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LIST OF PUBLICATIONS


Horst R. Thieme


Department of Mathematics
Arizona State University
Tempe, AZ 85287-1804




Diplomarbeit (Master's thesis)

Ein a-priori-Modell aus der mathematischen Theorie der Epidemien (An a priori model from the mathematical theory of epidemics). Universität Münster (Germany) 1973


Dissertation (Ph.D thesis)

Die räumliche Ausbreitung einer Epidemie in einer Population von suszeptiblen Individuen (The spatial spread of an epidemic in a population of susceptible individuals). Universität Münster (Germany) 1976 (see $[1], [2]$ in the subsequent list)


Habilitationsschrift (habilitation thesis)

Lineare und nicht lineare Erneuerungssätze (Linear and nonlinear renewal theorems). Universität Heidelberg (Germany) 1982 (see [11], [12], [13] in the subsequent list)


Refereed Publications


$[1]$ A model for the spatial spread of an epidemic. J. Math. Biology 4 (1977), 337-351

$[2]$ The asymptotic behaviour of solutions of nonlinear integral equations. Math. Zeitschrift 157 (1977), 141-154

$[3]$ Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. J. Reine Angew. Math. 306 (1979), 94-121

$[4]$ Density-dependent regulation of spatially distributed populations and their asymptotic speed of spread. J. Math. Biology 8 (1979), 173-187

$[5]$ On a class of Hammerstein integral equations. Manuscr. math. 29 (1979), 49-84

$[6]$ On the boundedness and the asymptotic behaviour of the non-negative solutions to Volterra-Hammerstein integral equations. Manuscr. math. 31 (1980), 379-412

$[7]$ Local stability in epidemic models for heterogeneous populations. Mathematics in Biology and Medicine (V. Capasso, E. Grosso, S.L. Paveri-Fontana, eds.), 185-189. Lecture Notes in Biomathematics 57. Springer 1985

$[8]$ (with O. Diekmann, H. Heijmans) On the stability of the cell size distribution. J. Math. Biology 19 (1984), 227-248

$[9]$ Renewal theorems for linear discrete Volterra equations. J. Reine Angew. Math. 353 (1984), 55-84

$[10]$ Renewal theorems for linear periodic Volterra integral equations. J. Integral Equations 7 (1984), 253-277

$[11]$ Renewal theorems for some mathematical models in epidemiology. J. Integral Equations 8 (1985), 185-216

$[12]$ (with O. Diekmann, H. Heijmans) On the stability of the cell size distribution. II. Time-periodic developmental rates. Computers and Mathematics with Applications Vol. 12 A (1986), Special Issue 'Advances in Hyperbolic Partial Differential Equations' Vol. 3, 491-512

$[13]$ (with H.W. Hethcote) Stability of the endemic equilibrium in epidemic models with subpopulations. Math. Biosciences 75 (1985), 205-227

$[14]$ (with Clément, Ph.; Diekmann, O.; Gyllenberg, M.; Heijmans, H.J.A.M.) Perturbation theory for dual semigroups. I. The sun-reflexive case. Math. Annalen 277 (1987), 709-725

$[15]$ Well-posedness of physiologically structured population models for Daphnia magna (How biological concepts can benefit by abstract mathematical analysis). J. Math. Biology 26 (1988), 299-317

$[16]$ Asymptotic proportionality (weak ergodicity) and conditional asymptotic equality of solutions to time-heterogeneous sublinear difference and differential equations. J. Differential Equations 73 (1988), 237-268

$[17]$ (with Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans) Perturbation theory for dual semigroups. II. Time-dependent perturbations in the sun-reflexive case. Proc. Royal Soc. Edinburgh 109 A (1988), 145-172

[18] (with K. Schumacher) Some theoretical and numerical aspects of modeling dispersion in the development of ectotherms. Computers and Mathematics with Applications 15 (1988), 565-594

[19] (with V. Capasso) A threshold theorem for a reaction diffusion epidemic system. Differential Equations and Applications (R. Aftabizadeh, ed.) Ohio Univ. Press, 1988

