P van den Driessche

Summary

Affiliation: University of Victoria
Country: Canada

Publications

  1. ncbi request reprint A simple SIS epidemic model with a backward bifurcation
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, B C, Canada
    J Math Biol 40:525-40. 2000
  2. ncbi request reprint Modeling diseases with latency and relapse
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada, V8W 3P4
    Math Biosci Eng 4:205-19. 2007
  3. ncbi request reprint Modeling relapse in infectious diseases
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
    Math Biosci 207:89-103. 2007
  4. ncbi request reprint Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
    Math Biosci 180:29-48. 2002
  5. doi request reprint Impact of group mixing on disease dynamics
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W3R4, Canada
    Math Biosci 228:71-7. 2010
  6. doi request reprint Cholera models with hyperinfectivity and temporary immunity
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, BC, Canada
    Bull Math Biol 74:2423-45. 2012
  7. ncbi request reprint Extending the type reproduction number to infectious disease control targeting contacts between types
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
    J Math Biol 67:1067-82. 2013
  8. doi request reprint The importance of contact network topology for the success of vaccination strategies
    Junling Ma
    Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4
    J Theor Biol 325:12-21. 2013
  9. doi request reprint Effective degree household network disease model
    Junling Ma
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
    J Math Biol 66:75-94. 2013
  10. doi request reprint Effective degree network disease models
    Jennifer Lindquist
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
    J Math Biol 62:143-64. 2011

