On the interplay between mathematics and biology

Bellomo, Nicola; Ełaiw, A. M.; Althiabi, Abdullah M.; Alghamdi, Mohammed

doi:10.1016/j.plrev.2014.12.002

Cited by 49 publications

(22 citation statements)

References 132 publications

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“…The result, which consists in a system of n × m differential-integral equations, is obtained by a balance of particles within the elementary volume [u, u + du] of the space of the microscopic states. This approach is documented in the already cited survey [37] as well as in various papers concerning specific applications such as the immune competition [34,66] or learning dynamics [56]. Therefore, only a concise description of the technical aspects of the approach will be given here referring to the existing literature for further details.…”

Section: Mathematical Structures and Models Of Interactionsmentioning

confidence: 99%

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Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

Marsan

Bellomo

Gibelli

2016

Math. Models Methods Appl. Sci.

132

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This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living evolutionary ensemble composed by many individuals, who express specific strategies, cooperate, compete and might aggregate into groups which pursue a common interest. A critical analysis on the complexity features of social system is developed and a differential structure is derived to provide a general framework toward modeling.

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Section: Mathematical Structures and Models Of Interactionsmentioning

confidence: 99%

“…Detailed calculations are not reported here as the interested reader can find them in some recent papers such as [40,66] and [34]. The result of the said calculations is the following structure:…”

Section: Dynamics Of the Number Of Active Particles = Net Flux Due Tomentioning

confidence: 99%

Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

Marsan

Bellomo

Gibelli

2016

Math. Models Methods Appl. Sci.

132

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“…Our approach follows the research line first proposed by Bellomo and Forni in [6] and then essentially developed in papers [2,3,4,7]. For a further reading on the interplay between mathematics and biology, we suggest the recent review on the subject presented in [5] and the references therein cited.…”

Section: The Mathematical Model For Autoimmunitymentioning

confidence: 99%

A kinetic model of T cell autoreactivity in autoimmune diseases

2019

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We construct a mathematical model of kinetic type in order to describe the immune system interactions in the context of autoimmune disease. The interacting populations are self-antigen presenting cells, self reactive T cells and the set of immunosuppressive cells consisting of regulatory T cells and Natural Killer cells. The main aim of our work is to develop a qualitative analysis of the model equations and investigate the existence of biologically realistic solutions. Having this goal in mind we describe the interactions between cells during an autoimmune reaction based on biological considerations that are given in the literature and we show that the corresponding system of integro-differential equations has finite positive solutions. The asymptotic behaviour of the solution of the system is also studied. We complement our mathematical analysis with numerical simulations that study the sensitivity of the model to parameters related to proliferation of immunosuppressive cells, destruction of self-antigen presenting cells and self reactive T cells and tolerance of SRTCs to self-antigens.

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“…In the past, the modelers were often from mathematics or engineering backgrounds, and had little training in biology. Nowadays the trend is that modelers have realized that biological systems are not simply analogical to physical systems or chemical systems, and therefore they need to understand the functions and mechanisms of biological systems [ 8 ]. This has led to more and more modelers and biologists working together, with the models playing a role in simulation, prediction, and guidance of real experiments [ 9 ].…”

Section: Introductionmentioning

confidence: 99%

From systems to biology: A computational analysis of the research articles on systems biology from 1992 to 2013

Zou

Laubichler

2018

PLoS ONE

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Systems biology is a discipline that studies biological systems from a holistic and interdisciplinary perspective. It brings together biologists, mathematicians, computer scientists, physicists, and engineers, so it has both biology-oriented components and systems-oriented components. We applied several computational tools to analyze the bibliographic information of published articles in systems biology to answer the question: Did the research topics of systems biology become more biology-oriented or more systems-oriented from 1992 to 2013? We analyzed the metadata of 9923 articles on systems biology from the Web of Science database. We identified the most highly cited 330 references using computational tools and through close reading we divided them into nine categories of research types in systems biology. Interestingly, we found that articles in one category, namely, systems biology’s applications in medical research, increased tremendously. This finding was corroborated by computational analysis of the abstracts, which also suggested that the percentages of topics on vaccines, diseases, drugs and cancers increased over time. In addition, we analyzed the institutional backgrounds of the corresponding authors of those 9923 articles and identified the most highly cited 330 authors over time. We found that before the mid-1990s, systems-oriented scientists had made the most referenced contributions. However, in recent years, researchers from biology-oriented institutions not only represented a huge percentage of the total number of researchers, but also had made the most referenced contributions. Notably, interdisciplinary institutions only produced a small percentage of researchers, but had made disproportionate contributions to this field.

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On the interplay between mathematics and biology

Cited by 49 publications

References 132 publications

Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

A kinetic model of T cell autoreactivity in autoimmune diseases

From systems to biology: A computational analysis of the research articles on systems biology from 1992 to 2013

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