Publications

Books

  1. Spatial Ecology via Reaction-Diffusion Equations (with Chris Cosner), John Wiley and Sons Computational and Mathematical Biology Series, John Wiley and Sons, Chichester, U.K., October 2003, 411 pages.
  2. Spatial Ecology (co-edited with Chris Cosner and Shigui Ruan), Chapman Hall/CRC Press, Boca Raton, FL, October 2009, 362 pages.

Juried Journal Articles (all co-authorships are considered equal in mathematics and are listed alphabetically)

  1. Evolution of natal dispersal in spatially heterogeneous environments (with Chris Cosner, Yuan Lou and Sebastian Schreiber), Mathematical Biosciences 283 (2017), 136-144.
  2. Perceptual ranges, information gathering and foraging success in dynamic landscapes (with William F. Fagan, Eliezer Guarie, Sharon Bewick, Allison Howard, and Chris Cosner), The American Naturalist, to appear (Fagan lead author)
  3. A tridiagonal patch model of bacteria inhabiting a nanofabricated landscape (with Brian Coomes and Yifan Sha), Mathematical Biosciences and Engineering, to appear
  4. A PDE model of intraguild predation with cross-diffusion (with Xinru Cao, King-Yeung Lam, and Tian Xiang), Discrete and Continuous Dynamical Systems B, to appear.
  5. Modeling and control of local outbreaks of West Nile virus in the United States (with Jing Chen, Jicai Huang, John C. Beier, R. S. Cantrell, C. Cosner, D. L. DeAngelis, Douglas O. Fuller, Guoyan Zhang and Shigui Ruan), Discrete and Continuous Dynamical Systems B 21 (2016), 2423-2449 (Chen lead author)
  6. How resource phenology alters consumer population dynamics (with Sharon Bewick, Chris Cosner, and William F. Fagan), The American Naturalist 187 (2016), 151-166. (Bewick lead author)
  7. Population dynamics of Rift Valley fever virus: effects of live and killed vaccines on epizootic outbreaks and enzootic maintenance (with Farida Chamchod, Chris Cosner, John Beier and Shigui Ruan), Frontiers in Microbiology (Virology Section), 10.3389/fmicb2016.00061 (2016) (Chamchod lead author)
  8. A model for the coupling of the Greater Bairam and local environmental factors in promoting Rift-Valley Fever epizootics in Egypt, (with Harold Gil, W.A. Qualls, Chris Cosner, Don DeAngelis, Ali Hassan, Abel Gad, Shigui Ruan and John Beier). (Gil lead author) Public Health 130 (2016), 64-71.
  9. From within host dynamics to the epidemiology of infectious disease: Scientific overview and challenges, Mathematical Biosciences 270B (2015), 143-155. (with Juan Gutierrez, Mary Galinski, and Eberhard Voit) (Gutierrez lead author)
  10. Modelling the effects of seasonality and socioeconomic impact on the transmission of Rift Valley virus (with Yanyu Xiao, John Beier, Chris Cosner, Don DeAngelis and Shigui Ruan) PLOS Neglected Tropical Diseases 9(1) (2015) (16 pages) (Xiao lead author)
  11. Avoidance behavior in intraguild communities: A cross-diffusion model (with Dan Ryan), Discrete and Continuous Dynamical Systems A 35 (2015), 1641-1663. (Ryan lead author).
  12. A modeling approach to investigate epizootic outbreaks and enzootic maintenance of Rift Valley fever virus (with Farida Chamchod, Chris Cosner, Ali Hassan, John C. Beier, and Shigui Ruan), Bulletin of Mathematical Biology 76 (2014), 2052-2072. (Chamchod lead author)
  13. How climate extremes - not means - define a species' geographic range boundary via a demographic tipping point (with Heather J. Lynch, Marc Rhainds, Justin M. Calabrese, Chris Cosner and William F. Fagan), Ecological Monographs 84 (2014), 131-149. (Lynch lead author)
  14. Phenologically explicit models for studying plant-pollinator interactions under climate change (with Sharon Bewick, Chris Cosner, William F. Fagan, David W. Inouye, and Isabela Galarda Varassin), Theoretical Ecology 7 (2014), 289-297. (Fagan lead author)
  15. Modeling the spatial spread of Rift Valley Fever in Egypt (with Daozhou Gao, Chris Cosner, John C. Beier and Shigui Ruan), Bulletin of Mathematical Biology 75 (2013), 523-542. (Gao lead author)
  16. Random dispersal versus fitness-dependent dispersal (with Chris Cosner, Yuan Lou, and Chao Xie), Journal of Differential Equations 254 (2013), 2905-2941.
