@article{banks_karr_nguyen_samuels_2008, title={Sensitivity to noise variance in a social network dynamics model}, volume={66}, ISSN={["1552-4485"]}, DOI={10.1090/S0033-569X-08-01124-0}, abstractNote={Abstract : The dynamics of social networks are modeled with a system of continuous Stochastic Ordinary Differential Equations (SODE). With the proper amount of noise input, the SODE model captures dynamic features that are lacking in the corresponding deterministic ODE model. Therefore, sensitivity to noise levels is investigated by considering four different regimes: essentially deterministic, noise-enriched, noise-enlarged, and noise-dominated. Each regime is defined based on the behavior of solutions of the SODE, and the geometry of the regimes is categorized with stochastic simulations.}, number={2}, journal={QUARTERLY OF APPLIED MATHEMATICS}, author={Banks, H. T. and Karr, A. F. and Nguyen, H. K. and Samuels, J. R., Jr.}, year={2008}, pages={233–247} }
@article{kepler_nguyen_webster-cyriaque_banks_2007, title={A dynamic model for induced reactivation of latent virus}, volume={244}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2006.08.020}, abstractNote={We develop a deterministic mathematical model to describe reactivation of latent virus by chemical inducers. This model is applied to the reactivation of latent KSHV in BCBL-1 cell cultures with butyrate as the inducing agent. Parameters for the model are first estimated from known properties of the exponentially growing, uninduced cell cultures. Additional parameters that are necessary to describe induction are determined from fits to experimental data from the literature. Our initial model provides good agreement with two independent sets of experimental data, but also points to the need for a new class of experiments which are required for further understanding of the underlying mechanisms.}, number={3}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Kepler, G. M. and Nguyen, H. K. and Webster-Cyriaque, J. and Banks, H. T.}, year={2007}, month={Feb}, pages={451–462} }
@article{banks_dediu_nguyen_2007, title={Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space}, volume={4}, DOI={10.3934/mbe.2007.4.403}, abstractNote={We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Banks, H. T. and Dediu, S. and Nguyen, H. K.}, year={2007}, pages={403–430} }
@article{bai_banks_dediu_govan_last_lloyd_nguyen_olufsen_rempala_slenning_2007, title={Stochastic and deterministic models for agricultural production networks}, volume={4}, url={https://publons.com/publon/12886434/}, DOI={10.3934/mbe.2007.4.373}, abstractNote={An approach to modeling the impact of disturbances in an agricultural production network is presented. A stochastic model and its approximate deterministic model for averages over sample paths of the stochastic system are developed. Simulations, sensitivity and generalized sensitivity analyses are given. Finally, it is shown how diseases may be introduced into the network and corresponding simulations are discussed.}, number={3}, journal={Mathematical Biosciences and Engineering}, author={Bai, P. and Banks, H. T. and Dediu, S. and Govan, A. Y. and Last, M. and Lloyd, Alun and Nguyen, H. K. and Olufsen, M. S. and Rempala, G. and Slenning, B. D.}, year={2007}, pages={373–402} }
@article{banks_dediu_nguyen_2007, title={Time delay systems with distribution dependent dynamics}, volume={31}, ISSN={["1367-5788"]}, DOI={10.1016/j.arcontrol.2007.02.002}, abstractNote={General delay dynamical systems in which uncertainty is present in the form of probability measure dependent dynamics are considered. Several motivating examples arising in biology are discussed. A functional analytic framework for investigating well-posedness (existence, uniqueness and continuous dependence of solutions), inverse problems, sensitivity analysis and approximations of the measures for computational purposes is surveyed.}, number={1}, journal={ANNUAL REVIEWS IN CONTROL}, author={Banks, H. T. and Dediu, Sava and Nguyen, Hoan K.}, year={2007}, pages={17–26} }
@article{banks_nguyen_2006, title={Sensitivity of dynamical systems to Banach space parameters}, volume={323}, ISSN={["0022-247X"]}, DOI={10.1016/j.jmaa.2005.09.084}, abstractNote={We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.}, number={1}, journal={JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, author={Banks, H. T. and Nguyen, Hoan K.}, year={2006}, month={Nov}, pages={146–161} }