Mathematical epidemiology is not an oxymoron

BMC Public Health

Volumn 9, Issue SUPPL. 1, 2009, Pages

  Brauer, Fred ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

MEASLES VACCINE; SMALLPOX VACCINE; ZIDOVUDINE;

ACQUIRED IMMUNE DEFICIENCY SYNDROME; BACTERIAL IMMUNITY; BLOOD TRANSFUSION; CHAGAS DISEASE; CHICKENPOX; CHILDHOOD DISEASE; CHINA; COMMUNICABLE DISEASE; DEATH; DIPHTHERIA; DISEASE TRANSMISSION; ENDEMIC DISEASE; EPIDEMIC; ERADICATION THERAPY; EUROPE; GENETIC HETEROGENEITY; GONORRHEA; HERD IMMUNITY; HISTORY; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS; HUMAN IMMUNODEFICIENCY VIRUS INFECTION; IMMUNOPATHOLOGY; INFLUENZA; MALARIA; MATHEMATICAL MODEL; MEASLES; MENINGITIS; MORTALITY; MOSQUITO; MYCOBACTERIUM TUBERCULOSIS; QUALITY OF LIFE; REINFECTION; REVIEW; RUBELLA; SEXUAL BEHAVIOR; SEXUAL TRANSMISSION; SEXUALLY TRANSMITTED DISEASE; SMALLPOX; TUBERCULOSIS; VACCINATION; VERTICAL TRANSMISSION; VIRUS IMMUNITY; YELLOW FEVER; ARTICLE; EPIDEMIOLOGY; THEORETICAL MODEL;

COMMUNICABLE DISEASES; EPIDEMIOLOGIC RESEARCH DESIGN; HISTORY, 19TH CENTURY; HISTORY, 20TH CENTURY; HISTORY, ANCIENT; HISTORY, MEDIEVAL; HUMANS; MODELS, THEORETICAL;

EID: 72849115796     PISSN: None     EISSN: 14712458     Source Type: Journal    
DOI: 10.1186/1471-2458-9-S1-S2     Document Type: Review

References (163)

1. WH McNeill, Plagues and Peoples, Doubleday, New York 1976
2. Modelling Disease Ecology with Mathematics. RJ Smith? American Institute of Mathematical Sciences, Springfield 2008
3. A contribution to the mathematical theory of epidemics. WO Kermack AG McKendrick, Proc Royal Soc London 1927 115 700 721
4. Essai d'une nouvelle analyse de la mortalité causée par la petite vérole. D Bernoulli, Mém Math Phys Acad Roy Sci Paris 1760 1 1 45
5. On the course of epidemics of some infectious diseases. PD En'ko, Vrach. St. Petersburg 1889 1008 1010 1039-1042, 1061-1063.
