User:Herbert W Hethcote

Herbert W Hethcote


Born	1941 (age 81) Villisca, Iowa, U.S.A.

Citizenship	 United States of America

Education

University of Colorado (BS in Applied Mathematics), 1964

University of Michigan (PhD in Mathematics), 1968

Scientific career

Fields

Applied Mathematics, Mathematical Biology, Mathematical Modelling of Infectious Diseases

Institutions

University of Iowa, Iowa City, Iowa

Main
Herbert W. Hethcote (born 1941) is an American Mathematician, who was a Professor of Mathematics at the University of Iowa in Iowa City from 1969-2006, and is now an Emeritus Professor.[1] He was the Director of the interdisciplinary Program in Applied Mathematical and Computational Sciences for 22 years (1982-2005). He specialized in mathematical biology, developing models for infectious disease transmission, and using mathematical and computer models to compare vaccination strategies for specific diseases.[2,3]

Contributions
In mathematical biology, Hethcote’s contributions include important work on formulating, mathematically analyzing, and applying deterministic mathematical models for infectious diseases. His first compartmental models in epidemiology included homogeneously mixing populations and thresholds for different behaviors. His later models had increasing complexity such as multiple interacting groups, variable population sizes, age structure, nonlinear incidence, delay-differential equations, periodicity, and Hopf bifurcations. Hethcote used these infectious disease models to study vaccination policy and control strategies for specific diseases such as gonorrhea, HIV/AIDS, measles, rubella, varicella (chickenpox and shingles), pertussis (whooping cough), influenza, and smallpox.[2,3]

Professor Hethcote’s highly cited 2000 paper, "The Mathematics of Infectious Diseases” clearly presents the basics of infectious disease modeling using compartments and gives relevant applications.[4] His joint paper in 1991 with Pauline van den Driessche on Some epidemiological models with nonlinear incidence” showed that periodic solutions can arise by Hopf bifurcation in an SEIRS model with nonlinear incidence.[5]  His joint paper in 1987 with Weimin Liu and Simon Levin on "Dynamical behavior of epidemiological models with nonlinear incidence rates” showed how models with nonlinear incidence rates have a much wider range of dynamical behaviors than models with bilinear incidence rates.[6]

His monograph in 1984 with James A. Yorke on "Gonorrhea Transmission Dynamics and Control” showed the importance of a core group in understanding gonorrhea transmission.[7] His joint research with Oncologist Alfred Knudson on modeling the incidence of retinoblastoma supported Knudson’s two-mutation hypothesis before the actual mutations were known.[8] =References=  
 * 1)   https://math.uiowa.edu/people/herbert-hethcote
 * 2) https://math.uiowa.edu/sites/math.uiowa.edu/files/field/cv/Hethcote%20Curriculum%20Vitae%20Apr2019_0.pdf
 * 3) 	https://scholar.google.com/citations?user=mFUSi3kAAAAJ&hl=en
 * 4) 	H.W. Hethcote, The Mathematics of Infectious Diseases, SIAM Review 42 (2000) 599-653
 * 5) 	H.W. Hethcote and P. van den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Biology 29 (1991) 271-287
 * 6) W. Liu, H.W. Hethcote, S.A. Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, Journal of Mathematical Biology 25 (1987), 359-380
 * 7) 	H.W. Hethcote and J.A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, Berlin, 1984
 * 8) A.G. Knudson, Jr., H.W. Hethcote and B.W. Brown, Mutation and childhood cancer: A probabilistic model for the incidence of retinoblastoma, Proc. Nat. Acad. Sci. U.S.A. 72 (1975) 5116-5120
 * 1) 	H.W. Hethcote and P. van den Driessche, Some epidemiological models with nonlinear incidence, J. Math. Biology 29 (1991) 271-287
 * 2) W. Liu, H.W. Hethcote, S.A. Levin, Dynamical behavior of epidemiological models with nonlinear incidence rates, Journal of Mathematical Biology 25 (1987), 359-380
 * 3) 	H.W. Hethcote and J.A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, Berlin, 1984
 * 4) A.G. Knudson, Jr., H.W. Hethcote and B.W. Brown, Mutation and childhood cancer: A probabilistic model for the incidence of retinoblastoma, Proc. Nat. Acad. Sci. U.S.A. 72 (1975) 5116-5120
 * 1) 	H.W. Hethcote and J.A. Yorke, Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, Berlin, 1984
 * 2) A.G. Knudson, Jr., H.W. Hethcote and B.W. Brown, Mutation and childhood cancer: A probabilistic model for the incidence of retinoblastoma, Proc. Nat. Acad. Sci. U.S.A. 72 (1975) 5116-5120
 * 1) A.G. Knudson, Jr., H.W. Hethcote and B.W. Brown, Mutation and childhood cancer: A probabilistic model for the incidence of retinoblastoma, Proc. Nat. Acad. Sci. U.S.A. 72 (1975) 5116-5120