Mathematical models are valuable tools used to understand and predict the behaviour of complex physiological systems. In this thesis, ordinary differential equation (ODE) modelling is applied to the following two areas: (i) the development of digital twins for human physiolog- ical systems, specifically modelling drug metabolism in in vitro liver systems and simulating cardiovascular blood flow using lumped parameter models (LPMs); and (ii) modelling of biochemical processes, focusing on insulin-glucose (IG) regulatory systems in the context of type 2 diabetes mellitus (T2DM). The drug testing process faces challenges such as high costs, lengthy timelines, and poor predictability of human responses, especially in estimating first-in-human doses. While advancements in microphysiological systems (MPS) and organ-on-chip (OoC) technologies offer more human-relevant testing, they still rely on conventional mathematical models that fail to capture biological processes adequately. This study aims to enhance the predictive power of MPS and OoC by integrating them into a digital twin framework (DigiLoCs) for better prediction of liver clearance. A compartmental physiological model of the liver using ODEs is developed to estimate pharmacokinetic parameters for in vitro liver-on-chip systems. Digital twinning is also applied to model the blood flow in the human circulatory system using zero-dimensional LPMs. LPMs approximate the cardiovascular network as a set of discrete compartments accounting for vascular pressure of blood flow, impedance to the flow of blood, the volume of blood in the vessels and the elasticity of the vessels. By applying electrical circuit principles, these models predict cardiovascular dynamics. The simulations facilitate the exploration of scenarios that are difficult to observe experimentally, such as blood flow in internal organs, making them useful for diagnosing and monitoring disease progression. The thesis then explores biochemical processes starting with clustering-based methods to study T2DM. Using an unsupervised clustering algorithm three subgroups of uncontrolled T2DM patients were identified and characterised based on patho-clinical features. The signifi- cance of heterogeneity in T2DM is uncovered, challenging the assumption of its homogeneity and emphasising the need to reconsider uniform treatment protocols. Given obesity as a significant risk factor in T2DM, a distinction between estimated oral minimal model (OMM) parameters for obese and non-obese T2DM subjects is identified. Furthermore, the existing OMM is augmented to include the role of body mass index (BMI) and leptin (a hormone secreted by adipose tissue), leading to better simulation results.