Browsing by Author "Li, B"

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    Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation
    (2017-04-23) Dai, S; Li, B; Lu, J
    We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals--Cahn--Hilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the Poisson--Boltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics---its potential, free energy, and dielectric boundary force---with respect to the perturbation of dielectric boundary. We also prove the $\Gamma$-convergence of the phase-field free-energy functionals to their sharp-interface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals--Cahn--Hilliard functionals with minimal assumptions.
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    Dynamics of data availability in disease modeling: An example evaluating the tradeoffs of ultra-fine-scale factors applied to human West Nile virus disease models in the Chicago area, USA
    (PLoS ONE, 2021-05-01) Uelmen, JA; Irwin, P; Brown, WM; Karki, S; Ruiz, MO; Li, B; Smith, RL
    Background Since 1999, West Nile virus (WNV) has moved rapidly across the United States, resulting in tens of thousands of human cases. Both the number of human cases and the minimum infection rate (MIR) in vector mosquitoes vary across time and space and are driven by numerous abiotic and biotic forces, ranging from differences in microclimates to sociodemographic factors. Because the interactions among these multiple factors affect the locally variable risk of WNV illness, it has been especially difficult to model human disease risk across varying spatial and temporal scales. Cook and DuPage Counties, comprising the city of Chicago and surrounding suburbs, experience some of the highest numbers of human neuroinvasive cases of WNV in the United States. Despite active mosquito control efforts, there is consistent annual WNV presence, resulting in more than 285 confirmed WNV human cases and 20 deaths from the years 2014-2018 in Cook County alone. Methods A previous Chicago-area WNV model identified the fifty-five most high and low risk locations in the Northwest Mosquito Abatement District (NWMAD), an enclave the size of the combined Cook and DuPage county area. In these locations, human WNV risk was stratified by model performance, as indicated by differences in studentized residuals. Within these areas, an additional two-years of field collections and data processing was added to a 12-year WNV dataset that includes human cases, MIR, vector abundance, and land-use, historical climate, and socio-economic and demographic variables, and was assessed by an ultra-fine-scale (1 km spatial x 1 week temporal resolution) multivariate logistic regression model. Results Multivariate statistical methods applied to the ultra-fine-scale model identified fewer explanatory variables while improving upon the fit of the previous model. Beyond MIR and climatic factors, efforts to acquire additional covariates only slightly improved model predictive performance. Conclusions These results suggest human WNV illness in the Chicago area may be associated with fewer, but increasingly critical, key variables at finer scales. Given limited resources, these findings suggest large variations in model performance occur, depending on covariate availability, and provide guidance in variable selection for optimal WNV human illness modeling.