6. Epidemic disease in England - the evidence of variability and of persistency of type. WH Hamer, The Lancet 1906 167 4306 655 662
7. Statistical studies in immunity: the theory of an epidemic. J Brownlee, Proc Roy Soc Edinburgh 1906 26 484 521
8. R Ross, The Prevention of Malaria (with Addendum), John Murray, London 2 1911
9. Contributions to the mathematical theory of epidemics, part II. WO Kermack AG McKendrick, Proc Roy Soc London 1932 138 55 83
10. Contributions to the mathematical theory of epidemics, part III. WO Kermack AG McKendrick, Proc Roy Soc London 1933 141 94 112
11. The first epidemic model: A historical note on P.D. En'ko, Australian. K Dietz, J Stat 1988 30A 56 65
12. Perspectives on the basic reproductive ratio. JM Heffernan RJ Smith LM Wahl, J Roy Soc Interface 2005 2 281 293
13. O Diekmann JAP Heesterbeek JAJ Metz, The legacy of Kermack and McKendrick, Epidemic Models: Their Structure and Relation to Data Cambridge University Press, Cambridge, UK, Mollison D, 1995 95 115
14. Interpretation of periodicity in disease prevalence. HE Soper, J Roy Statist Soc Ser B 1929 92 34 73
15. The incidence of infectious diseases under the influence of seasonal fluctuations. K Dietz, Mathematical Models in Medicine, Lecture Notes in Biomathematics Springer-Verlag, Berlin-New York - Heidelberg, Berger J, Buhler W, Repges R, Tautu P, 1976 11 1 15
16. A simple model for complex dynamical transitions in epidemics. DJD Earn P Rohani BM Bolker BT Grenfell, Science 2000 287 667 670
17. Oscillatory phenomena in a model of infectious diseases. Z Grossman, Theor Pop Biol 1980 18 204 243
18. Recurrent outbreaks of measles, chickenpox and mumps I: seasonal variation in contact rates. WP London JA Yorke, Am J Epidem 1973 98 453 468
19. An age-structured model of pre- and post-vaccination measles transmission. D Schenzle, IMA J Math Med Biol 1984 1 169 191
20. NTJ Bailey, The Mathematical Theory of Infectious Diseases, Hafner, New York 1957
21. Epidemics and rumours: A survey. K Dietz, J Roy Statist Soc, Ser A 1967 130 505 528
22. Qualitative analysis for communicable disease models. HW Hethcote, Math Biosciences 1976 28 335 356
23. D Ludwig KL Cooke (eds), Epidemiology, SIAM, Philadelphia 1975
24. Deterministic Threshold Models in the Theory of Epidemics. P Waltman, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York 1974 1
25. NTJ Bailey, The Mathematical Theory of Infectious Diseases and its Applications, Griffin, London second 1975
26. Nonlinear oscillations in epidemic models. HW Hethcote HW Stech P van den Driessche, SIAM J Math Anal 1981 40 1 9
27. The saturating contact rate in marriage and epidemic models. JAP Heesterbeek JAJ Metz, J Math Biol 1993 31 529 539
28. A thousand and one epidemic models. HW Hethcote, Frontiers in Theoretical Biology, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York, Levin SA, 1994 100 504 515
29. The mathematics of infectious diseases. HW Hethcote, SIAM Review 2000 42 599 653
30. How should pathogen transmission be modelled? H McCallum N Barlow J Hone, Trends in Ecology and Evolution 2001 16 295 300
31. Dynamical behavior of an epidemic model with a nonlinear incidence rate. S Ruan W Wang, J Diff Equations 2003 188 135 163
32. 0in models for infectious diseases in heterogeneous populations. O Diekmann JAP Heesterbeek JAJ Metz, J Math Biol 1990 28
33. 0. JAP Heesterbeek, PhD Thesis CWI, Amsterdam 1992
34. Population biology of infectious diseases I. RM Anderson RM May, Nature 1979 280 361 367
35. RM Anderson RM May (eds), Population Biology of Infectious Diseases Springer-Verlag, Berlin-Heidelberg-New York 1982
36. Population biology of infectious diseases II. RM May RM Anderson, Nature 1979 280 455 461
