CONTROLLABILITY AND OBSERVABILITY OF BLOOD GLUCOSE LEVELS AND THE IMPACT OF COVID-19 ON DIABETIC PATIENTS

Diabetes is a metabolic disorder that is characterized by high blood glucose concentrations resulting from insulin deficiency in case of type 1 or insulin inefficiency in case of type 2. While no cure for diabetes exists, the artificial pancreas is a possible way to manage diabetes, especially for type 1 diabetics. Where an artificial pancreas is a closed-loop control system with an integrated mathematical model. This control system imitates the function of a healthy pancreas. The first part of this thesis is concerned with the control system of an artificial pancreas that is based on Bergman’s minimal model of glucose-insulin dynamics. The aim of the first part of this thesis is to prove both the controllability and the observability of the minimal model which is a fundamental step in the design of an optimal control system. These proofs are based on several mathematical tools such as the insertion of time delays, and theorems such as the Banach contraction mapping theorem in addition to the results of previous related works. On a different note, COVID-19 is a highly infectious global pandemic that targets the respiratory system. The symptoms of this disease were found to be more severe towards patients with comorbidities including diabetes, and so, the second part of this thesis is concerned with the relation of COVID-19 with comorbidities, where a COVID-19 disease transmission model that focuses on comorbidity populations is presented. This model aims at determining the major factors that contribute to the transmission of this disease. The results of this model can aid in implementing strategies that can help in controlling the spread of this pandemic. Parameter estimations of the model are presented in addition to several related calculations including the basic reproduction number and the sensitivity indices of the model’s parameters