A Mathematical Modeling And Analysis Of Covid-19 And Diabetes Co-Infection With Optimal Control And Cost-Effectiveness

Abstract

The coronavirus disease 2019 (COVID-19) pandemic has emerged as one of the greatest challenges faced by humankind in the recent past. People with diabetes and related co morbidities are at increased risk of its complications and of COVID-19-related death. In this thesis, we studied the dynamics of COVID-19 and DIABETES co-infection. For this, we formulated a deterministic mathematical model to describe the transmission dynamics of COVID-19 and DIABETIC sub-models and analyzed each sub-models with analytical meth ods. The biological meaningfulness of each sub-models was proved and the stability analysis was performed by obtaining the basic reproduction number. In each sub-models the disease free equilibrium points are proved to be both locally and globally stable if the reproduction numbers are less than unity and the endemic equilibrium point is also both locally and glob ally stable if the reproduction numbers are greater than unity. The sensitivity analysis of each sub-models parameters has also been performed by using the normalized forward analysis. We have then proposed a deterministic mathematical model of the coinfection of COVID 19 and DIABETES. The coinfection model is qualitatively studied by proving the properties such as existence and uniqueness, boundedness, and positivity of the solutions. We computed the basic reproduction number of the coinfection and the disease free equilibrium point is locally stable and globally not stable and the system has no endemic equilibrium point. Fur thermore, the coinfection model is extended in to an optimal control problem by adding three control measures as the prevention techniques against COVID-19, treatments for COVID-19 infections, and awareness program for DIABETIC without complications to optimally man age the disease. The optimal control was analyzed with Pontryagin’s Minimum Principle. Different simulation cases were performed using MATLAB to supplement the analytical re sults and to identify the most appropriate control intervention strategies. The simulation results show that the prevalence of the coinfection was reduced when all three control mea sures were concurrently implemented. The most cost-effective control measure is determined through cost-effectiveness analysis