Deterministic and random analysis of the discrete suscepti̇ble diabetes complication model

In this study, the mathematical model (DC) of diabetes is discussed. In this model, (D) divides people into uncomplicated diabetes and (C) complex diabetes. In addition, diabetes is a known disease caused by genetic and environmental factors, and this factor is one of the main causes of genetic disorders at birth. Considering these two factors, a susceptible diabetes complication (SDC) model is developed from the diabetes complication (DC) model. In this model, a nonlinear differential equation system is transformed into a responsive diabetes complication (SDC) model into a discrete time equation system. The positivity and limitation of the model solutions are examined. The basic reproduction number of R_0 is calculated. If R_0<1, it has a globally asymptotically stable equilibrium for the condition that there is no genetic disorder at birth, and forR_0>1, the system has an unstable equilibrium. In addition, discrete time probability distributions such as Uniform, Binomial, Geometric, Hypergeometric and Poisson were used for random behaviors of the discrete model. In addition, the results of the model obtained as a result of stochastic effect are compared and interpreted. Keywords: Equilibrium points, Susceptible Diabetes Complication (SDC) model, Global stability, discrete time probability distributions.