37. Demographic change and persistence of HIV/AIDS in a heterogeneous population. S Busenberg KL Cooke HR Thieme, SIAM J App Math 1991 51 1030 1052
38. Three basic epidemiological models. HW Hethcote, Applied Mathematical Ecology, Biomathematics Springer-Verlag, Berlin-Heidelberg-New York, Levin SA, Hallam TG, Gross LJ, 1989 18 119 144
39. Dynamic models of infectious diseases as regulators of population size. J Mena-Lorca HW Hethcote, J Math Biol 1992 30 693 716
40. Models for the spread of universally fatal diseases. F Brauer, J Math Biol 1990 28 451 462
41. Analysis of a disease model in a population with varying size. S Busenberg P van den Driessche, J Math Biol 1990 28 257 270
42. Disease transmission models with density-dependent demographics. L Gao HW Hethcote, J Math Biol 1992 30 717 731
43. A general solution of the problem of mixing of subpopulations and its application to risk-and age-structured epidemic models. S Busenberg C Castillo-Chavez, IMA J Math Appl Med Biol 1991 8 1 29
44. On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS), Part 1: Single population models. C Castillo-Chavez KL Cooke W Huang SA Levin, J Math Biol 1989 27 373 398
45. On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS). C Castillo-Chavez KL Cooke W Huang SA Levin, Part 2: Multiple group models, Mathematical and Statistical Approaches to AIDS Epidemiology, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York, Castillo-Chavez C, 1989 83 200 217
46. Pair formation with maturation period. KP Hadeler, J Math Biol 1993 32 1 15
47. Structured mixing: Heterogeneous mixing by the definition of activity groups, Mathematical and Statistical Approaches to AIDS Epidemiology. JA Jacquez CP Simon J Koopman, Lecture Notes in Biomath, Castillo-Chavez C, 1989 83 301 315
48. A deterministic model for gonorrhea in a nonhomogeneous population. A Lajmanovich JA Yorke, Math Biosc 1976 28 221 236
49. Gonorrhea Transmission Dynamics and Control. HW Hethcote JA Yorke, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York 1984 56
50. A core group model for disease transmission. KP Hadeler C Castillo-Chavez, Math Biosc 1993 128 41 55
51. Mathematical Structures of Epidemic Systems. V Capasso, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York 1993 83
52. Transmission and control of arbovirus diseases. K Dietz, Epidemiology SIAM, Philadelphia, Ludwig D, Cooke KL, 1975 104 121
53. FC Hoppensteadt, Mathematical Theories of Populations: Demographics, Genetics, and Epidemics, SIAM, Philadelphia 1975
54. Population biology of macroparasitic infections, Mathematical Ecology. RM May, An Introduction, Biomathematics Springer-Verlag, Berlin-Heidelberg-New York, Hallam TG, Levin SA, 1986 18 405 442
55. GF Webb, Theory of Nonlinear Age-dependent Population Dynamics Marcel Dekker, New York 1985
56. Existence and uniqueness of endemic states for the age-structured S-I-R epidemic model. Y Cha M Ianelli F Milner, Math Biosc 1998 150 177 190
57. Analytical and numerical results for the age-structured S-I-S epidemic model with mixed inter-intracohort transmission. M Ianelli F Milner A Pugliese, SIAM J Math Anal 1992 23 662 688
58. Instability in an SIR-model with age dependent susceptibility. V Andreasen, Mathematical Population Dynamics: Analysis of Heterogeneity, Theory of Epidemics Wuerz, Winnipeg, Arino O, Axelrod D, Kimmel M, Langlais M, 1995 1 3 14
59. Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases. HR Thieme, Differential Equations Models in Biology, Epidemiology and Ecology, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York, Busenberg S, Martelli M, 1990 92 139 158
60. Detecting nonlinearity and chaos in epidemic data. S Ellner R Gallant J Theiler, Epidemic Models: Their Structure and Relation to Data Cambridge University Press, Cambridge, Mollison D, 1995 229 247
