## 1 Introduction
It is also a known fact that NIDDM is responsible for a high risk of treatment failure, mortality, and relapse among patients with active tuberculosis infections. Tuberculosis can also lead to glucose intolerance and severely affect glycemic control [18]. As of today, there is no known cure for NIDDM, but it can be well managed with patient education, healthy diets, lifestyle changes, expertise availability, medication, screening for complications associated with diabetes, proper glycemic control, and sustained observational follow-up [19; 20]. The convergence, comorbidity, and concomitant conditions of tuberculosis and noninsulin-dependent diabetes mellitus have been presented in several epidemiological studies [7; 12; 14; 17; 21; 22; 23]. [PERSON] et al. [12] developed and analyzed a compartmental TB model that assesses the impact of NIDDM in the spread of the tuberculosis disease in a community. [PERSON] et al. [24] presented a mathematical modeling study on the effect of NIDDM on TB disease control in thirteen countries with a high burden of TB disease. [PERSON] et al. [25] studied and assessed the role of diabetes in the progression of TB using a non-integer order model. [PERSON] et al. [26] used a fractional modeling approach to investigate the clinical implications of the comorbidity of tuberculosis and NIDDM. [PERSON] et al. [27] examined the effectiveness of TB disease treatment therapy while taking into consideration the impact of associated diseases (NIDDM and HIV/AIDS). [PERSON] et al. [28] used a mathematical modeling approach that utilized a recently developed age-structure NIDDM and TB co-infection dynamics to predict, estimate, and investigate the impact of noninsulin-dependent diabetes mellitus on mycobacterium tuberculosis epidemiology in Indonesia between 2020 and 2050. [PERSON] et al. [7] extended the study carried out in [12] by presenting the optimal control and some cost-effectiveness strategies for the mathematical model of TB and NIDDM co-infection dynamics. In [29], a deterministic mathematical model of the SEIS type that accounts for the saturated treatment of individuals exposed to mycobacterium TB in the latent form, along with crowding and psychological effects, was introduced to further study the impact of NIDDM in the transmission mechanism of TB in a community. Recently, [PERSON] et al. [30] employ supervised machine learning algorithms to develop models that effectively predict diabetes from patients electronic health records (EHRs). For more detailed work on integer and non-integer compartmental models, see [31; 32; 33; 34; 35; 36; 37]. Over the years, several mathematical epidemiologists have developed and incorporated control strategies into disease models. [PERSON] et al. [38] incorporated both pharmaceutical and non-pharmaceutical intervention strategies into a deterministic COVID-19 model used to garner insight into the transmission mechanism of the pandemic in the USA, South Africa, Italy, and Nigeria. [PERSON] et al. [39] proposed and analyzed the autonomous and non-autonomous mathematical model of the third wave of the novel coronavirus in Nigeria. [PERSON] et al. [40] analyzed a malaria transmission model with protected travelers and partial immunity, where four preventive and control measures are implemented. Following the lead of the aforementioned studies above, we formulate and analyze a non-autonomous deterministic model that evaluates the effect of the optimal treatment and prevention of the active and latent forms of tuberculosis infections among diabetic patients and nondiabetic individuals towards attaining the WHO's global strategy to end the present TB epidemic by 2035.