Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA.
J R Soc Interface. 2012 Aug 7;9(73):1983-97. doi: 10.1098/rsif.2011.0829. Epub 2012 Feb 15.
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.
数学模型可以帮助我们更好地理解儿童传染病的动态变化，但这些模型依赖于适当的参数值，而这些参数通常是未知的，必须根据疾病病例数据进行估计。在本文中，我们开发了一个使用包含模型和测量噪声的连续微分方程来高效估计具有季节性传播参数的儿童传染病模型的框架。该问题采用同时方法进行公式化，其中所有状态变量都被离散化，并且离散微分方程被包含为约束条件，从而得到一个大规模的代数非线性规划问题，可以使用非线性原始对偶内点求解器来解决。该技术使用来自三个具有不同学校假期时间表的不同地点的麻疹病例数据进行了演示，我们对传播参数季节性的估计与学校学期假期具有很强的相关性。我们的方法在效率上有了显著提高，与其他已发表的方法相比，解决时间减少了 40-400 倍。虽然我们的方法相对于积分整个未知状态空间的技术更容易受到偏差的影响，但详细的模拟研究表明没有偏差的证据。此外，与计算强度更高的方法相比，我们的方法的计算效率允许对更大的模型空间进行研究。