61. Vaccination campaigns for common childhood diseases. D Greenhalgh, Math Biosc 1990 100 201 240 (Pubitemid 20250965)
62. An age structured model for pertussis transmission. HW Hethcote, Math Biosc 1997 145 89 136
63. Modeling the effects of varicella vaccination programs on the incidence of chickenpox and shingles. MC Schuette HW Hethcote, Bull Math Biol 1999 61 1031 1064
64. Optimal vaccination patterns in age-structured populations II: optimal strategies. KP Hadeler J Müller, Models for Infectious Human Diseases: Their Structure and Relation to Data Cambridge University Press, Cambridge, UK, Isham V, Medley G, 1996 102 114
65. Optimal vaccination patterns in age structured populations. J Müller, SIAM J Appl Math 1998 59 222 241
66. The global stability analysis for an SIS model with age and infection age structure. Y Zhou B Song Z Ma, Mathematical Approaches for Emerging and Re-emerging Diseases: Models, Methods, and Theory Springer-Verlag, Berlin-Heidelberg-New York, Castillo-Chavez C, Blower S, van den Driessche P, Kirschner D, Yakubu A-A, 2002 313 335
67. How may infection-age dependent infectivity affect the dynamics of HIV/AIDS? HR Thieme C Castillo-Chavez, SIAM J Appl Math 1993 53 1447 1479
68. J Murray, Mathematical Biology, Biomathematics Texts Springer-Verlag, Berlin-Heidelberg-New York 1991 19
69. O Diekmann JAP Heesterbeek, Mathematical epidemiology of infectious diseases: Model building, analysis and interpretation John Wiley & Sons, New York 2000
70. BT Grenfell A Dobson (eds), Ecology of Infectious Diseases in Natural Populations Cambridge University Press, Cambridge, UK 1995
71. The velocity of spatial population expansion. F van den Bosch JAJ Metz O Diekmann, J Math Biol 1990 28 529 565
72. Population dynamics of fox rabies in Europe. RM Anderson HC Jackson RM May AM Smith, Nature 1981 289 765 771
73. The asymptotic spread of propagation of a simple epidemic. DG Aronson, Nonlinear Diffusion, Research Notes in Mathematics Pitman, London, Fitzgibbon WG, Walker HF, 1977 14
74. Thresholds and travelling waves for the geographical spread of infection. O Diekmann, J Math Biol 1978 6 109 130
75. Run for your life. a note on the asymptotic speed of propagation of an epidemic. O Diekmann, J Diff Eqns 1978 33 58 73
76. Spatial contact models for ecological and epidemic spread. D Mollison, J Roy Stat Soc Ser B 1977 39 283 326
77. The asymptotic spread of propagation of the deterministic non-reducible n-type epidemic. J Radcliffe L Rass, J Math Biol 1986 23 341 359
78. Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. HR Thieme, J Reine Angew Math 1979 306 94 121
79. Some deterministic models for the spread of genetic and other alterations. HF Weinberger, Biological Growth and Spread, Lecture Notes in Biomathematics Springer Verlag, Berlin-Heidelberg-New York, Jaeger W, Rost H, Tautu P, 1981 38 320 333
80. Diffusive epidemic models with spatial and age-dependent heterogeneity. WE Fitzgibbon ME Parrott GF Webb, Discrete Contin Dyn Syst 1995 1 35 57
81. A diffusive age-structured SEIRS epidemic model. WE Fitzgibbon ME Parrott GF Webb, Methods Appl Anal 1996 3 358 369
82. Quarantine in a multispecies epidemic model with spatial dynamics. J Arino R Jordan P van den Driessche, Math Bisoc 2007 206 46
83. The basic reproduction number in a multi-city compartmental epidemic model. J Arino P van den Driessche, Lecture Notes in Control and Information Science 2003 294 135 142
84. A multi-city epidemic model. J Arino P van den Driessche, Mathematical Population Studies 2003 10 175 93
85. J Arino P van den Driessche, Metapopulation epidemic models, Fields Institute Communications 2006 48 1 13
