Exploration of Biological Mathematical Modeling Based on Constant Coefficients

Abstract

Constant coefficient differential equations are commonly employed in modeling physics, ecology, and systems biology. However, the uncertainty in the parameters of the established constant differential equation models often leads to decreased accuracy of the mathematical models. Consequently, research on biological mathematical modeling ideas based on constant coefficients holds significant practical relevance. To address this, we introduce Markov chains into the conventional constant coefficient differential equation models and verify the feasibility of this approach using the biological system Lotka-Volterra as an example. Numerical simulation experiments demonstrate that this approach not only achieves accurate estimation of model parameters but also provides insights into model construction.