“…Numerous scholars have examined time-delay differential equation (DDE) and in recent decades (see, for example, [27][28][29][30]), since they are extremely useful for modelling a broad number of scenarios in traditional fields like engineering and science, as well as relatively new fields like transmission of infection, clinical science, optimized drug rehabilitation, bio-economics, farming, financial management, insurance, and protection of the environment. Many fields, including population trends [31], epidemiology [32], and computer systems [33,34], have adopted DDE for investigation.…”