86. Dispersal, disease and life history. C Castillo-Chavez A-A Yakubu, Math Biosc 2001 173 35 53
87. SA Levin TM Powell J Steele (eds), Patch Dynamics, Lecture Notes in Biomathematics Springer-Verlag 1993 96
88. A structured epidemic model incorporating geographic mobility among regions. L Sattenspiel K Dietz, Math Biosci 1995 128 71 91
89. On an epidemic in a stratified population. RK Watson, J Appl Probability 1972 9 659 666
90. Stochastic and deterministic models for SIS epidemics among a population partitioned into households. F Ball, Math Biosci 1999 156 41 67
91. F Ball OD Lyne, Epidemics among a population of households, Mathematical Approaches fo r Emerging and Re-emerging Diseases: Models, Methods, and Theory Springer-Verlag, Berlin-Heidelberg-New York, Castillo-Chavez C, Blower S, van den Driessche P, Kirschner D, Yakubu A-A, 2002 115 142
92. Epidemics with two levels of mixing. F Ball D Mollison G Scalia-Tomba, Ann Appl Probab 1997 7 46 87
93. Stability analysis for a vector disease model. KL Cooke, Rocky Mountain Math J 1979 9 31 42
94. Renewal theorems for some mathematical models in epidemiology. HR Thieme, J Integral Equations 1985 8 185 216
95. S Busenberg KL Cooke, Vertically Transmitted Diseases, Biomathematics Springer-Verlag, Berlin-Heidelberg-New York 1993 23
96. The effect of integral conditions in certain equations modeling epidemics and population growth. S Busenberg KL Cooke, J Math Biol 1980 10 13 22
97. Prelude to Hopf bifurcation in an epidemic model: analysis of a characteristic equation associated with a nonlinear Volterra equation. Diekmann R Montijn, J Math Biol 1982 14 117 127
98. The differential-difference equation for epidemics. JE Wilkins, Bull Math Biophys 1945 7 149 150
99. The epidemic curve. EB Wilson MH Burke, Proc Nat Acad Sci 1942 28 361 367
100. A second approximation to Soper's epidemic curve. EB Wilson J Worcester, Proc Nat Acad Sci 1944 30 37 44
101. Periodicity and stability in epidemic models: a survey. HW Hethcote HW Stech P van den Driessche, Differential Equations and Applications in Ecology, Epidemics and Population Problems, Busenberg SN, Cooke KL, 1981 65 82
102. HR Thieme, The transition through stages with arbitrary length distribution, and applications in epidemics, Mathematical Approaches for Emerging and Re-emerging Diseases: Models, Methods, and Theory Springer-Verlag, Berlin-Heidelberg-New York, Castillo-Chavez C, Blower S, van den Driessche P, Kirschner D, Yakubu A-A, 2002 45 84
103. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Z Feng, Math Biosci & Eng 2007 4 675 693
104. Epidemiological models with non-exponentially distributed disease stages and applications to disease control. Z Feng D Xu H Zhao, Bull Math Biol 2007 69 1511 1536
105. Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics. AL Lloyd, Theor Pop Biol 2001 60 59 71
106. Appropriate models for the management of infectious diseases. HJ Wearing P Rohani MJ Keeling, PLOS Medicine 2005 2 621 627
107. HW Hethcote SA Levin, Periodicity in epidemic models, Applied Mathematical Ecology, Biomathematics Springer-Verlag, Berlin-Heidelberg-New York, Levin SA, Hallam TG, Gross LJ, 1989 18 193 211
108. Endemic models with arbitrarily distributed periods of infection I: General theory. Z Feng HR Thieme, SIAM J Appl Math 2000 61 803 833
109. Endemic models with arbitrarily distributed periods of infection II: Fast disease dynamics and permanent recovery. Z Feng HR Thieme, SIAM J Appl Math 2000 61 983 1012
110. RM Anderson (ed), Population Dynamics of Infectious Diseases Chapman & Hall (London) 1982
111. RM Anderson RM May, Infectious Diseases of Humans. Dynamics and Control Oxford University Press, Oxford 1991
