Research Topics
 Patrick De LeenheerSummaryAffiliation: University of Florida Country: USA Publications
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Publications
 The chemostat with lateral gene transferPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
J Biol Dyn 4:60720. 2010..These results can explain why the antibioticresistant strains persist in the pathogen population...  Immune response to a malaria infection: properties of a mathematical modelPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, FL, USA
J Biol Dyn 2:10220. 2008..We provide criteria for global stability, competitive exclusion and persistence. We also demonstrate that the disease equilibrium can be destabilized by nonsymmetric crossreactive responses...  On predatorprey systems and smallgain theoremsPatrick De Leenheer
Department of Mathematics, University of Florida 411 Little Hall, Gainesville, FL 32611 8105
Math Biosci Eng 2:2542. 2005....  Global stability in a chemostat with multiple nutrientsPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
J Math Biol 52:41938. 2006..For a broad class of uptake and growth functions it is proved that a nontrivial equilibrium may exist. Moreover, if it exists it is unique and globally stable, generalizing a result in [15]...  Multistrain virus dynamics with mutations: a global analysisPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
Math Med Biol 25:285322. 2008..Moreover, using a perturbation result due to Smith & Waltman (1999), we show that this steady state also preserves global stability...  Withinhost virus models with periodic antiviral therapyPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, USA
Bull Math Biol 71:189210. 2009..All our results will be illustrated on an HIV model by means of numerical examples based on uptodate knowledge of parameter values in the model...  Failure of antibiotic treatment in microbial populationsPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, USA
J Math Biol 59:56379. 2009..Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections...  Senescence and antibiotic resistance in an agestructured population modelPatrick De Leenheer
Department of Mathematics, University of Florida, Gainesville, FL, 32611 8105, USA
J Math Biol 61:47599. 2010..This steady state persists under an antibiotic treatment if the level of antibiotics is below a certain threshold; if the level exceeds this threshold, the washout state becomes a globally attracting equilibrium...  Traveling waves in response to a diffusing quorum sensing signal in spatiallyextended bacterial coloniesJessica B Langebrake
Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, United States Electronic address
J Theor Biol 363:5361. 2014..Our results can be used to predict the direction and activating or deactivating nature of a wave of gene expression in experimentally controlled bacterial populations subject to a diffusing autoinducer signal. ..  The effectiveness of marine protected areas for predator and prey with varying mobilitySergei S Pilyugin
Department of Mathematics, University of Florida, United States Electronic address
Theor Popul Biol 110:6377. 2016..The mathematical approaches advocated here complement and enhance the numerical and theoretical approaches that are commonly applied to more complex models in the context of MPA design. ..  Discrete threestage population model: persistence and global stability resultsAzmy S Ackleh
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA
J Biol Dyn 2:41527. 2008..If it is larger than one the existence of a unique positive fixed point is proved and the persistence of the system is established. Finally, for certain parameter ranges global stability of the positive fixed point is proved...  Quorum activation at a distance: spatiotemporal patterns of gene regulation from diffusion of an autoinducer signalGabriel E Dilanji
Department of Physics, University of Florida, Gainesville, Florida 32611 8440, United States
J Am Chem Soc 134:561826. 2012..Our results show that a chemical signal transported only by diffusion can be remarkably effective in synchronizing gene expression over macroscopic distances...  Feedback control for chemostat modelsPatrick De Leenheer
Arizona State University, Department of Mathematics, Tempe, AZ 85287, USA
J Math Biol 46:4870. 2003..In all our results the coexistence takes its simplest form: a global asymptotically stable equilibrium point in the interior of the nonnegative orthant...