  17. Evolutionary stability of ideal free dispersal strategies: A nonlocal dispersal model (with Chris Cosner, Yuan Lou and Dan Ryan), Canadian Applied Mathematics Quarterly 20 (2012), 15-38.
  18. Evolutionary stability of ideal free dispersal strategies in patchy environments (with Chris Cosner and Yuan Lou), J. Math. Biology 65 (2012), 943-65.
  19. Global bifurcation of solutions for crime modeling equations (with Chris Cosner and Raul Manasevich), SIAM Journal on Mathematical Analysis, 44 (2012), 1340-1358.
  20. Leadership, social learning, and the maintenance (or collapse) of migratory populations (with Chris Cosner, William F. Fagan, Thomas Mueller, and Andrew Noble), Theoretical Ecology 5 (2012), 253-265. (Fagan lead author)
  21. The implications of model formulation when transitioning from spatial to landscape ecology (with Chris Cosner and William F. Fagan), Mathematical Biosciences and Engineering 9 (2012), 27-60.
  22. Steady-state solutions of a logistic equation with nonlinear boundary conditions (with Chris Cosner and Salome Martinez), Rocky Mountain Journal of Mathematics, 41 (2011), 445-455.
  23. Evolution of dispersal and the ideal free distribution (with Chris Cosner and Yuan Lou), Mathematical Biosciences and Engineering 7 (2010), 17-36.
  24. The effects of human movement on the persistence of vector borne diseases (with Chris Cosner, John Beier, Daniel Impoinvil, Lev Kapitanski, Matthew Potts, Adriana Troyo, and Shigui Ruan), Journal of Theoretical Biology 258 (2009), 550-560. (Cosner lead author)
  25. Approximating the ideal free distribution via reaction-diffusion-advection equations (with Chris Cosner and Yuan Lou), Journal of Differential Equations 245 (2008), 3687-3703.
  26. Interspecific variation in critical patch size and gap-crossing ability as determinants of geographical range size distributions (with Chris Cosner, William F. Fagan and Subramanian Ramakrishnan), The American Naturalist 173 (2009), 363-375. (Faculty of 1000 Listed)
  27. Global bifurcation of solutions to diffusive logistic equations in bounded domains subject to nonlinear boundary conditions (with Chris Cosner and Salome Martinez), Proceedings of the Royal Society of Edinburgh 139A (2009), 45-56.
  28. The ideal free distribution as an evolutionarily stable strategy (with Chris Cosner, Donald De Angelis and Victor Padron), Journal of Biological Dynamics 1 (2007), 249-271.
  29. Density dependent behavior habitat boundaries and the Allee effect (with Chris Cosner). Bulletin of Mathematical Biology 69 (2007), 2339-2360.
  30. Movement toward better environments and the evolution of rapid diffusion (with Chris Cosner and Yuan Lou), Mathematical Biosciences 204 (2006), 199-214.
  31. Advection-mediated coexistence of competing species (with Chris Cosner and Yuan Lou), Proceedings of the Royal Society of Edinburgh 137 (2007), 497-518.
  32. On the effects of nonlinear boundary conditions in diffusive logistic equations on bounded domains (with Chris Cosner), Journal of Differential Equations 231 (2006), 768-804.
  33. Edge-linked dynamics and the scale-dependence of competitive dominance (with Chris Cosner and William Fagan), Mathematical Biosciences and Engineering 4 (2005), 833-868.
  34. Persistence of fish populations in time and space as a key to sustainable fisheries (with Donald B. Olson, Chris Cosner and Alan Hastings), Bulletin of Marine Science 76 (2005), 213-232.
  35. Multiple reversals of competitive dominance in ecological reserves via external habitat degradation (with Chris Cosner and Yuan Lou), Journal of Dynamics and Differential Equations, 16 (2004), 973-1010.
  36. Deriving reaction-diffusion models in ecology from interacting particle systems (with Chris Cosner), Journal of Mathematical Biology 48 (2004), 187-217.
  37. Intraspecific interference and consumer-resource dynamics (with Chris Cosner and Shigui Ruan), Discrete and Continuous Dynamical Systems B 4 (2004), 527-546.
  38. Habitat edges and predator-prey interactions: effects on critical patch size (with Chris Cosner and William F. Fagan), Mathematical Biosciences 175 (2002), pp 31-55.
  39. Conditional persistence in logistic models via nonlinear diffusion (with Chris Cosner), Proceedings of the Royal Society of Edinburgh 132A (2002), pp 267-281.