$[20]$ A Hille-Yosida theorem for a class of weakly$^\star$ continuous semigroups. Semigroup Forum 38 (1989), 157-177

$[21]$ (with Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans) Perturbation theory for dual semigroups. III. Nonlinear Lipschitz continuous perturbations in the sun-reflexive case. Proceedings of the meeting Volterra Integro-Differential Equations in Banach Spaces and Applications, Trento 1987. Longman 1989

[22] (with H.J. Bremermann) A competitive exclusion principle for pathogen virulence. J. Math. Biology 27 (1989), 179-190

[23] (with J.A.P. Heesterbeek) How to estimate the efficacy of periodic control of an infectious plant disease. Math. Biosciences 93 (1989), 15-19

[24] (with Ph. Clément, O. Diekmann, M. Gyllenberg, H.J.A.M. Heijmans) Perturbation theory for dual semigroups. IV. The intertwining formula and the canonical pairing. Proceedings on the meeting Semigroup Theory and Applications, Trieste 1987. Marcel Dekker 1989

[25] (with H.L. Smith) Quasiconvergence and stability for strongly order preserving semiflows. SIAM J. Math. Analysis 21 (1990), 673-692

[26] (with H.L. Smith) Monotone semiflows in scalar non-quasi-monotone functional differential equations. J. Math. Analysis and Applications 150 (1990), 289-306

$[27]$ "Integrated semigroups" and integrated solutions to the abstract Cauchy problem. J. Math. Analysis and Applications 152 (1990), 416-447

[28] Semiflows generated by Lipschitz perturbations of non-densely defined operators. Differential and Integral Equations 3 (1990), 1035-1066

[29] Analysis of age-structured population models with an additional structure. Mathematical Population Dynamics, Proceedings of the 2$^{nd}$ International Conference, Rutgers Univ. 1989 (O. Arino, D.E. Axelrod, M. Kimmel, eds.). Lecture Notes in Pure and Applied Mathematics 131, 115-126. Marcel Dekker 1991

[30] (with S. Busenberg and K.L. Cooke) Demographic change and persistence of HIV/AIDS in a heterogeneous population. SIAM J. Appl. Math. 51 (1991), 1030-1052

[31] (with H.L. Smith) Convergence for strongly order preserving semiflows. SIAM J. Math. Anal. 22 (1991), 1081-1101

[32] (with O. Diekmann, M. Gyllenberg) Perturbation theory for dual semigroups V. Variation of constants formulas. Semigroup Theory and Evolution Equations (Ph. Clément, E. Mitidieri, B. de Pagter, eds.), 107-123. Proceedings of the $2^{nd}$ International Conference in Delft, Sep. 1989. Marcel Dekker 1991

[33] (with O. Diekmann, M. Gyllenberg) Semigroups and renewal equations on dual Banach spaces with application to population dynamics. Delay Differential Equations and Dynamical Systems (S. Busenberg, M. Martelli; eds.), 116-120. Lecture Notes in Mathematics 1475, Springer 1991

[34] (with H.L. Smith) Strongly order preserving semiflows generated by functional differential equations. JDE 93 (1991), 332-363

[35] (with S. Busenberg and M. Iannelli) Global Behavior of an age-structured S-I-S model. SIAM J. Math. Anal. 22 (1991), 1065-1080

[36] Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases. Differential Equations Models in Biology, Epidemiology and Ecology (S. Busenberg, M. Martelli, eds.), 139-158. Proceedings of the International Conference in Claremont, Jan. 1990. Lecture Notes in Biomathematics 92, Springer 1991

[37] Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations. J. Math. Biol. 30 (1992), 755-763

[38] Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations. Math. Biosci. 111 (1992), 99-130

[39] (with O. Diekmann and M. Gyllenberg) Perturbing semigroups by solving Stieltjes renewal equations. Diff. Integral Equations 6 (1993), 155-181

[40] Persistence under relaxed point-dissipativity (with applications to an endemic model) SIAM J. Math. Anal. 24, (1993) 407-435

