Research / Publications

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

  • 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