  40. Spatial heterogeneity and critical patch size: area effects via diffusion in closed environments (with Chris Cosner), Journal of Theoretical Biology 209 (2001), pp 161-171.
  41. How predator incursions affect critical patch size: the role of the functional response (with Chris Cosner and William Fagan), The American Naturalist 158 (2001), pp 368-375.
  42. Effects of domain size on the persistence of populations in a diffusive food-chain model with Beddington-DeAngelis functional response (with Chris Cosner), Natural Resource Modeling, 14 (2001), pp. 335-367.
  43. Brucellosis, botflies and brainworms: the impact of edge habitats on pathogen transmission and species extinction (with Chris Cosner and William F. Fagan), Journal of Mathematical Biology, 42 (2001), pp.95-119.
  44. On the dynamics of predator-prey models with the Beddington-DeAngelis functional response (with Chris Cosner), Journal of Mathematical Analysis and Applications, 257 (2001), pp. 206-222.
  45. Upper and lower solutions for a homogeneous Dirichlet problem with nonlinear diffusion and the principle of linearized stability (with Chris Cosner), Rocky Mountain Journal of Mathematics, 30 (2000), pp. 1229-1236.
  46. A comparison of foraging strategies in a patchy environment (with Chris Cosner), Mathematical Biosciences 160 (1999), pp. 25-46.
  47. Diffusion models for population dynamics incorporating individual behavior at boundaries: applications to refuge design (with Chris Cosner), Theoretical Population Biology 55 (1999) pp.189-207.
  48. How habitat edges change species interactions (with Chris Cosner and William F. Fagan), The American Naturalist 153 (1999), pp.165-182. (Fagan lead author).
  49. Skew Brownian motion: a model for diffusion with interfaces? (with Chris Cosner), Proceedings of the International Conference on Mathematical Models in the Medical and Health Sciences, Vanderbilt University Press (1998), pp. 73-78.
  50. Competitive reversals inside ecological reserves: the role of external habitat degradation (with Chris Cosner and William F. Fagan), Journal of Mathematical Biology 37 (1998), pp. 491-533.
  51. On the effects of spatial heterogeneity on the persistence of interacting species (with Chris Cosner), Journal of Mathematical Biology 37 (1998), pp103-145.
  52. Practical persistence in diffusive food chain models (with Chris Cosner), Natural Resource Modeling 11 (1998), pp. 21-34.
  53. Permanence of three competitors in seasonal ecological models with spatial heterogeneity (with Eric Avila), Canadian Applied Mathematics Quarterly 5 (1997), pp. 1-24.
  54. On competition-mediated coexistence (with James Ward, Jr.), SIAM Journal on Applied Mathematics 57 (1997), pp. 1311-1327.
  55. Bounds on trajectories in diffusive predator-prey models (with Chris Cosner), Proceedings of the 4th International Conference on Mathematical Population Dynamics, in Advances in Mathematical Population Dynamics: Molecules, Cells and Man, World Scientific Publishing, (1997), pp. 733-746.
  56. Spatially explicit models for the population dynamics of a species colonizing an island (with Chris Cosner and Vivian Huston), Mathematical Biosciences 136 (1996), pp. 65-107.
  57. Models for predator-prey systems at multiple scales (with Chris Cosner), SIAM Review 38 (1996), pp. 256-286.
  58. Ecological models, permanence and spatial heterogeneity (with Chris Cosner and Vivian Hutson), Rocky Mountain Journal of Mathematics 26 (1996), pp. 1-35.
  59. Antibifurcation and the n-species Lotka-Volterra competition model with diffusion, Differential and Integral Equations 9 (1996), pp. 305-322.
  60. Practical persistence in ecological models via comparison methods (with Chris Cosner), Proceedings of the Royal Society of Edinburgh 126A (1996), pp. 247-272.
  61. Insular biogeographic theory and diffusion models in population dynamics (with Chris Cosner), Theoretical Population Biology 45 (1994), pp. 117-202.
  62. Permanence in ecological systems with spatial heterogeneity (with Chris Cosner and Vivian Hutson), Proceedings of the Royal Society of Edinburgh 123A (1993), pp. 533-559.
  63. Should a park be an island? (with Chris Cosner), SIAM Journal on Applied Mathematics 53 (1993), pp. 219-252.
  64. Permanence in some diffusive Lotka-Volterra models for three interacting species (with Chris Cosner and Vivian Hutson), Dynamic Systems 2 (1993), pp. 505-530.
