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## Hethcote, Herbert W.

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 Author ID: hethcote.herbert-w Published as: Hethcote, H.; Hethcote, H. W.; Hethcote, Herbert; Hethcote, Herbert W.
 Documents Indexed: 54 Publications since 1970, including 2 Books
all top 5

#### Co-Authors

 19 single-authored 8 van den Driessche, Pauline 4 Castillo-Chavez, Carlos 4 Li, Yi 3 Gao, Linda Q. 3 Levin, Simon Asher 3 Liu, Wei-min 3 Mena-Lorca, Jaime 3 Stech, Harlan W. 2 Andreasen, Viggo 2 Del Valle, Sara Y. 2 Hyman, James M. 2 van Ark, James W. 2 Wang, Wendi 2 Yorke, James Alan 1 Becker, Niels G. 1 Chowell, Gerardo 1 Cintrón-Arias, Ariel 1 Gao, Linda 1 Han, Litao 1 Jing, Zhujun 1 Lewis, Mark Alun 1 Li, Tong 1 Lin, Xiaodong 1 Ma, Zhien 1 Nold, Annett 1 Rouderfer, Vladimir 1 Saenz, Roberto A. 1 Sánchez, Fabio 1 Schuette, Matthew C. 1 Shengbing, Liao 1 Song, Baojun 1 Thieme, Horst R. 1 Tudor, David W. 1 Waltman, Paul Elvis 1 Zhien, Ma 1 Zhou, Jinshi
all top 5

#### Serials

 15 Mathematical Biosciences 12 Journal of Mathematical Biology 3 Mathematical and Computer Modelling 2 Bulletin of Mathematical Biology 2 SIAM Review 2 Lecture Notes in Biomathematics 1 International Journal of Mathematical Education in Science and Technology 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Proceedings of the American Mathematical Society 1 Theoretical Population Biology 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 The Canadian Applied Mathematics Quarterly 1 Mathematical Biosciences and Engineering
all top 5

#### Fields

 50 Biology and other natural sciences (92-XX) 18 Ordinary differential equations (34-XX) 7 Integral equations (45-XX) 6 Partial differential equations (35-XX) 5 Dynamical systems and ergodic theory (37-XX) 2 Numerical analysis (65-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

