Manuscript Topics

Theoretical modeling is the preferred tool not only for mathematicians, but also for physicists, biologists and bioengineers to describe and predict the behavior of complex interacting biological systems. In mathematics, computer science, and physics, a deterministic system is a system in which randomness does not participate in the development of future states of the system. Thus, a deterministic model will always give the same result given the initial conditions or initial state. Deterministic models allow accurate calculation of a future event without unpredictable stochastic influence. If something is deterministic, you have all the data you need to confidently predict the outcome.

In systems biology, models are usually deterministic and biological problems are translated into systems of equations that can be solved numerically. The equations describe the dynamics of interactions between biomolecules that help to explain and understand many aspects of biological processes occurring at the molecular level in the cells of living organisms. The usefulness of quantitative modeling, including equation-based models, is ultimately related to the quality and abundance of observations obtained for the system being modeled. Equation-based modeling, although an integrative approach, complements and expands the potential of traditional approaches to statistical inference.

The purpose of this special issue is state-of-the-art research devoted to analytical and numerical studies of differential and difference equations modeling biological systems, through a collection of original research, as well as review papers, ranging from fundamental science to applications. It includes various aspects of equation-based modeling, its underlying assumptions, strengths and weaknesses, and provides specific examples of simple models. The scope of this Special Issue covers all aspects of theoretical analyses and numerical simulations of biological models, including, but not limited to the following equations:

• Ordinary Differential Equations
• Partial Differential Equations
• Linear Differential Equations
• Nonlinear Differential equations
• Delayed Differential Equations
• Homogeneous Differential Equations
• Nonhomogeneous Differential Equations
• Fractional Differential Equations
• Difference Equations (iterative maps)

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