[41] (with C. Castillo-Chavez) How may infection-age dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53 (1993), 1447-1479

[42] (with O. Diekmann, M. Gyllenberg, J.A.J. Metz) The 'cumulative' formulation of (physiologically) structured population models. Evolution Equations, Control Theory, and Biomathematics (Ph. Clément, G. Lumer; eds.), 145-154. Lecture Notes in Pure and Applied Mathematics 155. Marcel Dekker 1994

[43] Asymptotically autonomous differential equations in the plane. Rocky Mountain J. Math. 24 (1994), 351-380

[44] Asymptotically autonomous differential equations in the plane. II. Stricter Poincaré-Bendixson type results. Differential Integral Equ. 7 (1994), 1625-1640

[45] (with C. Castillo-Chavez) Asymptotically autonomous epidemic models. Mathematical Population Dynamics: Analysis of Heterogeneity Vol. One: Theory of Epidemics (O. Arino, D. Axelrod, M. Kimmel, M. Langlais; eds.), 33-50. Wuerz 1995

[46] (with K. Mischaikow and Hal L. Smith) Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions. Trans. Amer. Math. Soc. 347 (1995), 1669-1685

[47] (with O. Diekmann and M. Gyllenberg) Perturbing evolutionary systems by step responses and cumulative outputs. Diff. Int. Eq. 8 (1995), 1205-1244

[48] (with Zhilan Feng) Recurrent outbreaks of childhood diseases revisited: the impact of isolation. Math. Biosci. 128 (1995), 93-130

[49] Positive perturbations of dual and integrated semigroups. Advances in Mathematical Sciences and Applications 6 (1996), 445-507

[50] (with T. Matsumoto, S. Oharu) Nonlinear perturbations of a class of integrated semigroups. Hiroshima Math. J. 26 (1996), 433-473

[51] On commutative sums of generators. Rendiconti Istit. Mat. Univ. Trieste 28 (1997), Suppl., 421-451

[52] Remarks on resolvent positive operators and their perturbation. Discrete and Continuous Dynamical Systems 4 (1998), 73-90

[53] (with O. Diekmann, M. Gyllenberg, J.A.J. Metz) On the formulation and analysis of general deterministic structured population models. I. Linear theory. J. Math. Biol. 36 (1998), 349 - 388

[54] Quasi-compact semigroups via bounded perturbation. Advances in Mathematical Population Dynamics: Molecules, Cells and Man (O. Arino, D. Axelrod, M. Kimmel; eds.), 691-711. World Scientific, 1997

[55] Balanced exponential growth of operator semigroups. J. Math. Anal. Appl. 223 (1998), 30-49

[56] Positive perturbation of operator semigroups: Growth bounds, essential compactness, and asynchronous exponential growth. Discrete and Continuous Dynamical Systems 4 (1998), 735-764

[57] (with N. Navarova) Remarks on an environmental control problem. Mathematical Models in Medical and Health Sciences (M.A. Horn, G. Simonett, G.F. Webb; eds.), 267-279. Vanderbilt University Press, 1998

[58] (with P. van den Driessche) Global stability in cyclic epidemic models with disease fatalities. (Proceedings of the conference on Differential Equations with Applications to Biology.) Fields Inst. Comm. 21 (1999), 459-472

[59] Uniform weak implies uniform strong persistence also for non-autonomous semiflows. Proc. Amer. Math. Soc. 127 (1999), 2395-2403

[60] (with O. Diekmann and M. Gyllenberg) Lack of uniqueness in transport equations with a nonlocal nonlinearity. Math. Models Methods Appl. Sci. 10 (2000), 581 - 591

[61] Uniform persistence and permanence for non-autonomous semiflows in population biology. Math. Biosci. 166 (2000), 173-201

[62] (with Zhilan Feng) Endemic models with arbitrarily distributed periods of infection. I. General theory SIAM J. Appl. Math. 61 (2000), 803-833