53 Publications have been cited 3,153 times in 2,084 Documents Cited by Year
The mathematics of infectious diseases. Zbl 0993.92033
Hethcote, Herbert W.
2000
Dynamical behavior of epidemiological models with nonlinear incidence rates. Zbl 0621.92014
Liu, Wei-min; Hethcote, Herbert W.; Levin, Simon A.
1987
Qualitative analyses of communicable disease models. Zbl 0326.92017
Hethcote, Herbert W.
1976
Gonorrhea. Transmission dynamics and control. Zbl 0542.92026
Hethcote, Herbert W.; Yorke, James A.
1984
Dynamic models of infectious diseases as regulators of population sizes. Zbl 0748.92012
Mena-Lorca, Jaime; Hethcote, Herbert W.
1992
Some epidemiological models with nonlinear incidence. Zbl 0722.92015
Hethcote, H. W.; van den Driessche, P.
1991
Effects of quarantine in six endemic models for infectious diseases. Zbl 1019.92030
Hethcote, Herbert; Zhien, Ma; Shengbing, Liao
2002
Disease transmission models with density-dependent demographics. Zbl 0774.92018
Gao, Linda Q.; Hethcote, Herbert W.
1992
Epidemiological models with age structure, proportionate mixing, and cross-immunity. Zbl 0715.92028
Castillo-Chavez, C.; Hethcote, H. W.; Andreasen, V.; Levin, S. A.; Liu, W. M.
1989
Epidemiological models for heterogeneous populations: Proportionate mixing, parameter estimation, and immunization programs. Zbl 0619.92006
Hethcote, Herbert W.; van Ark, James W.
1987
Nonlinear oscillations in epidemic models. Zbl 0469.92012
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
An immunization model for a heterogeneous population. Zbl 0392.92009
Hethcote, Herbert W.
1978
Population size dependent incidence in models for diseases without immunity. Zbl 0823.92027
Zhou, Jinshi; Hethcote, Herbert W.
1994
Stability of the endemic equilibrium in epidemic models with subpopulations. Zbl 0582.92024
Hethcote, Herbert W.; Thieme, Horst R.
1985
Four predator prey models with infectious diseases. Zbl 0999.92032
Han, Litao; Ma, Zhien; Hethcote, H. W.
2001
Periodicity and stability in epidemic models: a survey. Zbl 0477.92014
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
A thousand and one epidemic models. Zbl 0819.92020
Hethcote, Herbert W.
1994
An SIS epidemic model with variable population size and a delay. Zbl 0836.92022
Hethcote, Herbert W.; van den Driessche, P.
1995
Two SIS epidemiologic models with delays. Zbl 0959.92025
Hethcote, Herbert W.; van den Driessche, P.
2000
Modeling HIV transmission and AIDS in the United States. Zbl 0805.92026
Hethcote, Herbert W.; Van Ark, James W.
1992
Integral equation models for endemic infectious diseases. Zbl 0433.92026
Hethcote, Herbert W.; Tudor, David W.
1980
An epidemiological model with a delay and a nonlinear incidence rate. Zbl 0714.92021
Hethcote, H. W.; Lewis, M. A.; van den Driessche, P.
1989
Effects of behavioral changes in a smallpox attack model. Zbl 1065.92039
Del Valle, S.; Hethcote, H.; Hyman, J. M.; Castillo-Chavez, C.
2005
Optimal ages of vaccination for measles. Zbl 0643.92014
Hethcote, Herbert W.
1988
Asymptotic behavior in a deterministic epidemic model. Zbl 0279.92011
Hethcote, Herbert W.
1973
Stability analysis for models of diseases without immunity. Zbl 0475.92014
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
Error bounds for asymptotic approximations of zeros of transcendental functions. Zbl 0199.49902
Hethcote, H. W.
1970
Four SEI endemic models with periodicity and separatrices. Zbl 0834.92021
Gao, Linda Q.; Mena-Lorca, Jaime; Hethcote, Herbert W.
1995
An age-structured model for pertussis transmission. Zbl 0895.92027
Hethcote, Herbert W.
1997
An epidemiological model for HIV/AIDS with proportional recruitment. Zbl 0793.92011
Lin, Xiaodong; Hethcote, Herbert W.; van den Driessche, P.
1993
Optimal vaccination schedules in a deterministic model. Zbl 0266.92011
Hethcote, Herbert W.; Waltman, Paul
1973
Modeling heterogeneous mixing in infectious disease dynamics. Zbl 0884.92025
Hethcote, H. W.
1996
Waning immunity and its effects on vaccination schedules. Zbl 0804.92012
Rouderfer, Vladimir; Becker, Niels G.; Hethcote, Herbert W.
1994
Cross-immunity in the dynamics of homogeneous and heterogeneous populations. Zbl 0663.92010
Castillo-Chavez, Carlos; Hethcote, Herbert W.; Andreasen, Viggo; Levin, Simon A.; Liu, Weimin
