-
2
-
-
0003318955
-
Mathematical structures of epidemic systems
-
Springer, Berlin
-
Capasso V, Mathematical structures of epidemic systems, Lecture Notes in Biomath, Vol. 97, Springer, Berlin, 1993.
-
(1993)
Lecture Notes in Biomath
, vol.97
-
-
Capasso, V.1
-
4
-
-
42249093128
-
Mathematical epidemiology
-
Springer, Berlin, Heidelberg
-
Brauer F, van den Driessche P, Wu J (eds.), Mathematical epidemiology, Lecture Notes in Mathematics, Mathematical Biosciences Subseries, 1945. Springer, Berlin, Heidelberg, 2008.
-
(2008)
Lecture Notes in Mathematics, Mathematical Biosciences Subseries
, vol.1945
-
-
Brauer, F.1
Van Den Driessche, P.2
Wu, J.3
-
5
-
-
0015724094
-
Optimal vaccination schedules in deterministic epidemic model
-
Hethcote H, Waltman P, Optimal vaccination schedules in deterministic epidemic model, Math Biosci 18:365-381, 1973.
-
(1973)
Math Biosci
, vol.18
, pp. 365-381
-
-
Hethcote, H.1
Waltman, P.2
-
6
-
-
0005467684
-
On the optimal control of a deterministic epidemic
-
Morton R, Wickwire KH, On the optimal control of a deterministic epidemic, Adv Appl Probability 6:622-635, 1974.
-
(1974)
Adv Appl Probability
, vol.6
, pp. 622-635
-
-
Morton, R.1
Wickwire, K.H.2
-
7
-
-
84974873238
-
Optimal control of some simple deterministic epidemic models
-
Sethi SP, Staats PW, Optimal control of some simple deterministic epidemic models, J Oper Res Soc 29:129-136, 1978.
-
(1978)
J Oper Res Soc
, vol.29
, pp. 129-136
-
-
Sethi, S.P.1
Staats, P.W.2
-
8
-
-
0017481192
-
Mathematical models for the control of pests and infectious disease: A survey
-
Wickwire KH, Mathematical models for the control of pests and infectious disease: A survey, Theor Pop Biology 11:182-238, 1977.
-
(1977)
Theor Pop Biology
, vol.11
, pp. 182-238
-
-
Wickwire, K.H.1
-
9
-
-
0034313015
-
Optimal control of deterministic epidemics
-
DOI 10.1002/oca.678
-
Behncke H, Optimal control of deterministic epidemics, Optim Control Appl Meth 21:269-285, 2000. (Pubitemid 32286502)
-
(2000)
Optimal Control Applications and Methods
, vol.21
, Issue.6
, pp. 269-285
-
-
Behncke, H.1
-
10
-
-
52049111883
-
Optimal control of vaccine distribution in a rabies metapopulation model
-
Asano E, Gross LJ, Lenhart S, Real LA, Optimal control of vaccine distribution in a rabies metapopulation model, Math Biosci Eng 5:219-238, 2008.
-
(2008)
Math Biosci Eng
, vol.5
, pp. 219-238
-
-
Asano, E.1
Gross, L.J.2
Lenhart, S.3
Real, L.A.4
-
11
-
-
0042762770
-
Optimal control of treatments in a two-strain tuberculosis model
-
Jung E, Lenhart S, Feng Z, Optimal control of treatments in a two-strain tuberculosis model, Discrete Contin Dyn Syst Ser B 2:473-482, 2002. (Pubitemid 37073318)
-
(2002)
Discrete and Continuous Dynamical Systems - Series B
, vol.2
, Issue.4
, pp. 473-482
-
-
Jung, E.1
Lenhart, S.2
Feng, Z.3
-
12
-
-
36348961306
-
Optimal control applied to biological models
-
Chapman & Hall/CRC, Boca Raton, FL
-
Lenhart S, Workman JT, Optimal control applied to biological models, Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, FL, 2007.
-
(2007)
Chapman & Hall/CRC Mathematical and Computational Biology Series
-
-
Lenhart, S.1
Workman, J.T.2
-
13
-
-
77952674174
-
Backward bifurcation and optimal control in transmission dynamics of West Nile Virus
-
Blayneh KW, Gumel AB, Lenhart S, Clayton T, Backward bifurcation and optimal control in transmission dynamics of West Nile Virus, Bull Math Biol 72:1006-1028, 2010.