112. Mathematical and Statistical Approaches to AIDS Epidemiology. C Castillo-Chavez ed, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York 1989 83
113. Modeling HIV Transmission and AIDS in the United States. HW Hethcote JW Van Ark, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York 1992 95
114. I Nasell, Hybrid Models of Tropical Infections Springer-Verlag, Berlin-Heidelberg-New York 1985
115. J Chin (ed), Control of Communicable Diseases Manual, American Public Health Assoc 17 2000
116. LJS Allen, An Introduction to Stochastic Processes with Applications to Biology Pearson Education Inc., Upper Saddle River, N.J 2003
117. M Bartlett, Stochastic Population Models in Ecology and Epidemiology, Methuen, London 1960
118. DJ Daley J Gani, Epidemic Modelling An Introduction. Cambridge Studies in Mathematical Biology Cambridge Univ. Press, Cambridge 1999 15
119. NS Goel N Richter-Dyn, Stochastic Models in Biology Academic Press, New York 1974
120. P Jagers, Branching Processes with Biological Applications Wiley, London 1975
121. Stochastic Processes in Epidemiology. CJ Mode CK Sleeman, HIV/AIDS, Other Infectious Diseases and Computers World Scientific, Singapore, New Jersey 2000
122. The quasi-stationary distribution of the closed endemic SIS model. I Nasell, Adv Appl Prob 1996 28 895 932
123. On the quasi-stationary distribution of the stochastic logistic epidemic. I Nasell, Math Biosci 1999 156 21 40
124. Endemicity, persistence, and quasi-stationarity. I Nasell, Mathematical Approaches for Emerging and Reemerging Infectious Diseases An Introduction Springer-Verlag, New York, Castillo-Chavez C, Blower S, van den Driessche P, D Kirschner D, Yakubu A-A, 2002 199 227
125. Networks and epidemic models. MJ Keeling KTD Eames, J Roy Soc Interface 2006 2 295 307
126. Epidemiology: How viruses spread among computers and people. AL Lloyd RM May, Science 2001 292 1316 1317
127. Contact network epidemiology: Bond percolation applied to infectious disease prediction and control. LA Meyers, bull Am Math Soc 2007 44 63 86
128. Network theory and SARS: predicting outbreak diversity. LA Meyers B Pourbohloul MEJ Newman DM Skowronski RC Brunham, J Theor Biol 2005 232 71 81
129. Predicting epidemics on directed contact networks. LA Meyers MEJ Newman B Pourbohloul, J Theor Biol 2006 240 400 418
130. The spread of epidemic disease on networks. MEJ Newman, Phys Rev E 2002 66 016128
131. The structure and function of complex networks. MEJ Newman, SIAM Review 2003 45 167 256
132. Strategies for containing an emerging influenza pandemic in Southeast Asia. NM Ferguson DATt Cummings S Cauchemez C Fraser S Riley A Meeyai S Iamsirithaworn DS Burke, Nature 2005 437 209 214
133. Strategies for mitigating an influenza pandemic. NM Ferguson DAT Cummings C Fraser JC Cajka PC Cooley DS Burke, Nature 2006 442 448 452
134. Mitigation strategies for pandemic influenza in the United States. TC Germann K Kadau IM Longini CA Macken, Proc Nat Acad Sci 2006 103 5935 5940
135. Containing pandemic influenza with antiviral agents. IM Longini ME Halloran A Nizam Y Yang, Am J Epidem 2004 159 623 633
136. Containing pandemic influenza at the source. IM Longini A Nizam S Xu K Ungchusak W Hanshaoworakul DAT Cummings ME Halloran, Science 2005 309 1083 1087
137. G MacDonald, The Epidemiology and Control of Malaria Oxford University Press, Oxford, UK 1957
138. AS Benenson, Control of Communicable Diseases in Man American Public health Assoc., Washington, D.C 16 1995
139. F Fenner DA Henderson I Arita Z Jezek ID Ladnyi, Smallpox and its Eradication World Health organization, Geneva 1988
140. MBA Oldstone, Viruses, Plagues, and History Oxford University Press, New York 1998