1988
Gonorrhea modeling: A comparison of control methods. Zbl 0486.92024
Hethcote, Herbert W.; Yorke, James A.; Nold, Annett
1982
Bounds for zeros of some special functions. Zbl 0189.34404
Hethcote, H. W.
1970
Simulations of pertussis epidemiology in the United States: Effects of adult booster vaccinations. Zbl 0934.92032
Hethcote, Herbert W.
1999
Species coexistence and periodicity in host-host-pathogen models. Zbl 1077.92044
Hethcote, Herbert W.; Wang, Wendi; Li, Yi
2005
Periodic traveling waves in SIRS endemic models. Zbl 1165.35311
Li, Tong; Li, Yi; Hethcote, Herbert W.
2009
Competing species models with an infectious disease. Zbl 1089.92050
Saenz, Roberto A.; Hethcote, Herbert W.
2006
Oscillations in an endemic model for pertussis. Zbl 0919.92032
Hethcote, Herbert W.
1998
Modeling the effects of varicella vaccination programs on the incidence of chickenpox and shingles. Zbl 1323.92211
Schuette, Matthew C.; Hethcote, Herbert W.
1999
A model for HIV transmission and AIDS. Zbl 0682.92012
Hethcote, Herbert W.
1989
Note on determining the limiting susceptible population in an epidemic model. Zbl 0212.52104
Hethcote, H. W.
1970
Bifurcations in a host-parasite model with nonlinear incidence. Zbl 1140.34361
Wang, Wendi; Li, Yi; Hethcote, H. W.
2006
Simulations of rubella vaccination strategies in China. Zbl 1097.92040
Gao, Linda; Hethcote, Herbert
2006
Variations on a theme of SEI endemic models. Zbl 0920.92026
Gao, Linda Q.; Mena-Lorca, Jaime; Hethcote, Herbert W.
1996
Hopf bifurcation in models for pertussis epidemiology. Zbl 1043.92525
Hethcote, H. W.; Li, Yi; Jing, Zhujun
1999
A vaccination model for an endemic disease with maternal antibodies in infants. Zbl 0564.92015
Hethcote, Herbert W.
1985
New vaccination strategies for pertussis. Zbl 1021.92021
Hethcote, Herbert W.
2002
Mathematical modeling of pertussis epidemiology. Zbl 0886.92025
Hethcote, H. W.
1996
Schwarz lemma analogues for harmonic functions. Zbl 0355.31004
Hethcote, Herbert W.
1977
Geometric existence proofs for non-linear boundary value problems. Zbl 0242.34023
Hethcote, Herbert W.
1972
Periodic traveling waves in SIRS endemic models. Zbl 1165.35311
Li, Tong; Li, Yi; Hethcote, Herbert W.
2009
Competing species models with an infectious disease. Zbl 1089.92050
Saenz, Roberto A.; Hethcote, Herbert W.
2006
Bifurcations in a host-parasite model with nonlinear incidence. Zbl 1140.34361
Wang, Wendi; Li, Yi; Hethcote, H. W.
2006
Simulations of rubella vaccination strategies in China. Zbl 1097.92040
Gao, Linda; Hethcote, Herbert
2006
Effects of behavioral changes in a smallpox attack model. Zbl 1065.92039
Del Valle, S.; Hethcote, H.; Hyman, J. M.; Castillo-Chavez, C.
2005
Species coexistence and periodicity in host-host-pathogen models. Zbl 1077.92044
Hethcote, Herbert W.; Wang, Wendi; Li, Yi
2005
Effects of quarantine in six endemic models for infectious diseases. Zbl 1019.92030
Hethcote, Herbert; Zhien, Ma; Shengbing, Liao
2002
New vaccination strategies for pertussis. Zbl 1021.92021
Hethcote, Herbert W.
2002
Four predator prey models with infectious diseases. Zbl 0999.92032
Han, Litao; Ma, Zhien; Hethcote, H. W.
2001
The mathematics of infectious diseases. Zbl 0993.92033
Hethcote, Herbert W.
2000
Two SIS epidemiologic models with delays. Zbl 0959.92025
Hethcote, Herbert W.; van den Driessche, P.
2000
Simulations of pertussis epidemiology in the United States: Effects of adult booster vaccinations. Zbl 0934.92032
Hethcote, Herbert W.
1999
Modeling the effects of varicella vaccination programs on the incidence of chickenpox and shingles. Zbl 1323.92211
Schuette, Matthew C.; Hethcote, Herbert W.
1999
Hopf bifurcation in models for pertussis epidemiology. Zbl 1043.92525
Hethcote, H. W.; Li, Yi; Jing, Zhujun
1999
Oscillations in an endemic model for pertussis. Zbl 0919.92032
Hethcote, Herbert W.
1998
An age-structured model for pertussis transmission. Zbl 0895.92027
Hethcote, Herbert W.
1997
Modeling heterogeneous mixing in infectious disease dynamics. Zbl 0884.92025
Hethcote, H. W.
1996
Variations on a theme of SEI endemic models. Zbl 0920.92026
Gao, Linda Q.; Mena-Lorca, Jaime; Hethcote, Herbert W.
1996
