Juxtaposition across Mathematical Modeling, Stochastic Processes along with the Lenses of Philosophy of Science and AI integration in Medicine and Biology: An Overview

The ultimate reason for the ubiquity of mathematics in modern science entails the essence of mathematical thinking and processes so that complex phenomena including those emerging in medical and biological systems can be understood, and thus, scientific models at their crux can be generated. The consequent complexities and uncertainties require the applications of stochastic processes in mathematical modeling with Artificial Intelligence (AI) techniques used in realms of medicine and biology. Within these conditions, clinical evaluation evidence and model explainability are considered to ensure accountable, effective and safe uses of AI in clinical settings, along with robust, reliable as well as accurate understanding of various complex processes that manifest huge numbers of heterogeneous temporospatial scales. The role of philosophy within science can be expounded by its juxtaposition with models and empirical data explicated by philosophy whose pillars are driven into semantic, pragmatic and syntactic structures of scientific theory that also make up the foundational tenets of algorithmic thinking and patterns. While philosophy of science examines and reflects on the concepts, theories, arguments and methods of science, it should also be borne in mind that scientific theory, by its definition, relates to applications validated by its predictions as units of analyses. Concerning mathematical models, their structure and behavior in target systems are also to be addressed so that explicit common patterns that are implicit in scientific practice can be included in this complex influx. On the other hand, critical functions of mathematical modeling from the pragmatic aspect include the unification of models and data, model fitting to the data, identification of mechanisms depending on observations as well as predictions of future observations. Given these, philosophy of science in medical and biological fields is stated to prompt a comprehensive understanding to construct holistic mathematical models particularly in complex sciences including different attributes of complexity, evolution and adaptation. Regarding the position of AI, its algorithms and mathematical modeling, the methods of neural networks, statistics, operations research, fractional calculus, fractals, and so forth can be employed with AI being capable of uncovering hidden insights embedded in big data concerning medical and biological issues in view of contemporary scientific thinking and processes. In addition, the treatment and handling of uncertainty in clinical medicine and biological problems over their processes may disclose compelling challenges due the fact that uncertainties are one of the intrinsic features of nearly all mathematical models which are formed based on three basic types of uncertainty: interval, Bayesian and stochastic. Accordingly, the current overview aims at providing answers built on sophisticated models considering the explanation and interpretation of design and formulation considering that the extant research literature could have some fragmented points in terms of original and application-oriented works. To these ends, the opportunities, challenges, limitations and conjunctures with respect to mathematical modeling in medicine and biology are addressed while role of philosophy of science is discussed within the context of mathematical modeling and applications in medicine and biology. In addition to these points, the delineation of forecasting, prediction, estimation and approximation concerning different mathematical modeling with the integration of AI in medicine and biology is explained. Thereby, an overview is inclusively presented by comprising the principles underpinning the medical and biological systems within a framework in relation to the diagnostic and disease-related treatment processes and follow-up, which can provide new directions in novel formulations, designs and interpretations based on mathematical modeling processes to be constructed and solved through practicality as well as to-the-point specific means