## Research Topics- disease transmission
- paratuberculosis
- recurrence
- herpes simplex
- disease outbreaks
- human herpesvirus 1
- cattle diseases
- gonorrhea
- endemic diseases
- communicable diseases
- forecasting
- computer simulation
- epidemiologic methods
- population dynamics
- statistical models
- cattle
- risk assessment
- incidence
- algorithms
- cholera
- vibrio cholerae
- contact tracing
- vaccination
- stochastic processes
- cluster analysis
- epidemiologic factors
- family characteristics
- horizontal disease transmission
- disease susceptibility
- emigration and immigration
| ## P van den Driessche## SummaryAffiliation: University of Victoria Country: Canada ## 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*40:525-40. 2000 - 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*4:205-19. 2007 - Modeling relapse in infectious diseasesP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4*Math Biosci*207:89-103. 2007 - Reproduction numbers and sub-threshold 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*180:29-48. 2002 - Impact of group mixing on disease dynamicsP van den Driessche
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W3R4, Canada*Math Biosci*228:71-7. 2010 - Cholera models with hyperinfectivity and temporary immunityZhisheng Shuai
Department of Mathematics and Statistics, University of Victoria, BC, Canada*Bull Math Biol*74:2423-45. 2012 - 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*67:1067-82. 2013 - 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*325:12-21. 2013 - Effective degree household network disease modelJunling Ma
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada*J Math Biol*66:75-94. 2013 - Effective degree network disease modelsJennifer Lindquist
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada*J Math Biol*62:143-64. 2011
| ## Collaborators |

## 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*40:525-40. 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... - 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*4:205-19. 2007..Numerical simulations (for parameters appropriate for bovine tuberculosis in cattle) with R(0) > 1 indicate that solutions tend to this endemic state... - Modeling relapse in infectious diseasesP 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... - Reproduction numbers and sub-threshold 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*180:29-48. 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*228:71-7. 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... - Cholera models with hyperinfectivity and temporary immunityZhisheng 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... - 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*67:1067-82. 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. .. - 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*325:12-21. 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*66:75-94. 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*62:143-64. 2011..Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions... - A multi-species epidemic model with spatial dynamicsJulien 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... - A mathematical model of syphilis transmission in an MSM populationC M Saad-Roy

Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada Electronic address*Math Biosci*277:59-70. 2016..Final outbreak sizes are numerically determined for various parameter values, and its variation and robustness to parameter value changes is also investigated. Results quantify the importance of early treatment for syphilis control. .. - Estimation of Zika virus prevalence by appearance of microcephalyC M Saad-Roy

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada*BMC Infect Dis*16:754. 2016..We estimate the prevalence of ZIKV in an import region by the time a microcephaly case is detected, since microcephaly is presently the most significant indication of ZIKV presence... - A Modelling Framework for Gene Regulatory Networks Including Transcription and TranslationR Edwards

Department of Mathematics and Statistics, University of Victoria, STN CSC, PO Box 1700, Victoria, BC, V8W 2Y2, Canada*Bull Math Biol*77:953-83. 2015..Our results thus show that including mRNA as a variable may change the behaviour of solutions. .. - 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*234:118-26. 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... - Periodicity in piecewise-linear switching networks with delayR 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... - A Mathematical Model of Anthrax Transmission in Animal PopulationsC M Saad-Roy

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada*Bull Math Biol*. 2016..It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth... - The coexistence or replacement of two subtypes of influenzaSarder Mohammed Asaduzzaman

Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada Electronic address*Math Biosci*270:1-9. 2015..Vaccination against the seasonal subtype is found to slightly increase this range for pandemic replacement, with the range increasing with increasing vaccine protection and with the length of time that vaccine-induced immunity lasts. .. - Models of bovine babesiosis including juvenile cattleC M Saad-Roy

Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada*Bull Math Biol*77:514-47. 2015..The percentage of a particular population (for example, the adult bovine population) needed to be controlled to eradicate the disease is evaluated numerically using Columbia data from the literature... - 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*9:393-411. 2012..If R0 > 1, then the disease persists in all groups or stages, and the endemic equilibrium is globally asymptotically stable... - Case fatality proportionJunling 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... - Control design for sustained oscillation in a two-gene regulatory networkRoderick 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... - 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*17:293-301. 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... - A model for influenza with vaccination and antiviral treatmentJulien 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... - A final size relation for epidemic modelsJulien 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... - 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*271:2223-32. 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... - Transmission assumptions generate conflicting predictions in host-vector 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*9:706-25. 2006..For West Nile virus, R(0) estimates for six common North American bird species indicate that all would be effective outbreak hosts... - Mathematical study of a staged-progression HIV model with imperfect vaccineA B Gumel

Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2*Bull Math Biol*68:2105-28. 2006.... - Quarantine in a multi-species epidemic model with spatial dynamicsJulien 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... - Dispersal delays, predator-prey stability, and the paradox of enrichmentPetra Klepac

Biology Department, MS 34, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 1049, USA*Theor Popul Biol*71:436-44. 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... - Stabilizing dispersal delays in predator-prey metapopulation modelsMichael 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...