[63] (with Zhilan Feng) Endemic models with arbitrarily distributed periods of infection. II. Fast disease dynamics and permanent recovery. SIAM J. Appl. Math. 61 (2000), 983-1012

[64] (with Jinling Yang) On the complex formation approach in modeling predator prey relations, mating and sexual disease transmission, Proceedings of the Conference on Nonlinear Differential Equations. Electron. J. Diff. Eqn. Conf. 5 (2000), 255-283

[65] (with X.-Q. Zhao) A nonlocal and delayed predator-prey reaction-diffusion model. Nonlinear Analysis RWA 2 (2001), 145-160

[66] Balanced exponential growth for perturbed operator semigroups. Advances in Mathematical Sciences and Applications 10 (2000), 775-819

[67] (with O. Diekmann, M. Gyllenberg, H. Huang, M. Kirkilionis, J.A.J. Metz) On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory. J. Math. Biol. 43 (2001), 157-189

[68] Disease extinction and disease persistence in age structured epidemic models. Nonlinear Analysis 47 (2001), 6181-6194

[69] (with Hal L. Smith) Stable coexistence and bi-stability for competitive systems on ordered Banach spaces. J. Diff. Eqn. 176 (2001), 195-222

[70] The transition through stages with arbitrary length distributions, and applications in epidemics, Mathematical Approaches for Emerging and Reemerging Infectious Diseases : Models, Methods and Theory ( C. Castillo-Chavez with S. Blower, P. van den Driessche, D. Kirschner, and A.-A. Yakubu, eds.), 45-84. Springer, 2002

[71] (with Hauke Voßeler) A Stieltjes type convolution for integrated semigroups of strong bounded variation and $L_p$ solutions to the abstract Cauchy problem. J. Diff. Integral Eqn. 15 (2002), 1171-1218

[72] (with Jinling Yang) An endemic model with variable re-infection rate and application to influenza. Math. Biosci. 180 (2002), 207-235

[73] (with André M. de Roos, Lennart Persson) Emergent Allee effects in top predators feeding on structured prey populations. Proc. R. Soc. Lond. B 270 (2003), 611618


Papers accepted for publication, refereed


[74] (with Maia Martcheva) Progression age enhanced backward bifurcation in an epidemic model with super-infection. J. Math. Biol., on line publication: DOI 10.1007/s00285-002-0181-7

[75] (with Hauke Voßeler) Semilinear perturbations of Hille Yosida operators. Banach Center Publ.


Papers submitted for publication


[76] (with J.I. Vrabie) Relatively compact orbits and compact attractors for a class of nonlinear evolution equations.

[77] (with X.-Q. Zhao): Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models



Non-refereed publications


$[1]$ Some mathematical considerations of how to stop the spatial spread of a rabies epidemic. Biological Growth and Spread (W. Jäger, H. Rost, P. Tautu, eds.), 310-319 . Lecture Notes in Biomathematics 38. Springer 1980

$[2]$ Global asymptotic stability in epidemic models. Proceedings Equadiff 82 (H.W. Knobloch, K. Schmitt, eds.), 608-615. Lecture Notes in Mathematics 1017. Springer 1983

$[3]$ A differential-integral equation modeling the dynamics of populations with a rank structure. The Dynamics of Physiologically Structured Populations. (Metz, J.A.J.; Diekmann, O.; eds.). Lecture Notes in Biomathematics 68, 496-511. Springer 1986

[4] (with C. Castillo-Chavez) On the role of variable infectivity in the dynamics of the human immunodefiency virus epidemic. Mathematical and Statistical Approaches to AIDS Epidemiology (C. Castillo-Chavez, ed.). Lecture Notes in Biomathematics 83. Springer 1989

[5] (with S. Busenberg and M. Iannelli) Dynamics of an age-structured epidemic model. Dynamical Systems (Liao Shan-Tao, Ye Yan-Qian, Ding Tong-Ren, eds.), 1 -19. World Scientific 1993


Books

to be published by Princeton University Press

Mathematics in Population Biology

      



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2003-04-29