Mathematical model for understanding the relationship between diabetes and novel coronavirus

•We proposed a new model to perceive the relationship between COVID-19 & diabetes.•Infections like omicron, coinfection, and variants other than omicron are examined.•Impact of vaccination is assessed for COVID-19 population with or without diabetes.•The different vaccine doses including booster dose are evaluated.•The sensitivity analysis and role of reproduction number in stability are explored.•The findings are compared with real data, and the effects of key parameters are seen. A new model is proposed to explore interactions between diabetes and novel coronavirus. The model accounted for both the omicron variant and variants varying from omicron. The model investigated compartments such as hospitalization, diabetes, co-infection, omicron variant, and quarantine. Additionally, the impact of different vaccination doses is assessed. Sensitivity analysis is carried out to determine disease prevalence and control options, emphasizing the significance of knowing epidemics and their characteristics. The model is validated using actual data from Japan. The parameters are fitted with the help of ”Least Square Curve Fitting” method to describe the dynamic behavior of the proposed model. Simulation results and theoretical findings demonstrate the dynamic behavior of novel coronavirus and diabetes mellitus (DM). Biological illustrations that illustrate impact of model parameters are evaluated. Furthermore, effect of vaccine efficacy and vaccination rates for the vaccine’s first, second, and booster doses is conducted. The impact of various preventive measures, such as hospitalization rate, quarantine or self-isolation rate, vaccine dose-1, dose-2, and booster dose, is considered for diabetic individuals in contact with symptomatic or asymptomatic COVID-19 infectious people in the proposed model. The findings demonstrate the significance of vaccine doses on people with diabetes and individuals infectious with omicron variant. The proposed work helps with subsequent prevention efforts and the design of a vaccination policy to mitigate the effect of the novel coronavirus.