Nonlinear Analysis for a Type-1 Diabetes Model with Focus on T-Cells and Pancreatic β-Cells Behavior

摘要: Type-1 diabetes mellitus (T1DM) is an autoimmune disease that has impact on mortality due to the destruction of insulin-producing pancreatic β -cells in islets Langerhans. Over past few years, interest analyzing this type disease, either a biological or mathematical sense, relied search for treatment guarantees full control glucose levels. Mathematical models inspired by natural phenomena, are proposed under prey–predator scheme. T1DM fits scheme complicated relationship between -cell population growth and leukocyte via immune response. In scenario, represent prey, leukocytes predator. This paper studies global dynamics reported Magombedze et al. 2010. model describes interaction resting macrophages, activated antigen cells, autolytic T-cells, -cells. Therefore, localization compact invariant sets applied provide bounded positive domain which one can ensure once enter into domain, they will remain with maximum minimum value. Furthermore, we analyzed closed-loop scenario based nonlinear theory, bases possible inputs, complementing them. These entries existing cell–cell role play unchaining diabetic condition. The analysis aims give deeper understanding T-cells nature innate system strengthens proposal, providing free illness—that is, condition wherein holds there no cells labeled macrophages.