Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of term...Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.展开更多
Multiple Sclerosis（MS） is a major cause of neurological disability in adults and has an annual cost of approximately $28 billion in the United States. MS is a very complex disorder as demyelination can happen in a v...Multiple Sclerosis（MS） is a major cause of neurological disability in adults and has an annual cost of approximately $28 billion in the United States. MS is a very complex disorder as demyelination can happen in a variety of locations throughout the brain; therefore, this disease is never the same in two patients making it very hard to predict disease progression. A modeling approach which combines clinical, biological and imaging measures to help treat and fight this disorder is needed. In this paper, I will outline MS as a very heterogeneous disorder, review some potential solutions from the literature, demonstrate the need for a biomarker and will discuss how computational modeling combined with biological, clinical and imaging data can help link disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism.展开更多
Multiple autoimmune diseases often exhibit a cyclic pattern of relapse and remission, with significant periods of loss of self-tolerance being interrupted by recurrent autoimmune events. In this article, we explore a ...Multiple autoimmune diseases often exhibit a cyclic pattern of relapse and remission, with significant periods of loss of self-tolerance being interrupted by recurrent autoimmune events. In this article, we explore a specific type of terminally differentiated regulatory T cell HLA−DR+TRegcells, and their application in existing autoimmune disease models. We also conduct an in-depth study on a multiple sclerosis model. This model incorporates a Holling-II type functional response mechanism. The focus of the study is to analyze whether the equilibrium points of the system have local asymptotic stability and determine the conditions for the existence of Hopf bifurcation. Furthermore, the direction of Hopf bifurcations and the stability of its periodic solutions can be analyzed through normal form theory and center manifold theorem.展开更多
文摘Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.
文摘Multiple Sclerosis（MS） is a major cause of neurological disability in adults and has an annual cost of approximately $28 billion in the United States. MS is a very complex disorder as demyelination can happen in a variety of locations throughout the brain; therefore, this disease is never the same in two patients making it very hard to predict disease progression. A modeling approach which combines clinical, biological and imaging measures to help treat and fight this disorder is needed. In this paper, I will outline MS as a very heterogeneous disorder, review some potential solutions from the literature, demonstrate the need for a biomarker and will discuss how computational modeling combined with biological, clinical and imaging data can help link disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism.
文摘Multiple autoimmune diseases often exhibit a cyclic pattern of relapse and remission, with significant periods of loss of self-tolerance being interrupted by recurrent autoimmune events. In this article, we explore a specific type of terminally differentiated regulatory T cell HLA−DR+TRegcells, and their application in existing autoimmune disease models. We also conduct an in-depth study on a multiple sclerosis model. This model incorporates a Holling-II type functional response mechanism. The focus of the study is to analyze whether the equilibrium points of the system have local asymptotic stability and determine the conditions for the existence of Hopf bifurcation. Furthermore, the direction of Hopf bifurcations and the stability of its periodic solutions can be analyzed through normal form theory and center manifold theorem.
