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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]

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]

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]