Parameter Estimation of Three Cell Interaction Using Lotka Volterra Differential Equations

Abstract

In mathematical biology, established differential system equations are used to model the growth of coexisting different species in a resource competing environment. As the biological system is nonlinear, techniques currently do not exist to offer explicit solutions. The dynamical parameters involved in modelling of predator-prey systems may appear straightforward, but a careful investigation of these model systems frequently leads to extremely complex and difficult challenges. The most crucial aspect of population modelling is that the mathematical model in question can demonstrate the observed characteristics. Ecological system dynamical modelling is typically a research field of continuous progress.This investigation is dedicated to parameter estimation of a generalised Lotka-Volterra system of three non-linear differential equations, given an experimental dataset of the interaction between epithelial cells, candida, and streptococci bacterium, utilising several MATLAB® optimisation functions by “fitting” the simulation model to the empirical data. Despite their simplicity, the Lotka-Volterra equations are still the most common models for describing species interactions.The data gathered and examined using experimental laboratory datasets revealed that each dataset has its own distinct characteristics. In each dataset, none of the approaches produced the best-expected result. Even when it appeared that fitting was achievable, one of the parameters would be problematic, leaving the optimisation problem unresolved in a complete and valid manner.Also, the analysis revealed that the generalised Lotka Volterra (gLV) ordinary differential equation utilised in this setting is insufficient to generate realistic parameter estimations. This conclusion is also supported by a number of scientific investigations that indicate how certain modifications and adaptations to the gLV mathematical model can lead to more accurate results and a more thorough examination. In systems biology, some other analytical methods in addition to ODE (ordinary differential equation) models to describe and explore dynamical biological systems have been proffered.