Research Topics
 P van den DriesscheSummaryAffiliation: University of Victoria Country: Canada Publications

Detail Information
Publications
 A simple SIS epidemic model with a backward bifurcationP van den Driessche
Department of Mathematics and Statistics, University of Victoria, B C, Canada
J Math Biol 40:52540. 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...  Modeling diseases with latency and relapseP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada, V8W 3P4
Math Biosci Eng 4:20519. 2007..Numerical simulations (for parameters appropriate for bovine tuberculosis in cattle) with R(0) > 1 indicate that solutions tend to this endemic state...  Modeling relapse in infectious diseasesP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
Math Biosci 207:89103. 2007..Numerical simulations, with parameters relevant for herpes, are presented to complement the theoretical results, and no evidence of sustained oscillatory solutions is found...  Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmissionP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4
Math Biosci 180:2948. 2002..The results are significant for disease control...  Impact of group mixing on disease dynamicsP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W3R4, Canada
Math Biosci 228:717. 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...  Cholera models with hyperinfectivity and temporary immunityZhisheng Shuai
Department of Mathematics and Statistics, University of Victoria, BC, Canada
Bull Math Biol 74:242345. 2012..Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically...  The importance of contact network topology for the success of vaccination strategiesJunling Ma
Department of Mathematics and Statistics, University of Victoria, Victoria BC, Canada V8W 3R4
J Theor Biol 325:1221. 2013..This demonstrates the importance of understanding the topology of realistic contact networks when evaluating vaccination strategies...  Effective degree household network disease modelJunling Ma
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
J Math Biol 66:7594. 2013..This model illustrates how households (clusters) can affect disease dynamics in a complicated way...  Effective degree network disease modelsJennifer Lindquist
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
J Math Biol 62:14364. 2011..Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions...  A multispecies epidemic model with spatial dynamicsJulien Arino
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3P4
Math Med Biol 22:12942. 2005..Simulations for the spread of a disease in one species and two patches are presented...  Sensitive dependence on initial conditions in gene networksA Machina
Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, British Columbia V8W 3R4, Canada
Chaos 23:025101. 2013....  Global dynamics of cholera models with differential infectivityZhisheng Shuai
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4
Math Biosci 234:11826. 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...  Periodicity in piecewiselinear switching networks with delayR Edwards
Department of Mathematics and Statistics, University of Victoria, BC, Canada
J Math Biol 55:27198. 2007..This behavior is in contrast to the nondelayed case, in which spiralling approach to fixed points on threshold boundaries can occur...  Extending the type reproduction number to infectious disease control targeting contacts between typesZhisheng Shuai
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
J Math Biol 67:106782. 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. ..  Impact of heterogeneity on the dynamics of an SEIR epidemic modelZhisheng Shuai
Department of Mathematics and Statistics, University of Victoria, Victoria, B C, Canada
Math Biosci Eng 9:393411. 2012..If R0 > 1, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable...  Control design for sustained oscillation in a twogene regulatory networkRoderick Edwards
Department of Mathematics and Statistics, University of Victoria, PO Box 3060, STN CSC, Victoria, BC, Canada
J Math Biol 62:45378. 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...  Case fatality proportionJunling Ma
Department of Mathematics and Statistics, University of Victoria, Victoria, Canada
Bull Math Biol 70:11833. 2008..The derived expressions for case fatality can be used to estimate the disease induced death rates from more readily available data...  Implication of Ariaal sexual mixing on gonorrheaC Connell McCluskey
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Am J Hum Biol 17:293301. 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...  A model for influenza with vaccination and antiviral treatmentJulien Arino
Department of Mathematics, University of Manitoba, Winnipeg, Man, Canada
J Theor Biol 253:11830. 2008..Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models...  A final size relation for epidemic modelsJulien Arino
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Math Biosci Eng 4:15975. 2007..Applications are given to specific models for influenza and SARS...  Quarantine in a multispecies epidemic model with spatial dynamicsJulien Arino
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada L8S 4K7
Math Biosci 206:4660. 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...  Transmission assumptions generate conflicting predictions in hostvector disease models: a case study in West Nile virusMarjorie J Wonham
Department of Biological Sciences, Centre for Mathematical Biology, University of Alberta, CAB 632, Edmonton, AB, Canada T6G 2G1
Ecol Lett 9:70625. 2006..For West Nile virus, R(0) estimates for six common North American bird species indicate that all would be effective outbreak hosts...  Mathematical study of a stagedprogression HIV model with imperfect vaccineA B Gumel
Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
Bull Math Biol 68:210528. 2006....  Dispersal delays, predatorprey stability, and the paradox of enrichmentPetra Klepac
Biology Department, MS 34, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 1049, USA
Theor Popul Biol 71:43644. 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...  Stabilizing dispersal delays in predatorprey metapopulation modelsMichael G Neubert
Biology Department, MS 34, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 1049, USA
Theor Popul Biol 61:33947. 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...  Modelling strategies for controlling SARS outbreaksAbba B Gumel
Institute of Industrial and Mathematical Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Proc Biol Sci 271:222332. 2004..A communitywide eradication of SARS is feasible if optimal isolation is combined with a highly effective screening programme at the points of entry...