-
(2010)
Bull Math Biol
, vol.72
, pp. 1006-1028
-
-
Blayneh, K.W.1
Gumel, A.B.2
Lenhart, S.3
Clayton, T.4
-
14
-
-
65549154257
-
Optimal control of tuberculosis with exogenous reinfection
-
Hattaf K, Rachik M, Saadi S, Tabit Y, Yousfi N, Optimal control of tuberculosis with exogenous reinfection, Appl Math Sci (Ruse) 3:231-240, 2009.
-
(2009)
Appl Math Sci (Ruse)
, vol.3
, pp. 231-240
-
-
Hattaf, K.1
Rachik, M.2
Saadi, S.3
Tabit, Y.4
Yousfi, N.5
-
15
-
-
68949184844
-
Optimal control strategy for prevention of avian influenza pandemic
-
Jung E, Iwami S, Takeuchi Y, Jo TC, Optimal control strategy for prevention of avian influenza pandemic, J Theor Biol 260:220-229, 2009.
-
(2009)
J Theor Biol
, vol.260
, pp. 220-229
-
-
Jung, E.1
Iwami, S.2
Takeuchi, Y.3
Jo, T.C.4
-
16
-
-
84872830053
-
-
Birkhauser, Boston
-
Anita S, Arnautu V, Capasso V, An Introduction to Optimal Control Problems in Life Sciences and Economics, Birkhauser, Boston, 2010.
-
(2010)
An Introduction to Optimal Control Problems in Life Sciences and Economics
-
-
Anita, S.1
Arnautu, V.2
Capasso, V.3
-
17
-
-
70349647743
-
Optimal control applied to vaccination and treatment strategies for various epidemiological models
-
Gaff H, Schaefer E, Optimal control applied to vaccination and treatment strategies for various epidemiological models, Math Biosci Eng 6:469-492, 2009.
-
(2009)
Math Biosci Eng
, vol.6
, pp. 469-492
-
-
Gaff, H.1
Schaefer, E.2
-
18
-
-
0003198862
-
Vertically, transmitted diseases. Models and dynamics
-
Springer, Berlin
-
Busenberg SN, Cooke K, Vertically, transmitted diseases. Models and dynamics, Biomathematics, Vol. 23, Springer, Berlin, 1993.
-
(1993)
Biomathematics
, vol.23
-
-
Busenberg, S.N.1
Cooke, K.2
-
19
-
-
18144413585
-
On pulse vaccination strategy in the SIR epidemic model with vertical transmission
-
DOI 10.1016/j.aml.2004.05.012, PII S0893965904003866
-
d'Onofrio A, On pulse vaccination strategy in the SIR epidemic model with vertical transmission, Appl Math Lett 18:729-732, 2005. (Pubitemid 40612586)
-
(2005)
Applied Mathematics Letters
, vol.18
, Issue.7
, pp. 729-732
-
-
D'Onofrio, A.1
-
20
-
-
0036222772
-
Global dynamics of an seir epidemic model with vertical transmission
-
PII S0036139999359860
-
Li MY, Smith HL, Wang L, Global dynamics of an SEIR epidemic model with vertical transmission, SIAM J Math Anal 62:58-69, 2001. (Pubitemid 33779898)
-
(2001)
SIAM Journal on Applied Mathematics
, vol.62
, Issue.1
, pp. 58-69
-
-
Li, M.Y.1
Smith, H.L.2
Wang, L.3
-
21
-
-
4644337889
-
Global stability in some SEIR epidemic models in Castillo-Chavez et al. (eds.) Mathematical Approaches for Emerging and Reemerging Infectious Diseases. Part II: Models methods and theory
-
Springer, Berlin
-
Li MY, Wang L, Global stability in some SEIR epidemic models, in Castillo-Chavez et al. (eds.), Mathematical Approaches for Emerging and Reemerging Infectious Diseases. Part II: Models, methods and theory. IMA Volumes in Mathematics and Its Applications, Vol. 126, Springer, Berlin, 295-311, 2002.
