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Given the risk and impact of infectious-contagious X diseases, which are expected to increase in frequency and unpredictability due to climate change and anthropogenic penetration of the wilderness, it is crucial to advance descriptions and explanations that improve the understanding and applicability of current theories. An inferential approach is to find analogies with better-studied contexts from which new questions and hypotheses can be raised through their concepts, propositions, and methods. Kinematics emerges as a promising analog field in physics by interpreting states' changes in a contagion process as a movement. Consequently, this work explores, for a contagion process, the representations and conceptual equivalents for position, displacement, velocity, momentum, and acceleration, introducing some metrics. It also discusses some epistemological aspects and proposes future perspectives. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis. [ABSTRACT FROM AUTHOR]

In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate B. We define this dynamic law by the differential equation B ′ / B = F ⊕ − F ⊖ , where F ⊖ represents a reaction factor reflecting the stress proportional to the active group's percentage variation. Conversely, F ⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F ⊕ = 0 , we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model's behavior and its implications for understanding disease transmission. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The impact of human actions on the environment poses several challenges at the global level, with solutions that deserve the productive and political sectors and civil society to be jointly involved. Resource scarcity, ecosystem degradation, and climate change must be addressed urgently; this is a paradigm change in the forms of production and consumption. This is a transition from a linear economy to a circular economy, which allows responsible disposal and reuse of waste along the links of production and use. However, despite notable advances in recycling and upcycling, landfill and dump disposal remain the primary waste disposal worldwide. Furthermore, a significant amount of waste is disposed of illegally, affecting the quality of life of communities that live in nearby areas. This work studies the trade-off between waste container removal and illegal micro-dumps cleaning using impulsive control. A type of strategic mathematical model is formulated, one that captures the minimal but relevant aspects of the phenomenon, to describe the dynamics of garbage. [ABSTRACT FROM AUTHOR]

This research studies a metapopulation model where each patch is considered a form of fragmentation of the environment produced by the spatio-temporal variability of anthropogenic noise. A deterministic mathematical model is proposed that describes two processes of migration between patches. The first process consists of migration due to chronic critical noise produced by an anthropogenic and biological source (self-generated acoustic signals of higher intensity, due to the Lombard effect). The second process consists of migration due to a higher level of stain occupancy. A simple and classical analysis of the local stability of the model is performed. The results indicate that no subpopulation goes extinct; in fact, a necessary condition for long-term stabilization of the size of the subpopulations is that the noise attenuation rate is higher. Moreover, as long as the noise is of low intensity the differences in the carrying capacity of each patch do not produce substantial, long-term differences in the sizes of the subpopulations. However, as the noise intensity increases, the difference in carrying capacities produce noticeable, long-term differences between subpopulation sizes. Finally, the results are corroborated by numerical simulations. [ABSTRACT FROM AUTHOR]

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 βSEIR 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. [ABSTRACT FROM AUTHOR]

1. An established framework to evaluate vulnerability to global warming is to associate the expected temperature trends with thermal performance curves, which indicate how fitness changes as a function of body temperature. 2. Mathematical modelling approaches allow synthesizing the mechanistic understanding of ecological processes, enabling the assessment of the potential impacts of global warming on populations. 3. epcc allows to model and simulate the effects of thermal sensitivity and the exposition to different trends in environmental temperature on the abundance dynamics of ectothermic populations. 4. epcc allows a synthesis of the possible consequences of global-and local-scale warming, constituting a useful tool for understanding the risk of extinction of populations. [ABSTRACT FROM AUTHOR]

In this paper, the global exponential stability and periodicity are investigated for delayed neural network models with continuous coefficients and piecewise constant delay of generalized type. The sufficient condition for the existence and uniqueness of periodic solutions of the model is established by applying Banach's fixed point theorem and the successive approximations method. By constructing suitable differential inequalities with generalized piecewise constant delay, some sufficient conditions for the global exponential stability of the model are obtained. Typical numerical examples with simulations are utilized to illustrate the validity and improvement in less conservatism of the theoretical results. This paper ends with a brief conclusion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An arithmetic based on the multiplication is the base of the Bigeometric (and Multiplicative) Calculus, a type of non-Newtonian Calculus which has had uses in the digital processing of images. In this work, we present the fundamental elements to construct a proposal of Multiplicative Linear Algebra with view of being a support for a Multiplicative Calculus in Several Variables and its applications. Some important concepts such as vector space, linear transformation and matrix representation are reviewed. In particular, we give a meaning and context to the operation: matrix raised to matrix. [ABSTRACT FROM AUTHOR]

From continuous standard SIR model, which is configured from two sequenced flows (a) susceptible – infectious and (b) infectious – removed, we obtain two impulsive SIR models assuming different time scales for (a) respect to (b) (one more quickly than the other and inversely). By associating respective stroboscopic maps to this impulsive systems, two discretizations are defined. The dynamics of these maps are analysed in order to get thresholds conditions for predicting (or to control) epidemic outbreaks. As it is traditional for SIR systems, we also find conditions for the final size of the susceptible group. [ABSTRACT FROM AUTHOR]

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 the most known of these descriptions and one of them will be used in a modified Volterra model. Moreover, of this ecological phenomenon, a simple and strong Allee effect affecting the prey population will be considered in the relationship. An important feature of the new model is to have until two positive equilibrium points, to the difference with the Volterra model (without Allee effect); hence different and interesting dynamic situations appear in the system. Conditions for the existence and local stability of equilibria are determined. The boundedness of solutions, the existence of a limit cycle and a separatrix curve are also proven. Besides, the main properties of the model are examined from an ecological point of view. To make a comparative discussion of our results, an Appendix is added with the main properties of models, in which neither the Allee effect nor the competition among predators is considered. Some simulations are shown to endorse our results. [ABSTRACT FROM AUTHOR]

Understanding the processes and consequences of habitat fragmentation is highly relevant since it represents a serious threat to biodiversity. However, fragmentation includes several facets that are difficult to dissect, such as loss of habitat connectivity, edge effects, and habitat loss. In this study, we analyze by mathematical and computational means a single isolated component of habitat fragmentation: the loss of connectivity. The main novelty of our approach is that we consider the entire temporal process by which a continuous habitat gets progressively divided into two isolated patches. For this purpose, we present a new mathematical model. Our results indicate that, in line with empirical evidence, connectivity loss derived from habitat fragmentation could lead to either a decrease or an increase in total population abundance during the process. We give some conditions under which the mentioned effects should occur. We conclude that connectivity loss could exert strong influences on non-equilibrium populations. [ABSTRACT FROM AUTHOR]

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 immunity), which moderately threatens its economic performance and the local biosecurity. In this context, a control strategy is proposed, which is described by a sequence of rotative partial quarantines, where a fraction of the infected livestock is isolated to receive special care (hospitalization). A parametric threshold is obtained, ensuring a future healthy livestock. Furthermore, some economic and epidemiologic consequences have been studied. [ABSTRACT FROM AUTHOR]

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 growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li-Yorke's sense). In addition, some open problems and new results are presented. [ABSTRACT FROM AUTHOR]

A self-cycling fermenter is a batch fermenter subject to recurrent emptyings of liquid volume followed by the refilling with new fresh substrate. This article constructs a modified model of self-cycling fermenter, which is described by an impulsive differential equation at impulse-dependent times, which have been recently introduced. The main result is a set of conditions depending of the fraction of removed volume, the concentration of new substrate introduced, and the maximal length between two impulses, which ensure the existence and attractiveness of a periodic cycle. A second result provides alternative conditions for the biomass extinction. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Animal species change their residence places due to the high temporal variability in the availability of resources. Thus, animals move to sites with higher productivity and they search environments with the necessary resources that allow it to develop the different stages of their life cycle. Here, we present a simple mathematical model that determines a no extinction condition (stable oscillation) in terms of the movement parameters for obligate-migration populations. We understand the obligate-migration as a movement seasonally predictable in distinct locations, which is associated with patterns of resource distribution. [ABSTRACT FROM AUTHOR]

Abstract: 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: the present impulse time, the state at this moment, and the value to which this state is impelled. We also establish the basic results of existence, uniqueness and continuation of solutions for these new impulsive differential equations. It is observed that the new equations have interesting applications in Bioeconomics, and sometimes they include, the traditional impulsive equations in variable times. [Copyright &y& Elsevier]

Abstract: 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 specific features of the population’s behavior. The purpose of this article is to obtain an epidemic threshold which allows us to decide how a sequence of epidemic events could destabilize the previous controlled scenario and how a new endemic equilibrium appears. A threshold is obtained when supposing a set of almost periodic properties in the model. [Copyright &y& Elsevier]

This work presents a new pulse vaccination strategy for a SIS (susceptible-infective-susceptible) disease in an endemic context. Here, given a time of vaccination, the instant of the next one is not predetermined, but it is a function of the present incidence and this function allows us to obtain an epidemic threshold ensuring the convergence of infectives toward the disease-free scenario. Numerical results show that our condition is sufficient but not necessary and that the convergence is faster compared with fixed time vaccination strategies. [ABSTRACT FROM AUTHOR]

• A mathematical model is used to describe Trypanosoma cruzi transmission in an endemic area. • The interaction between humans, Trypanosoma cruzi , vectors, and reservoirs is modeled. • Possible scenarios of Chagas disease dynamics in endemic areas are simulated. 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. [ABSTRACT FROM AUTHOR]

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.

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.

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., (Copyright © 2012 Elsevier Inc. All rights reserved.)