141. Optimal age of vaccination for measles. HW Hethcote, Math. Biosc 1988 89 29 52
142. The foot-and-mouth epidemic in Great Britain: Patterns of spreadand impact of interventions. NM Ferguson CA Donnelly RM Anderson, Science 2001 292 1155 1160
143. Dynamics of the 2001 UK foot and mouth epidemic: Stochastic dispersal in a heterogeneous landscape. MJ Keeling MEJ Westlake DJ Shaw L Matthews M Chase-Topping DT Haydon SJ Cornell J Kappay J Wilesmith BT Grenfell, Science 2001 294 813 817
144. SARS outbreaks in Ontario, Hong Kong and Singapore: The role of diagnosis and isolation as a control mechanism. G Chowell PW Fenimore M Castillo-Garsow C Castillo-Chavez, J Theor Biol 2003 224 1 8
145. Modeling strategies for controlling SARS outbreaks based on Toronto, Hong Kong, Singapore and Beijing experience. A Gumel S Ruan T Day J Watmough P van den Driessche F Brauer D Gabrielson C Bowman ME Alexander S Ardal BM Wu Sahai, Proc Roy Soc London 2004 271 2223 2232
146. Transmission dynamics and control of severe acute respiratory syndrome. M Lipsitch T Cohen B Cooper JM Robins S MA J Lyn G Gopalakrishna SK Chew CC Tan MH Samore D Fisman M Murray, Science 2003 300 1037 1040
147. Evaluation of control measures implemented in the severe acute respiratory syndrome outbreak in Beijing. X Pang Z Zhu F Xu J Guo X Gong D Liu Z Liu DD Chin DR Ferbin, JAMA 2003 290 3215 3221
148. Backwards bifurcations and catastrophe in simple models of fatal disease. J Dushoff W Huang C Castillo-Chavez, J Math Biol 1998 36 227 248
149. A model for tuberculosis with exogeneous infection. Z Feng A Capurro C Castillo-Chavez, Theo Pop Biol 2000 57 235 247
150. Subcritical endemic states in mathematical models for animal infections with incomplete immunity. D Greenhalgh O Diekmann MCM de Jong, Math Biosc 2000 165 1 25
151. Stability and bifurcation for a multiple group model for the dynamics of HIV transmission. W Huang KL Cooke C Castillo-Chavez, SIAM J Appl Math 1992 52 835 854
152. Vaccination strategies and backward bifurcation in an age-since-infection structured model. CM Kribs-Zaleta M Martcheva, Math Biosc 2002 177-178 317 332
153. A simple vaccination model with multiple endemic states. CM Kribs-Zaleta JX Velasco-Hernndez, Math Biosc 2000 164 183 201
154. A simple SIS epidemic model with a backward bifurcation. P van den Driessche J Watmough, J Math Biol 2000 40 522 540
155. Backward bifurcations in simple vaccination models. F Brauer, J Math Anal & Appl 2004 298 418 431
156. Backward bifurcation in epidemic control. KP Hadeler P van den Driessche, Math Biosc 1997 146 15 35
157. Using mathematics to understand HIV immune dynamics. DE Kirschner, Notices AMS 1996 43 191 202
158. RM May MA Nowak, Virus Dynamics: The Mathematical Foundations of Imunology and Virology Oxford University Press, Oxford UK 2000
159. A Perelson, Modeling the interaction of HIV with the immune system, Mathematical and Statistical Approaches to AIDS Epidemiology, Lect Notes in Biomath Springer-Verlag, Berlin-Heidelberg-New York, Castillo-Chavez C, 1989 83 350 370
160. A Perelson DE Kirschner, A model for the immune system response to HIV: AZT treatment studies, Mathematical Population Dynamics: Analysis of Heterogeneity, Theory of Epidemics Wuerz, Winnipeg, Arino O, Axelrod D, Kimmel M, Langlais M, 1995 1 295 310
161. + T cells. A Perelson DE Kirschner R DeBoer, Math Biosc 1993 114 81 125
162. Mathematical analysis of HIV-1 dynamics in vivo. A Perelson PW Nelson, SIAM Review 1999 41 3 44
163. F Brauer P van den Driessche, Some directions for epidemic modeling, Dynamical Systems and their Applications in Biology Fields Institute Communications No. 36, American Mathematical Society, Ruan S, Wolkowicz GSK, Wu J, 2003 95 112