论文标题
循环微分方程的分布式延迟微分方程表示
Distributed Delay Differential Equation Representations of Cyclic Differential Equations
论文作者
论文摘要
隔室的普通微分方程（ODE）模型在数学生物学中广泛使用。当隔室之间的转运以恒定速率发生时，众所周知的线性链技巧可用于表明ode模型等于Erlang分布式延迟微分方程（DDE）。在这里，我们证明具有非线性交通率和可能延迟参数的隔间模型也等同于标量分布式延迟微分方程。为了说明这些等价的效用，我们计算标量DDE的均衡，并计算特征函数 - 而无需计算决定因素。我们为数学生物学中的两个模型示例得出等效标量DDE，并使用DDE公式来识别ODE模型的隔室结构所隐藏的生理过程。
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is equivalent to an Erlang distributed delay differential equation (DDE). Here, we demonstrate that compartmental models with non-linear transit rates and possibly delayed arguments are also equivalent to a scalar distributed delay differential equation. To illustrate the utility of these equivalences, we calculate the equilibria of the scalar DDE, and compute the characteristic function-- without calculating a determinant. We derive the equivalent scalar DDE for two examples of models in mathematical biology and use the DDE formulation to identify physiological processes that were otherwise hidden by the compartmental structure of the ODE model.