Mathematical modeling of pertussis epidemiology. Zbl 0886.92025
Hethcote, H. W.
1996
An SIS epidemic model with variable population size and a delay. Zbl 0836.92022
Hethcote, Herbert W.; van den Driessche, P.
1995
Four SEI endemic models with periodicity and separatrices. Zbl 0834.92021
Gao, Linda Q.; Mena-Lorca, Jaime; Hethcote, Herbert W.
1995
Population size dependent incidence in models for diseases without immunity. Zbl 0823.92027
Zhou, Jinshi; Hethcote, Herbert W.
1994
A thousand and one epidemic models. Zbl 0819.92020
Hethcote, Herbert W.
1994
Waning immunity and its effects on vaccination schedules. Zbl 0804.92012
Rouderfer, Vladimir; Becker, Niels G.; Hethcote, Herbert W.
1994
An epidemiological model for HIV/AIDS with proportional recruitment. Zbl 0793.92011
Lin, Xiaodong; Hethcote, Herbert W.; van den Driessche, P.
1993
Dynamic models of infectious diseases as regulators of population sizes. Zbl 0748.92012
Mena-Lorca, Jaime; Hethcote, Herbert W.
1992
Disease transmission models with density-dependent demographics. Zbl 0774.92018
Gao, Linda Q.; Hethcote, Herbert W.
1992
Modeling HIV transmission and AIDS in the United States. Zbl 0805.92026
Hethcote, Herbert W.; Van Ark, James W.
1992
Some epidemiological models with nonlinear incidence. Zbl 0722.92015
Hethcote, H. W.; van den Driessche, P.
1991
Epidemiological models with age structure, proportionate mixing, and cross-immunity. Zbl 0715.92028
Castillo-Chavez, C.; Hethcote, H. W.; Andreasen, V.; Levin, S. A.; Liu, W. M.
1989
An epidemiological model with a delay and a nonlinear incidence rate. Zbl 0714.92021
Hethcote, H. W.; Lewis, M. A.; van den Driessche, P.
1989
A model for HIV transmission and AIDS. Zbl 0682.92012
Hethcote, Herbert W.
1989
Optimal ages of vaccination for measles. Zbl 0643.92014
Hethcote, Herbert W.
1988
Cross-immunity in the dynamics of homogeneous and heterogeneous populations. Zbl 0663.92010
Castillo-Chavez, Carlos; Hethcote, Herbert W.; Andreasen, Viggo; Levin, Simon A.; Liu, Weimin
1988
Dynamical behavior of epidemiological models with nonlinear incidence rates. Zbl 0621.92014
Liu, Wei-min; Hethcote, Herbert W.; Levin, Simon A.
1987
Epidemiological models for heterogeneous populations: Proportionate mixing, parameter estimation, and immunization programs. Zbl 0619.92006
Hethcote, Herbert W.; van Ark, James W.
1987
Stability of the endemic equilibrium in epidemic models with subpopulations. Zbl 0582.92024
Hethcote, Herbert W.; Thieme, Horst R.
1985
A vaccination model for an endemic disease with maternal antibodies in infants. Zbl 0564.92015
Hethcote, Herbert W.
1985
Gonorrhea. Transmission dynamics and control. Zbl 0542.92026
Hethcote, Herbert W.; Yorke, James A.
1984
Gonorrhea modeling: A comparison of control methods. Zbl 0486.92024
Hethcote, Herbert W.; Yorke, James A.; Nold, Annett
1982
Nonlinear oscillations in epidemic models. Zbl 0469.92012
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
Periodicity and stability in epidemic models: a survey. Zbl 0477.92014
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
Stability analysis for models of diseases without immunity. Zbl 0475.92014
Hethcote, Herbert W.; Stech, Harlan W.; van den Driessche, P.
1981
Integral equation models for endemic infectious diseases. Zbl 0433.92026
Hethcote, Herbert W.; Tudor, David W.
1980
An immunization model for a heterogeneous population. Zbl 0392.92009
Hethcote, Herbert W.
1978
Schwarz lemma analogues for harmonic functions. Zbl 0355.31004
Hethcote, Herbert W.
1977
Qualitative analyses of communicable disease models. Zbl 0326.92017
Hethcote, Herbert W.
1976
Asymptotic behavior in a deterministic epidemic model. Zbl 0279.92011
Hethcote, Herbert W.
1973
Optimal vaccination schedules in a deterministic model. Zbl 0266.92011
Hethcote, Herbert W.; Waltman, Paul
1973
Geometric existence proofs for non-linear boundary value problems. Zbl 0242.34023
Hethcote, Herbert W.
1972
Error bounds for asymptotic approximations of zeros of transcendental functions. Zbl 0199.49902
Hethcote, H. W.
1970
Bounds for zeros of some special functions. Zbl 0189.34404
Hethcote, H. W.
1970
Note on determining the limiting susceptible population in an epidemic model. Zbl 0212.52104
Hethcote, H. W.
1970
all top 5

