Diabetes affects the epidemiology of COVID-19 (Coronavirus Disease 2019), is correlated with the exorbitant threat of COVID-19 incidence and failure of treatment. Hence, studying the mechanisms behind the coexistence of diabetes and COVID-19 is useful for the development of better public health policies. In this article, we have developed a novel deterministic model for the co-infection of diabetes and COVID-19. It consists of five compartments corresponding to five population classes, namely, diabetes susceptible, diabetes patients, COVID-19 susceptible, COVID-19 infected and COVID19 recovered class. We have discussed the non-negativity and invariant region of the system. Next, the existence of equilibrium points and stabilities of different equilibria of the model are studied. Also, by using the next-generation matrix method the basic reproduction number (R0) is calculated. Further, we perform the sensitivity analysis of R0 and observed that reduction of transmission coefficient (α₁) from diabetes susceptible class to diabetes class is the most critical factor to control the co-infection. We endeavor to fit our model with the data given by the World Health Organization(WHO) and it suits well with the data. Moreover, the deterministic model is extended into the stochastic model. And by using numerical simulations our results of stochastic and deterministic models are compared. Our numerical findings are performed through computer simulation, which illustrates the robustness of our model from the eco-epidemiological perspective. The results obtained highlight the burden of diabetes and COVID-19 coinfection and the role of the α₁ in the severity of the disease.