Mathematical and data-driven modelling of glucose homeostasis system to understand diabetes pathways

  • Hannah Al Ali

    Student thesis: Doctoral ThesisDoctor of Philosophy


    Diabetes is a chronic disease which affects the glucose homeostasis system and its prevalence is rapidly increasing around the globe. Presently, the coronavirus disease 2019 (COVID-19) pandemic is a major issue for those with diabetes as the disease leads to more severe symptoms of the novel severe acute respiratory syndrome coronavirus 2 infection. In this study, mathematical models were developed and analysed to understand diabetes pathways. Dynamical systems theory were used to determine mathematical properties of the models and establish threshold quantities. Numerical simulations were performed to confirm the results of traditional mathematical analysis along with machine learning based sensitivity analysis to ascertain robustness of results. Sensitivity analysis was used to determine parameters influencing the dynamics of the glucose homeostasis system for the models. Analytical results of the first model showed three equilibrium points, a stable physio-logical, stable pathological (Type 1 diabetes state) and an unstable Type 2diabetes state, thus confirming known biological characteristics of the glucose homeostasis system. The model exhibits a backward bifurcation phenomenon when the model threshold quantity is less than unity, where an individual transit from unstable Type 2 diabetes state to a stable physiological state. This result demonstrates that Type 2 diabetes is reversible when acting on risk factors, and this is also true for biological findings. Sensitivity analysis identified all parameters that make up the threshold quantity as influential in determining model dynamics. The second model was developed to focus on Type 1 diabetes dynamics. The results showed two stable states, a physiological and pathological state, in line with known biological findings. Sensitivity analysis highlighted key parameters that determine the dynamics of the glucose homeostasis system and confirmed mathematical analysis findings. The two glucose homeostasis models developed were then fitted to published data on experimental mice with Type 1 diabetes using a Bayesian approach in order to determine a suitable model framework for Type 1 diabetes. The results from model selection suggest that the model with noβ-cells is more suitable in predicting Type 1 diabetes dynamics. Overall, the research highlights the importance of both traditional mathematical modelling and parameter based sensitivity analysis approaches in understanding important model parameter sand establishing diabetes pathways. Further, the study provided insights on a suitable model framework for understanding Type 1 diabetes.
    Date of AwardJun 2022
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorRichard Dashwood (Supervisor), Zindoga Mukandavire (Supervisor), Damien Foster (Supervisor) & Alireza Daneshkhah (Supervisor)

    Cite this