Patrick De Leenheer

Summary

Affiliation: University of Florida
Country: USA

Publications

  1. doi request reprint The chemostat with lateral gene transfer
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    J Biol Dyn 4:607-20. 2010
  2. doi request reprint Immune response to a malaria infection: properties of a mathematical model
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL, USA
    J Biol Dyn 2:102-20. 2008
  3. ncbi request reprint On predator-prey systems and small-gain theorems
    Patrick De Leenheer
    Department of Mathematics, University of Florida 411 Little Hall, Gainesville, FL 32611 8105
    Math Biosci Eng 2:25-42. 2005
  4. ncbi request reprint Global stability in a chemostat with multiple nutrients
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    J Math Biol 52:419-38. 2006
  5. doi request reprint Multistrain virus dynamics with mutations: a global analysis
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    Math Med Biol 25:285-322. 2008
  6. doi request reprint Within-host virus models with periodic antiviral therapy
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, USA
    Bull Math Biol 71:189-210. 2009
  7. doi request reprint Failure of antibiotic treatment in microbial populations
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, USA
    J Math Biol 59:563-79. 2009
  8. doi request reprint Senescence and antibiotic resistance in an age-structured population model
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL, 32611 8105, USA
    J Math Biol 61:475-99. 2010
  9. doi request reprint Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies
    Jessica B Langebrake
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, United States Electronic address
    J Theor Biol 363:53-61. 2014
  10. doi request reprint The effectiveness of marine protected areas for predator and prey with varying mobility
    Sergei S Pilyugin
    Department of Mathematics, University of Florida, United States Electronic address
    Theor Popul Biol 110:63-77. 2016

Collaborators

Detail Information

Publications13

  1. doi request reprint The chemostat with lateral gene transfer
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    J Biol Dyn 4:607-20. 2010
    ..These results can explain why the antibiotic-resistant strains persist in the pathogen population...
  2. doi request reprint Immune response to a malaria infection: properties of a mathematical model
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL, USA
    J Biol Dyn 2:102-20. 2008
    ..We provide criteria for global stability, competitive exclusion and persistence. We also demonstrate that the disease equilibrium can be destabilized by non-symmetric cross-reactive responses...
  3. ncbi request reprint On predator-prey systems and small-gain theorems
    Patrick De Leenheer
    Department of Mathematics, University of Florida 411 Little Hall, Gainesville, FL 32611 8105
    Math Biosci Eng 2:25-42. 2005
    ....
  4. ncbi request reprint Global stability in a chemostat with multiple nutrients
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    J Math Biol 52:419-38. 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]...
  5. doi request reprint Multistrain virus dynamics with mutations: a global analysis
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, USA
    Math Med Biol 25:285-322. 2008
    ..Moreover, using a perturbation result due to Smith & Waltman (1999), we show that this steady state also preserves global stability...
  6. doi request reprint Within-host virus models with periodic antiviral therapy
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, USA
    Bull Math Biol 71:189-210. 2009
    ..All our results will be illustrated on an HIV model by means of numerical examples based on up-to-date knowledge of parameter values in the model...
  7. doi request reprint Failure of antibiotic treatment in microbial populations
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, USA
    J Math Biol 59:563-79. 2009
    ..Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections...
  8. doi request reprint Senescence and antibiotic resistance in an age-structured population model
    Patrick De Leenheer
    Department of Mathematics, University of Florida, Gainesville, FL, 32611 8105, USA
    J Math Biol 61:475-99. 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...
  9. doi request reprint Traveling waves in response to a diffusing quorum sensing signal in spatially-extended bacterial colonies
    Jessica B Langebrake
    Department of Mathematics, University of Florida, Gainesville, FL 32611 8105, United States Electronic address
    J Theor Biol 363:53-61. 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. ..
  10. doi request reprint The effectiveness of marine protected areas for predator and prey with varying mobility
    Sergei S Pilyugin
    Department of Mathematics, University of Florida, United States Electronic address
    Theor Popul Biol 110:63-77. 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. ..
  11. doi request reprint Discrete three-stage population model: persistence and global stability results
    Azmy S Ackleh
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA
    J Biol Dyn 2:415-27. 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...
  12. doi request reprint Quorum activation at a distance: spatiotemporal patterns of gene regulation from diffusion of an autoinducer signal
    Gabriel E Dilanji
    Department of Physics, University of Florida, Gainesville, Florida 32611 8440, United States
    J Am Chem Soc 134:5618-26. 2012
    ..Our results show that a chemical signal transported only by diffusion can be remarkably effective in synchronizing gene expression over macroscopic distances...
  13. ncbi request reprint Feedback control for chemostat models
    Patrick De Leenheer
    Arizona State University, Department of Mathematics, Tempe, AZ 85287, USA
    J Math Biol 46:48-70. 2003
    ..In all our results the coexistence takes its simplest form: a global asymptotically stable equilibrium point in the interior of the non-negative orthant...