Physical Sciences and Mathematics Commons^™

A Comparison Of Five Malaria Transmission Models: Benchmark Tests And Implications For Disease Control, Dorothy I. Wallace, Ben S. Southworth, Xun Shi, Jonathan W. Chipman, Andrew K. Githeko

Dartmouth Scholarship

Background: Models for malaria transmission are usually compared based on the quantities tracked, the form taken by each term in the equations, and the qualitative properties of the systems at equilibrium. Here five models are compared in detail in order to develop a set of performance measures that further illuminate the differences among models.

Methods: Five models of malaria transmission are compared. Parameters are adjusted to correspond to similar biological quantities across models. Nine choices of parameter sets/initial conditions are tested for all five models. The relationship between malaria incidence in humans and (1) malaria incidence in vectors, (2) man-biting …

A Direct Solver With O(N) Complexity For Variable Coefficient Elliptic Pdes Discretized Via A High-Order Composite Spectral Collocation Method, A. Gillman, P. G. Martinsson

Dartmouth Scholarship

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designed for problems with smooth solutions. The resulting system of linear equations is solved using a direct (as opposed to iterative) solver that has optimal $O(N)$ complexity for all stages of the computation when applied to problems with nonoscillatory solutions such as the Laplace and the Stokes equations. Numerical examples demonstrate that the scheme is capable of computing solutions with a relative accuracy of $10^{-10}$ or better for challenging problems such as highly oscillatory …