  65. On solutions to coupled multiparameter nonlinear Sturm-Liouville boundary value problems whose state components have a specified nodal structure, Resultate der Mathematik 22 (1992), pp. 470-488.
  66. A switch in nodal structure in coupled systems of nonlinear Sturm-Liouville boundary value problems, Rocky Mountain Journal of Mathematics 21 (1991), pp. 1009-1028.
  67. Diffusive logistic equations with indefinite weights: population models in disrupted environments II (with Chris Cosner), SIAM Journal on Mathematical Analysis 22 (1991), pp. 1043-1064.
  68. The effects of spatial heterogeneity in population dynamics (with Chris Cosner), Journal of Mathematical Biology 29 (1991), pp.315-338.
  69. Parameter ranges for the existence of solutions whose state components have specified nodal structure in coupled multiparameter systems of nonlinear Sturm-Liouville boundary value problems, Proceedings of the Royal Society of Edinburgh 119A (1991), pp. 347-365.
  70. On eigenfunctions with sign definite components in weakly coupled linear elliptic systems (with Chris Cosner) Journal of Mathematical Analysis and Applications 140 (1989), pp. 310- 323.
  71. Diffusive logistic equations with indefinite weights: population models in disrupted environments (with Chris Cosner), Proceedings of the Royal Society of Edinburgh 112 (1989), pp. 293-318.
  72. Global preservation of nodal structure in coupled systems of nonlinear Sturm-Liouville boundary value problems, Proceedings of the American Mathematical Society 107 (1989), pp. 633-644.
  73. On the uniqueness and stability of positive solutions in the Lotka-Volterra competition model with diffusion (with Chris Cosner), Houston Journal of Mathematics 15 (1989), pp. 341-361.
  74. On the simplicity and uniqueness of positive eigenvalues admitting positive eigenfunctions for weakly coupled elliptic systems, Rocky Mountain Journal of Mathematics 18 (1988), pp. 269-275.
  75. On the convex case in the positone problem for elliptic systems (with Chris Cosner), Nonlinear Analysis: Theory, Methods, and Applications 12 (1988), pp. 827-853.
  76. On the generalized spectrum for second-order elliptic systems (with Chris Cosner), Transactions of the American Mathematical Society 303 (1987), pp. 345-363.
  77. Global higher bifurcations in coupled systems of nonlinear eigenvalue problems, Proceedings of the Royal Society of Edinburgh 106A (1987), pp. 113-120.
  78. On the steady-state problem for the Volterra-Lotka competition model with diffusion (with Chris Cosner), Houston Journal of Mathematics 13 (1987), pp. 337-352.
  79. On coupled multiparameter nonlinear elliptic systems, Transactions of the American Mathematical Society 294 (1986), pp. 263-285.
  80. On the eigenvalue problem for coupled elliptic systems (with Klaus Schmitt), SIAM Journal on Mathematical Analysis 17 (1986), pp. 850-862.
  81. On the positone problem for elliptic systems (with Chris Cosner), Indiana University Mathematics Journal 34 (1985), pp. 517-532.
  82. A homogeneity condition guaranteeing bifurcation in multiparameter nonlinear eigenvalue problems, Nonlinear Analysis: Theory, Methods and Applications 8 (1984), pp. 159-169.
  83. Multiparameter bifurcation problems and topological degree, Journal of Differential Equations 52 (1984), pp. 39-51.
  84. Multiparameter bifurcation problems for second order ordinary differential equations, Rocky Mountain Journal of Mathematics 12 (1982), pp. 795-806.

Other Works, Publications and Abstracts

  1. Permanence in periodic-parabolic ecological systems with spatial heterogeneity (with Eric Avila), in World Scientific Series in Applicable Analysis 4 (Dynamical Systems and Applications), World Scientific Publishing, (1995), pp. 63-76 (invited paper).
  2. Review of The Theory and Applications of Reaction-Diffusion Equations: Patterns and Waves by Peter Grindrod, Bulletin of Mathematical Biology 59 (1997), pp. 1199-1201.
  3. Effects of aggregative movement on population dynamics and critical patch size (with Chris Cosner), submitted.
  4. "Evolution of dispersal in heterogeneous landscapes" (with Chris Cosner and Yuan Lou), Spatial Ecology (R.S. Cantrell, C. Cosner and S. Ruan, eds.), Chapman Hall/CRC Press, Boca Raton, FL 2009, pp. 213-227 (refereed survey)
  5. Resident-invader dynamics in infinite dimensional systems (with Chris Cosner and King-Yeung Lam), conditionally accepted at the Journal of Differential Equations.