#### Cited by 3,035 Authors

 252 Mathematical Biosciences 137 Applied Mathematics and Computation 95 Journal of Theoretical Biology 94 Journal of Mathematical Biology 91 Bulletin of Mathematical Biology 80 Nonlinear Analysis. Real World Applications 59 Journal of Mathematical Analysis and Applications 59 International Journal of Biomathematics 54 Mathematical and Computer Modelling 52 Theoretical Population Biology 51 Journal of Biological Dynamics 45 Chaos, Solitons and Fractals 45 Applied Mathematical Modelling 45 Discrete and Continuous Dynamical Systems. Series B 39 Advances in Difference Equations 33 Journal of Biological Systems 29 Mathematical Methods in the Applied Sciences 29 Discrete Dynamics in Nature and Society 27 Computers & Mathematics with Applications 27 Abstract and Applied Analysis 26 Mathematical Biosciences and Engineering 21 Communications in Nonlinear Science and Numerical Simulation 20 Physica A 20 Journal of Differential Equations 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20 Computational & Mathematical Methods in Medicine 19 Journal of Computational and Applied Mathematics 14 Nonlinear Dynamics 13 Journal of Applied Mathematics 13 Journal of Applied Mathematics and Computing 13 Journal of Applied Analysis and Computation 12 Mathematics and Computers in Simulation 12 Journal of Dynamics and Differential Equations 12 Journal of Difference Equations and Applications 12 Mathematical Problems in Engineering 12 Mathematical Population Studies 12 Differential Equations and Dynamical Systems 12 Chaos 12 Mathematical Modelling of Natural Phenomena 10 Rocky Mountain Journal of Mathematics 10 Ricerche di Matematica 10 Applied Mathematics Letters 9 Journal of the Franklin Institute 9 SIAM Journal on Applied Mathematics 8 Applicable Analysis 8 European Journal of Operational Research 8 International Journal of Computer Mathematics 8 Computational and Applied Mathematics 8 Complexity 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Applied Mathematics and Mechanics. (English Edition) 6 Computational Mechanics 6 Journal of Systems Science and Complexity 6 Communications on Pure and Applied Analysis 6 International Journal of Applied and Computational Mathematics 5 Stochastic Analysis and Applications 5 Journal of Nonlinear Science 5 Mathematics 5 Nonlinear Analysis. Theory, Methods & Applications 4 Journal of Mathematical Economics 4 Acta Applicandae Mathematicae 4 Physica D 4 Journal of Integral Equations and Applications 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Linear Algebra and its Applications 4 Applied Mathematics. Series B (English Edition) 4 Discrete and Continuous Dynamical Systems 4 Advances in Complex Systems 4 Journal of Statistical Mechanics: Theory and Experiment 4 Nonlinear Analysis. Hybrid Systems 3 Journal of Statistical Physics 3 Proceedings of the American Mathematical Society 3 Applied Numerical Mathematics 3 Acta Mathematicae Applicatae Sinica. English Series 3 Annals of Operations Research 3 Japan Journal of Industrial and Applied Mathematics 3 Computational Mathematics and Mathematical Physics 3 Electronic Journal of Differential Equations (EJDE) 3 Economic Theory 3 International Journal of Nonlinear Sciences and Numerical Simulation 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Analysis and Applications (Singapore) 3 Discrete and Continuous Dynamical Systems. Series S 3 International Journal of Differential Equations 3 Science China. Mathematics 3 ISRN Applied Mathematics 3 Electronic Journal of Mathematical Analysis and Applications EJMAA 3 Cogent Mathematics 2 International Journal of Modern Physics B 2 Discrete Applied Mathematics 2 International Journal of Control 2 Journal of Engineering Mathematics 2 Nonlinearity 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Automatica 2 Biometrics 2 BIT 2 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 2 Calcolo 2 Information Sciences ...and 124 more Serials