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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 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**

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

The asymptotic behaviour of solutions of nonlinear integral
equations. *Math. Zeitschrift* **157** (1977), 141-154
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
Density-dependent regulation of spatially distributed
populations and their asymptotic speed of spread. *J. Math. Biology*
**8** (1979), 173-187
On a class of Hammerstein integral equations. *Manuscr. math.* **29**
(1979), 49-84
On the boundedness and the asymptotic behaviour of the
non-negative solutions to Volterra-Hammerstein integral equations.
*Manuscr. math.* **31** (1980), 379-412
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
(with O. Diekmann, H. Heijmans) On the stability of the cell
size distribution. *J. Math. Biology* **19** (1984), 227-248
Renewal theorems for linear discrete Volterra equations.
*J. Reine Angew. Math.* **353** (1984), 55-84
Renewal theorems for linear periodic Volterra integral
equations. *J. Integral Equations* **7** (1984), 253-277
Renewal theorems for some mathematical models in epidemiology.
*J. Integral Equations* **8** (1985), 185-216
(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
(with H.W. Hethcote) Stability of the endemic equilibrium in
epidemic models with subpopulations. *Math. Biosciences* **75**
(1985), 205-227
(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
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
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
(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
A Hille-Yosida theorem for a class of weakly continuous
semigroups. *Semigroup Forum* **38** (1989), 157-177
(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
"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 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 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
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), 611–618

**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**

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

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