Influence of incubation delays on COVID-19 transmission in diabetic and non-diabetic populations – an endemic prevalence case

Abstract

The study of dynamics of diabetic population infected by COVID-19 is of pressing concern as people with diabetes are considered to be at higher risk of severe illness from COVID-19. A three-compartment mathematical model to describe the interactions of diabetic population and non-diabetic population both infected by COVID-19 with a susceptible population is considered. Time delays in incubation periods of COVID-19 in diabetic and non-diabetic populations are introduced. Besides the basic properties of such a dynamical system, both local and global stability of endemic equilibrium, are studied. The lengths of time delays are estimated for which the stability of the system is preserved locally, while sufficient conditions on system parameters are obtained for global stability. Numerical examples are provided to establish the theory, and simulations are provided to visualize the examples. It is noted that an increase in length of time delay in either of infected populations leads to oscillations in susceptible population but has no impact on infected populations.