades infecciosas genéricas, el objetivo del presente artículo es cuantificar y representar la responsabilidad social individual en relación al acto o no de vacunación individual. Aunque la finalidad de este análisis es meramente educativo y de divulgación masiva, el enfoque implementado está basado en el clásico modelo matemático Susceptible-Infectado-Recuperado (SIR) usando una estrategia impulsiva de vacunación. Día de vacunación y fracción de individuos vacunados son utilizados como parámetros del modelo, mientras que simulaciones numéricas son generadas para representar el comportamiento en la reducción de casos infectados a través de tablas y gráficos.

Modeling the epidemiological impact of a preventive behavioral group. / Modelización del impacto epidemiológico de la existencia de un grupo conductual preventivo.

Concerning health, experience indicates that in all human groups a percentage of individuals behave conscientiously when facing contagious diseases. This aware group responds with activities to prevent disease transmission and to minimize risk. In contrast, other individuals tend to behave with less engagement except in catastrophic cases. Assuming the theoretical and methodological framework provided by mathematical epidemiology, and based on a Susceptible – Infectious - Recovered (SIR) model, we evaluated the factors of size and intensity of the behaviours in the aware group to determine the basic reproduction number. This number is the reduction in the number of secondary cases that would be produced by a first infectious individual. Additionally, we calculated the total and individual prevented prevalence for each aware individual for different parametric scenarios. Lastly, we suggest that distance and interpersonal contact should be included as factors associated to the potential of transmission.

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 existen grupos con una orientación hacia la prevención en sus actividades para atenuar el riego, mientras que en general la mayoría lo hace distraídamente. La excepción la constituyen los casos de orden catastrófico. Asumiendo el marco teórico y metodológico que otorga la epidemiología matemática, se evaluaron los factores tamaño e intensidad de la conducta del grupo cuidadoso en la determinación del número reproductivo básico, basándose en un modelo tipo SIR (susceptibles - infecciosos - recuperados). Es decir, se midió la reducción en la cantidad de casos secundarios que produciría un primer caso infeccioso. Junto con estos indicadores, se procedió a evaluar la prevalencia evitada total e individual por cada sujeto cuidadoso en diferentes escenarios paramétricos. Finalmente, se plantea la necesidad de integrar en futuros estudios la variable distancia y el contacto interpersonal como factores asociados al potencial de transmisión.

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, at which the abundance reaches a certain predetermined level, then falls abruptly by a constant capture quota (pulse harvesting). So, the abundance is modeled by a stochastic impulsive type differential equation, incorporating a standard Brownian motion in the per capita rate of growth. With this random effect, the pulse times are "stopping times" of the stochastic process. The proof of the finite expectation of the next access time, i.e., the feasibility of regulation, is the main result.

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 process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold which determines either the sustainability of the fishery or the extinction of the resource.