Detail Information

Publications26

  1. ncbi request reprint A simple SIS epidemic model with a backward bifurcation
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, B C, Canada
    J Math Biol 40:525-40. 2000
    ..The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria...
  2. ncbi request reprint Modeling diseases with latency and relapse
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada, V8W 3P4
    Math Biosci Eng 4:205-19. 2007
    ..Numerical simulations (for parameters appropriate for bovine tuberculosis in cattle) with R(0) > 1 indicate that solutions tend to this endemic state...
  3. ncbi request reprint Modeling relapse in infectious diseases
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
    Math Biosci 207:89-103. 2007
    ..Numerical simulations, with parameters relevant for herpes, are presented to complement the theoretical results, and no evidence of sustained oscillatory solutions is found...
  4. ncbi request reprint Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
    Math Biosci 180:29-48. 2002
    ..The results are significant for disease control...
  5. doi request reprint Impact of group mixing on disease dynamics
    P van den Driessche
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W3R4, Canada
    Math Biosci 228:71-7. 2010
    ..In this latter case, depending on the distribution functions and the group mixing strengths, the disease either persists at a constant endemic level or exhibits sustained oscillatory behavior...
  6. doi request reprint Cholera models with hyperinfectivity and temporary immunity
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, BC, Canada
    Bull Math Biol 74:2423-45. 2012
    ..Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically...
  7. ncbi request reprint Extending the type reproduction number to infectious disease control targeting contacts between types
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
    J Math Biol 67:1067-82. 2013
    ..Relationships among the basic, type and target reproduction numbers are established. Examples of infectious disease models from the literature are given to illustrate the use of the target reproduction number. ..
  8. doi request reprint The importance of contact network topology for the success of vaccination strategies
    Junling Ma
    Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4
    J Theor Biol 325:12-21. 2013
    ..This demonstrates the importance of understanding the topology of realistic contact networks when evaluating vaccination strategies...
  9. doi request reprint Effective degree household network disease model
    Junling Ma
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
    J Math Biol 66:75-94. 2013
    ..This model illustrates how households (clusters) can affect disease dynamics in a complicated way...
  10. doi request reprint Effective degree network disease models
    Jennifer Lindquist
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
    J Math Biol 62:143-64. 2011
    ..Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions...
  11. ncbi request reprint A multi-species epidemic model with spatial dynamics
    Julien Arino
    Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4
    Math Med Biol 22:129-42. 2005
    ..Simulations for the spread of a disease in one species and two patches are presented...
  12. doi request reprint Sensitive dependence on initial conditions in gene networks
    A Machina
    Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, British Columbia V8W 3R4, Canada
    Chaos 23:025101. 2013
    ....
  13. doi request reprint Global dynamics of cholera models with differential infectivity
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4
    Math Biosci 234:118-26. 2011
    ..When input and death are neglected, the model is used to determine a final size equation or inequality, and simulations illustrate how assumptions on cholera transmission affect the final size of an epidemic...
  14. ncbi request reprint Periodicity in piecewise-linear switching networks with delay
    R Edwards
    Department of Mathematics and Statistics, University of Victoria, BC, Canada
    J Math Biol 55:271-98. 2007
    ..This behavior is in contrast to the non-delayed case, in which spiralling approach to fixed points on threshold boundaries can occur...
  15. doi request reprint Impact of heterogeneity on the dynamics of an SEIR epidemic model
    Zhisheng Shuai
    Department of Mathematics and Statistics, University of Victoria, Victoria, B C, Canada
    Math Biosci Eng 9:393-411. 2012
    ..If R0 > 1, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable...
  16. doi request reprint Control design for sustained oscillation in a two-gene regulatory network
    Roderick Edwards
    Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, BC, Canada
    J Math Biol 62:453-78. 2011
    ..As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior...
  17. ncbi request reprint Case fatality proportion
    Junling Ma
    Department of Mathematics and Statistics, University of Victoria, Victoria, Canada
    Bull Math Biol 70:118-33. 2008
    ..The derived expressions for case fatality can be used to estimate the disease induced death rates from more readily available data...
  18. ncbi request reprint Implication of Ariaal sexual mixing on gonorrhea
    C Connell McCluskey
    Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
    Am J Hum Biol 17:293-301. 2005
    ..Thus, the persistence of gonorrhea in the population must be due to factors not included in the model, for example, a core group of commercial sex workers or concurrent partnerships...
  19. ncbi request reprint A model for influenza with vaccination and antiviral treatment
    Julien Arino
    Department of Mathematics, University of Manitoba, Winnipeg, Man, Canada
    J Theor Biol 253:118-30. 2008
    ..Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models...
  20. ncbi request reprint A final size relation for epidemic models
    Julien Arino
    Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
    Math Biosci Eng 4:159-75. 2007
    ..Applications are given to specific models for influenza and SARS...
  21. ncbi request reprint Quarantine in a multi-species epidemic model with spatial dynamics
    Julien Arino
    Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada L8S 4K7
    Math Biosci 206:46-60. 2007
    ..The influence of various parameters on the spatial and temporal spread of the disease is studied numerically, with particular focus on the role of quarantine in the form of travel restriction...
  22. ncbi request reprint Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus
    Marjorie J Wonham
    Department of Biological Sciences, Centre for Mathematical Biology, University of Alberta, CAB 632, Edmonton, AB, Canada T6G 2G1
    Ecol Lett 9:706-25. 2006
    ..For West Nile virus, R(0) estimates for six common North American bird species indicate that all would be effective outbreak hosts...
  23. ncbi request reprint Mathematical study of a staged-progression HIV model with imperfect vaccine
    A B Gumel
    Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
    Bull Math Biol 68:2105-28. 2006
    ....
  24. ncbi request reprint Dispersal delays, predator-prey stability, and the paradox of enrichment
    Petra Klepac
    Biology Department, MS 34, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 1049, USA
    Theor Popul Biol 71:436-44. 2007
    ..We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment...
  25. ncbi request reprint Stabilizing dispersal delays in predator-prey metapopulation models
    Michael G Neubert
    Biology Department, MS 34, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 1049, USA
    Theor Popul Biol 61:339-47. 2002
    ..Our results include those of previous studies as special cases and show that the stabilizing effect continues to operate when the dispersal process is modeled more realistically...
  26. pmc Modelling strategies for controlling SARS outbreaks
    Abba B Gumel
    Institute of Industrial and Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
    Proc Biol Sci 271:2223-32. 2004
    ..A community-wide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry...