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Paper-based microfluidic devices are popular for their ability to automate multistep assays for chemical or biological sensing at a low cost, but the design of paper microfluidic networks has largely relied on experimental trial and error. A few mathematical models of flow through paper microfluidic devices have been developed and have succeeded in explaining experimental flow behavior. However, the reverse engineering problem of designing complex paper networks guided by appropriate mathematical models is largely unsolved. In this article, we demonstrate that a two-dimensional paper network (2DPN) designed to sequentially deliver three fluids to a test zone on the device can be computationally designed and experimentally implemented without experimental trial and error. This was accomplished by three new developments in modeling flow through paper networks: (i) coupling of the Richards equation of flow through porous media to the species transport equation, (ii) modeling flow through assemblies of multiple paper materials (test membrane and wicking pad), and (iii) incorporating limited-volume fluid sources. We demonstrate the application of this model in the optimal design of a paper-based signal-enhanced immunoassay for a malaria protein, PfHRP2. This work lays the foundation for the development of a computational design toolbox to aid in the design of paper microfluidic networks. ©