A new model of the spread of COVID-19 among diabetes population: a mathematical analysis and optimal control approach for intervention strategies

Abstract

In this work, we study an original mathematical model which describe the dynamic of transmission of Covid-19 virus in population with diabetes. Firstly, we analysis the mathematical model by using Routh-Hurwitz criteria to obtain the local stability of Covid-Diabetes-free equilibrium and Covid-Diabetes equilibrium. The second aim of this paper is to reduce the number of infected people with complications by control strategies using three variables of controls: the awareness program to diabetic people, also the strict glycemic control with a multidisciplinary medical follow-up in hospital and early diagnosis for diabetic people. We prove the existence of optimal controls, and a characterization of the controls in terms of states and adjoint functions principally based on Pontryagin’s maximum principle. A numerical simulations for different scenarios affirm the performance of the optimization approach.