Sürdürülebilir Kalkınma Amaçları
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- MakaleAçık Erişim2021Global stability of Susceptible Diabetes Complication (SDC) model in discrete time
Şi̇Şman, Şeyma; Merdan, Mehmet
In this study, the mathematical model (DC) of diabetes disease is discussed. This model divides people into (D) uncomplicated and (C) complex diabetics two. In addition, diabetes is a disease known to be caused by genetic and environmental factors, and this factor is one of the main causes of genetic disorder at birth. Considering these two factors, the diabetes complication (SDC) model, which is sensitive from the diabetes complication (DC) model, is being developed. In this model, the responsive diabetes complication (SDC) model of a nonlinear system of differential equations is transformed into a discrete-time system of equations. The positivity and limitation of Model solutions were examined R0 the basic increment number is calculated. If R0 < 1, it has a global asymptotically stable balance for the situation where there is no genetic disorder at birth, and for R0 < 1, the system has an unstable balance. In addition, random behavior of the discrete model was examined for different probability distributions.
- MakaleYalnız künye2019GLOBAL STABILITY IN A PATHOGEN-SPECIFIC CD8 IMMUNE RESPONSE PREDICTION MODEL
Anaç, Halil; Merdan, Mehmet; Beki̇Ryazici, Zafer
In this study, a system of ordinary differential equations used for modeling pathogen-specific CD8 cell immune response is studied. The positivity and the limitation of the model solutions are proven. The equilibrium points in the cases with the presence and the absence of the pathogen are determined and their stabilities are investigated. Furthermore, the essential reproduction number is obtained for the system. The conditions of the reproduction number for the stability of the equilibrium are shown and numerical examples are given for supporting the analytical results.