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
  references
• Mathematical modeling of waterborne diseases such as cholera
• Research team at UCF
• Erdös number = 2

Publications  Google Scholar

• Spectral monotonicity of perturbed quasi-positive matrices with applications in population dynamics (with S. Chen, J. Shi and Y. Wu).
  SIAM Journal on Applied Mathematics, 82 (2022), 654-676. pdf
• Global dynamics of a Lotka-Volterra competition patch model (with S. Chen, J. Shi and Y. Wu).
  Nonlinearity, 35 (2022), 817-842. pdf
• Impact of varying community networks on disease invasion (with S. Kirkland, P. van den Driessche and X. Wang).
  SIAM Journal on Applied Mathematics, 81 (2021), 1166-1189. pdf
  Highlighted as a Research Nugget of SIAM News, Changing Community Networks Impact Disease Spread, June 10, 2021.
  Also see the News Medical Report
• A mathematical model for vibrio-phage interactions (with C.G. Botelho, J.D. Kong, M.A.B. Lucien and H. Wang).
  Mathematical Biosciences and Engineering, 18 (2021), 2688-2712. pdf
• Asymptotic profiles of the steady states for an SIS epidemic patch model with asymmetric connectivity matrix (with S. Chen, J. Shi and Y. Wu).
  Journal of Mathematical Biology, 80 (2020), 2327-2361. pdf
• A general theory for target reproduction numbers with applications to ecology and epidemiology (with M.A. Lewis and P. van den Driessche).
  Journal of Mathematical Biology, 78 (2019), 2317-2339. pdf
• 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
• 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
• UCF College of Sciences