## 1 Introduction  
Currently, there is no universally accepted standard for quantitative modeling in systems biology, as it must be highly customized to the specific biological problem at hand. Each model can only offer an approximate representation of nature, and a key challenge is to apply or develop modeling techniques that best address the questions posed while balancing effort and accuracy. Deterministic and stochastic methods are commonly employed in modeling biological systems, leading to the question of what is the most suitable modeling framework for a given biological system. A straightforward analysis reveals the complexity of this decision. A single molecule behaves in a completely stochastic manner, but as the number of molecules increases, stochastic effects diminish due to balancing interactions. The level of stochasticity, represented by the function \(\frac{1}{\sqrt{n}}\) of the number of components \(n\) in the biological system, decreases as \(n\) increases. In the thermodynamic limit, \(n\rightarrow\infty\), a stochastic formulation effectively reduces to the deterministic one [1]. Weknow that sparse biological systems primarily exhibit stochastic behavior, whereas systems with a high density of components tend to follow deterministic patterns. Determining whether a particular biological system is sparse or dense can be challenging. In the following discussion, we will focus on the scale and density characterization of biological systems to determine if a given system is predominantly sparse or dense. Biological organization spans various spatial scales, with the most notable being intracellular, cellular, intercellular, and population-wide [2; 3]. Intracellular processes occur within the cell and involve interactions at the molecular level such as gene regulatory, metabolic, and signal transduction pathways. Intracellular processes take place at the microscopic level. Cellular processes occur at the mesoscopic level but are not limited to a single cell. Cell biology as a whole is fundamentally mesoscopic biology. For example, cell communication involves multiple cells, but takes place at the cellular level. Cellular processes involve interconnected physiological systems that regulate cell function, including biochemical cascades both within and between cells. Intercellular biology focuses on the various structures that cells use to communicate with each other, either directly or through the surrounding biological environment, typically at the tissue level, contributing to organ functionality. Finally, population-wide processes study how populations interact with their environment, such as the spread of epidemiological diseases such as COVID-19 in specific geographical regions [4; 5; 6]. Intercellular and population-wide processes both occur at the macroscopic level. Intracellular and cellular processes form microscopic and mesoscopic systems, respectively, that consist of a relatively low number of biological components and can, therefore, be described as sparse biological systems. Due to their inherent randomness, these processes are best investigated using stochastic methods. In contrast, intercellular and population-wide processes are macroscopic systems represented by a crowd of biological components and, therefore, are characterized by high density. Deterministic models are most suitable for modeling these macroscopic systems. Figure 1 illustrates how the spatial scale and density analysis of biological systems discussed previously affects the selection of modeling methods. It is common for a biological phenomenon to take place at varying rates. The reaction rates are typically vague and rather uncertain. This vagueness affects the stoichiometry of the reactions and the quantitative relationships between substances in biochemical reactions. As a result, quantitative kinetic models inherently possess some degree of uncertainty. Fuzzy logic [7] is often used to manage the uncertainty inherent in biological systems.