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    A Bayesian generalized linear model for Crimean–Congo hemorrhagic fever incidents
    (Springer, 2018) Ryu, Duchwan; Bilgili, Devrim; Liang, Faming; Ebrahimi, Nader; Ergönül, Önder; Faculty Member; School of Medicine; 110398
    Global spread of the Crimean-Congo hemorrhagic fever (CCHF) is a fatal viral infection disease found in parts of Africa, Asia, Eastern Europe and Middle East, with a fatality rate of up to 30%. A timely prediction of the prevalence of CCHF incidents is highly desirable, while CCHF incidents often exhibit nonlinearity in both temporal and spatial features. However, the modeling of discrete incidents is not trivial. Moreover, the CCHF incidents are monthly observed in a long period and take a nonlinear pattern over a region at each time point. Hence, the estimation and the data assimilation for incidents require extensive computations. In this paper, using the data augmentation with latent variables, we propose to utilize a dynamically weighted particle filter to take advantage of its population controlling feature in data assimilation. We apply our approach in an analysis of monthly CCHF incidents data collected in Turkey between 2004 and 2012. The results indicate that CCHF incidents are higher at Northern Central Turkey during summer and that some beforehand interventions to stop the propagation are recommendable. Supplementary materials accompanying this paper appear on-line.
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    Modeling reflex asymmetries with implicit delay differential equations
    (Elsevier, 1998) Mallet-Paret, J; Department of Mathematics; Atay, Fatihcan; Faculty Member; Department of Mathematics; College of Sciences; 253074
    Neuromuscular reflexes with time-delayed negative feedback, such as the pupil light reflex, have different rates depending on the direction of movement. This asymmetry is modeled by an implicit first-order delay differential equation in which the value of the rate constant depends on the direction of movement. Stability analyses are presented for the cases when the rate is: (1) an increasing and (2) a decreasing function of the direction of movement. It is shown that the stability of equilibria in these dynamical systems depends on whether the rate constant is a decreasing or increasing function. In particular, when the asymmetry has the shape of an increasing step function, it is possible to have stability which is independent of the value of the time delay or the steepness (i.e., gain) of the negative feedback. (C) 1998 Society for Mathematical Biology.