Some Publications of Herbert W. Hethcote

Books

(H.W. Hethcote and J.W. Van Ark), Modeling HIV Transmission and AIDS in the United States, Lecture Notes in Biomathematics 95,Springer, Berlin, 1992, 234 pages, ISBN 0-387-55904-3.

(H.W. Hethcote and J.A. Yorke), Gonorrhea Transmission Dynamics and Control, Lecture Notes in Biomathematics 56, Springer, Berlin, 1984, 105 pages, ISBN 0-387-13870-6.

Three chapters (pages 1-128) in Mathematical Understanding of Infectious Disease Dynamics, S. Ma and Y. Xia (eds.), Vol. 16 in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, 2008, 240 pages, https://www.worldscibooks.com/mathematics/7020.html

Published Articles

(T. Li, Y. Li, H.W. Hethcote) Periodic traveling waves in SIRS endemic models, Mathematical and Computer Modelling 49 (2009) 393-401.

Three chapters (pages 1-128) in Mathematical Understanding of Infectious Disease Dynamics, S. Ma and Y. Xia (eds.), Vol. 16 in Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, 2008, 240 pages, https://www.worldscibooks.com/mathematics/7020.html

(L.Q.Gao, H.W.Hethcote) A mathematical model and projection of various rubella vaccination strategies. Chinese Journal of Vaccines and Immunization 14-3 (2008) 193-197 (in Chinese with English abstract).

(S. Del Valle, J.M. Hyman, H.W. Hethcote, and S.G. Eubank) Mixing patterns between age groups in social networks, Social Networks 29 (2007) 539554.

(W. Wang, Y. Li and H.W. Hethcote) Dynamics in a host-parasite model with nonlinear incidence, International Journal of Bifurcation and Chaos 16-11 (2006) 3291-3307.

(G. Chowell, A. Cintron-Arias, S. Del Valle, F. Sanchez, B. Song, J.M. Hyman, H.W. Hethcote, C. Castillo-Chavez) Mathematical applications associated with the deliberate release of infectious agents, in Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges, A. Gumel, C. Castillo-Chavez, R.E. Mickens, and D.P. Clemence (eds.), Volume 410 in Contemporary Mathematics Series, American Mathematical Society, 2006, 51-71.

(R.A. Saenz, H.W. Hethcote, and G.C. Gray), Confined animal feeding operations as amplifiers of influenza, Vector-Borne and Zoonotic Diseases 6 (2006) 338-346.

(L.Q. Gao and H.W. Hethcote) Simulations of rubella vaccination strategies in China, Mathematical Biosciences 202 (2006) 371-385.

(R.A. Saenz and H.W. Hethcote) Competing species models with an infectious disease, Mathematical Biosciences and Engineering 3 (2006) 219-235.

(H.W. Hethcote, W. Wang, and Y. Li) Species coexistence and periodicity in host-host-pathogen models, J Math Biology 51 (2005) 629-660.

(S. Del Valle, H.W. Hethcote, J.M. Hyman, and C. Castillo-Chavez) Effects of Behavioral Changes in a Smallpox Attack Model, Mathematical Biosciences 195 (2005) 228-251.

(H.W. Hethcote, W. Wang, L. Han, and Z. Ma) A Predator Prey Model with Infected Prey, Theoretical Population Biology 66 (2004) 259-268.

(A. Van Rie and H.W. Hethcote) Adolescent and adult pertussis vaccination: computer simulations of five new strategies, Vaccine 22 (2004) 3154-3165.

(H.W. Hethcote, P. Horby, and P. McIntyre) Using computer simulations to compare pertussis vaccination strategies in Australia, Vaccine 22 (2004) 2181-2191.

(H.W. Hethcote, Z. Ma, and S. Liao) Effects of Quarantine in Six Endemic Models for Infectious Diseases, Math. Biosci. 180 (2002) 141-160.

New vaccination strategies for pertussis, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, C. Castillo-Chavez, S. Blower, P. van den Driessche, and D. Kirschner (eds.), Volume 125 IMA Series on Mathematics and Its Applications, Springer, New York, 2001, 97-118.

(L. T. Han, Z. Ma, and H.W. Hethcote) Four Predator Prey Models with Infectious Diseases, Math. & Comp. Modelling 34 (2001) 849-858.

The mathematics of infectious diseases, SIAM Review 42 (2000) 599-653. (54 page invited review paper)

(H.W. Hethcote and P. van den Driessche) Two SIS epidemiologic model models with delays, J. Math. Biol. 40 (2000) 3-26.

(H.W. Hethcote, Y. Li, and Z. Jing) Hopf bifurcation in models for pertussis epidemiology, Math. Comp. Modelling 30 (1999) 29-45.

(M.C. Schuette and H.W. Hethcote) Modeling the effects of varicella vaccination programs on the incidence of chickenpox and shingles, Bull. Math. Biol. 61 (1999) 1031-1064

Simulations of pertussis epidemiology in the United states: Effects of adult booster doses, Math. Biosci. 158 (1999) 47-73.

