Research Highlights
- A graph-theoretic approach to the construction of Lyapunov functions for large-scale differential equation systems
references
- Target reproduction numbers with application to ecology and epidemiology
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- Mathematical modeling of waterborne diseases such as cholera
- Research team at UCF
- Erdös number = 2
- A mathematical model of syphilis transmission in an MSM population (with C.M. Saad-Roy and P. van den Driessche).
Mathematical Biosciences, 277 (2016) 59-70. pdf
- Disease invasion risk in a growing population (with S. Yuan, P. van den Driessche, F. Willeboordse and J. Ma).
Journal of Mathematical Biology, 73 (2016) 665-681. pdf
- Models of Bovine Babesiosis including juvenile cattle (with C.M. Saad-Roy and P. van den Driessche).
Bulletin of Mathematical Biology, 77 (2015) 514-547. pdf
- Disease invasion on community networks with environmental pathogen movement (with J.H. Tien, M.C. Eisenberg, and P. van den Driessche).
Journal of Mathematical Biology, 70 (2015) 1065-1092. pdf
- Modelling and control of cholera on networks with a common water source (with P. van den Driessche).
Journal of Biological Dynamics, 9 (2015) 90-103. pdf
- Walks and cycles on a digraph with application to population dynamics (with J.W. Moon and P. van den Driessche).
Linear Algebra and its Applications, 451 (2014) 182-196. pdf
- A cholera model in a patchy environment with water and human movement (with M.C. Eisenberg, J.H. Tien, and P. van den Driessche).
Mathematical Biosciences, 246 (2013) 105-112. pdf
- Global stability of infectious disease models using Lyapunov functions (with P. van den Driessche).
SIAM Journal on Applied Mathematics, 73 (2013) 1513-1532. pdf
- Dynamics of an age-of-infection cholera model (with F. Brauer and P. van den Driessche).
Mathematical Biosciences and Engineering, 10 (2013) 1335-1349. pdf
- Extending the type reproduction number to infectious disease control targeting contacts between types (with J.A.P. Heesterbeek and P. van den Driessche).
Journal of Mathematical Biology, 67 (2013) 1067-1082. pdf erratum
- Cholera models with hyperinfectivity and temporary immunity (with J.H. Tien and P. van den Driessche).
Bulletin of Mathematical Biology, 74 (2012) 2423-2445. pdf
- Reproduction numbers for infections with free-living pathogens growing in the environment (with M. Bani-Yaghoub, R. Gautam, P. van den Driessche, and R. Ivanek).
Journal of Biological Dynamics, 6 (2012) 923-940. pdf
- Global dynamics of a general class of multi-stage models for infectious diseases (with H. Guo and M.Y. Li).
SIAM Journal on Applied Mathematics, 72 (2012) 261-279. pdf
- Impact of heterogeneity on the dynamics of an SEIR epidemic model (with P. van den Driessche).
Mathematical Biosciences and Engineering, 9 (2012) 393-411. pdf
- Global dynamics of cholera models with differential infectivity (with P. van den Driessche).
Mathematical Biosciences, 234 (2011) 118-126. pdf
- Global dynamics of a disease model including latency with distributed delays (with P. van den Driessche).
Canadian Applied Mathematics Quarterly, 19 (2011) 235-253. pdf
- Global-stability problem for coupled systems of differential equations on networks (with M.Y. Li).
Journal of Differential Equations, 248 (2010) 1-20. pdf
- Global stability of multi-group epidemic models with distributed delays (with M.Y. Li and C. Wang).
Journal of Mathematical Analysis and Applications, 361 (2010) 38-47. pdf
- Global stability of an epidemic model in a patchy environment (with M.Y. Li).
Canadian Applied Mathematics Quarterly, 17 (2009) 175-187. pdf
- A graph-theoretic approach to the method of global Lyapunov functions (with H. Guo and M.Y. Li).
Proceedings of the American Mathematical Society, 136 (2008) 2793-2802. pdf
- Optimization problems for general simple population with n-impulsive harvest (with L. Bai and K. Wang).
Journal of Mathematical Analysis and Applications, 329 (2007) 634-646. pdf
- Global stability of the endemic equilibrium of multigroup SIR epidemic models (with H. Guo and M.Y. Li).
Canadian Applied Mathematics Quarterly, 14 (2006) 259-284. pdf
- Optimal impulsive harvest policy for an autonomous system (with L. Bai and K. Wang).
Taiwanese Journal of Mathematics, 8 (2004) 245-258. pdf
- Persistence and extinction of single population in a polluted environment (with Z. Li and K. Wang).
Electronic Journal of Differential Equations, 108 (2004) 1-5. pdf
- Optimal impulsive harvesting policy for single population (with X. Zhang and K. Wang).
Nonlinear Analysis: Real World Applications, 4 (2003) 639-651. pdf
Funding Acknowledgement
- National Science Foundation
- Simons Foundation
- UCF Office of Research & Commercialization
- UCF College of Sciences