Oscillations in an endemic model for pertussis, Canad. Appl. Math. Quart., 6 (1998) 61-88.

An age-structured model for pertussis transmission, Math. Biosci. 145 (1997) 89-136.

Mathematical modeling of pertussis epidemiology, Z. Angew. Math. Mech. 76:Suppl.2 (1996) 429-432.

(L. Gao, J. Mena-Lorca and H.W. Hethcote) Variations on a theme of SEI endemic models, In Differential Equations and Applications to Biology and to Industry, M. Martelli et. al. , World Scientific, Singapore, 1996, 191-207.

Modeling heterogeneous mixing in infectious disease dynamics, In Models for Infectious Human Diseases, V. Isham and G.F.H. Medley, {eds.}, Cambridge University Press, Cambridge, 1996, 215-238.

(L. Gao, J. Mena-Lorca and H.W. Hethcote) Four SEI endemic models with periodicity and separatrices, Math. Biosci. 128 (1995) 157-184.

(H.W. Hethcote and P. van den Driessche) An SIS epidemic model with variable population size and a delay, J. Math. Biol. 34 (1995) 177-194.

(V. Rouderfer, N. Becker and H.W. Hethcote) Waning immunity and its effects on vaccination schedules, Math. Biosci., 124 (1994) 59-82.

(J. Zhou and H.W. Hethcote) Population size dependent incidence in models for diseases without immunity, J. Math. Biol. 32 (1994) 809-834.

A thousand and one epidemic models, In Frontiers in Mathematical Biology, S. Levin, ed., Lecture Notes in Biomathematics 100, Springer, Berlin, 1994, 504-515.

Modeling AIDS prevention programs in a population of homosexual men, In Modeling the AIDS Epidemic: Planning, Policy and Prediction ,E.H. Kaplan and M.L. Brandeau, {eds.}, Raven Press, New York, 1994, 91-107.

(X. Lin, H.W. Hethcote and P. van den Driessche) An epidemiological model for HIV/AIDS with proportional recruitment, Math. Biosci. 118 (1993) 181-195

(J. Mena-Lorca and H.W. Hethcote) Dynamic models of infectious diseases as regulators of population sizes, J. Math. Biology 30 (1992) 693-716.

(L.Q. Gao and H.W. Hethcote) Disease transmission models with density dependent demographics, J. Math. Biology 30 (1992) 717-731.

(H.W. Hethcote and J.W. Van Ark) Weak linkage between HIV epidemics in homosexual men and intravenous drug users in New York City, In AIDS Epidemiology: Methodological Issues, N.P. Jewell, K. Dietz and V.T.Farewell, {eds.}, Birkhauser, Boston Basel Berlin, 1992, 174-208.

(H.W. Hethcote and P. van den Driessche) Some epidemiological models with nonlinear incidence, J. Math. Biology 29 (1991) 271-287.

(H.W. Hethcote, J.W. Van Ark and I.M. Longini) A simulation model of AIDS in San Francisco I: Model formulation and parameter estimation, Math. Biosci. 106 (1991) 203-222.

(H.W. Hethcote, J.W. Van Ark and J.M. Karon) A simulation model of AIDS in San Francisco II: Simulations, therapy and sensitivity analysis, Math. Biosci. 106 (1991) 223-247.

(H.W. Hethcote, M.A. Lewis and P. van den Driessche) An epidemiological model with a delay and a nonlinear incidence rate, J. Math. Biology 27 (1989) 49-64.

(C. Castillo-Chavez, H.W. Hethcote, V. Andreasen, S.A. Levin and W.M. Liu) Epidemiological models with age structure and proportionate mixing, J. Math. Biology 27 (1989) 223-258.

(I.M. Longini, W.S. Clark, R.H. Byers, G.F. Lemp, J.W. Ward, W.W. Darrow and H.W. Hethcote) Statistical analysis of stages of HIV infection using a Markov model, Stat. in Med. 8 (1989) 831-843.

Three basic epidemiological models, In Applied Mathematical Ecology, L. Gross, T.G. Hallam and S.A. Levin, {eds}., Springer, Berlin, 1989, 119-144.

Rubella, In Applied Mathematical Ecology}, L. Gross, T.G. Hallam and S.A. Levin, {eds.,} Springer, Berlin, 1989, 212-234.

(H.W. Hethcote and S.A. Levin) Periodicity in epidemiological models, In Applied Mathematical Ecology, L. Gross, T.G. Hallam and S.A. Levin, {eds.}, Springer, Berlin, 1989, 193-211.

(S.J. Schwager, C. Castillo-Chavez and H.W. Hethcote) Statistical and mathematical approaches in HIV/AIDS Modeling: A review, In Mathematical and Statistical Approaches to AIDS Epidemiology, C. Castillo-Chavez, {ed.}, Lecture Notes in Biomathematics 83, Springer, Berlin Heidelberg New York, 1989, 2-37.

Optimal ages of vaccination for measles, Math. Biosci. 89 (1988) 29-52.