-
(2002)
IMA Volumes in Mathematics and Its Applications
, vol.126
, pp. 295-311
-
-
Li, M.Y.1
Wang, L.2
-
22
-
-
0037431579
-
Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious disease with periodic contact rates and disease-dependent demographic factors in the population
-
d'Onofrio A, Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious disease with periodic contact rates and disease-dependent demographic factors in the population, Appl Math Comput 140:537-547, 2003.
-
(2003)
Appl Math Comput
, vol.140
, pp. 537-547
-
-
D'Onofrio, A.1
-
23
-
-
79958207252
-
A simple analysis of vaccination strategies for rubella
-
Buonomo B, A simple analysis of vaccination strategies for rubella, Math Biosci Eng, 8: 677-687, 2001.
-
(2001)
Math Biosci Eng
, vol.8
, pp. 677-687
-
-
Buonomo, B.1
-
24
-
-
0003726932
-
An Introduction to the theory of competitive and cooperative systems
-
Monotone Dynamical Systems. American Mathematical Society, Providence, RI
-
Smith HL, Monotone Dynamical Systems. An Introduction to the theory of competitive and cooperative systems. Mathematical Surveys and Monographs, Vol. 41, American Mathematical Society, Providence, RI, 1995.
-
(1995)
Mathematical Surveys and Monographs
, vol.41
-
-
Smith, H.L.1
-
25
-
-
0036845274
-
Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
-
DOI 10.1016/S0025-5564(02)00108-6, PII S0025556402001086
-
van den Driessche P, Watmough J, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math Biosci 180:29-48, 2002. (Pubitemid 35304346)
-
(2002)
Mathematical Biosciences
, vol.180
, pp. 29-48
-
-
Van Den Driessche, P.1
Watmough, J.2
-
26
-
-
1042298863
-
Global results for an epidemic model with vaccination that exhibits backward bifurcation
-
Arino J, McCluskey CC, van den Driessche P, Global results for an epidemic model with vaccination that exhibits backward bifurcation, SIAM J Appl Math 64:260-276, 2003.
-
(2003)
SIAM J Appl Math
, vol.64
, pp. 260-276
-
-
Arino, J.1
McCluskey, C.C.2
Van Den Driessche, P.3
-
27
-
-
0030544879
-
A geometric approach to global-stability problems
-
Li MY, Muldowney JS, A geometric approach to global-stability problems, SIAM J Math Anal 27:1070-1083, 1996.
-
(1996)
SIAM J Math Anal
, vol.27
, pp. 1070-1083
-
-
Li, M.Y.1
Muldowney, J.S.2
-
28
-
-
50249100249
-
On the use of the geometric approach to global stability for three-dimensional ODE systems: A bilinear case
-
Buonomo B, Lacitignola D, On the use of the geometric approach to global stability for three-dimensional ODE systems: A bilinear case, J Math Anal Appl 348:255-266, 2008.
-
(2008)
J Math Anal Appl
, vol.348
, pp. 255-266
-
-
Buonomo, B.1
Lacitignola, D.2
-
29
-
-
77951691230
-
Optimal control methods applied to disease models
-
Contemp. Math., Amer. Math. Soc., Providence, RI
-
Joshi HR, Lenhart S, Li MY, Wang L, Optimal control methods applied to disease models, in: Mathematical Studies on Human Disease Dynamics, 187-207, Contemp. Math., Vol. 410, Amer. Math. Soc., Providence, RI, 2006.
-
(2006)
Mathematical Studies on Human Disease Dynamics
, vol.410
, pp. 187-207
-
-
Joshi, H.R.1
Lenhart, S.2
Li, M.Y.3
Wang, L.4
-
30
-
-
77950881784
-
Control of epidemics by quarantine and isolation strategies in highly mobile populations
-
Yan X, Zou Y, Control of epidemics by quarantine and isolation strategies in highly mobile populations, Int J Inform Sys Science 5:271-286, 2009.
-
(2009)
Int J Inform Sys Science
, vol.5
, pp. 271-286
-
-
Yan, X.1
Zou, Y.2
-
31
-
-
0036369855
-
Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks
-
DOI 10.1007/s002850100110
-
Billings L, Schwartz IB, Exciting chaos with noise: Unexpected dynamics in epidemic outbreaks, J Math Biol 44:31-48, 2002. (Pubitemid 44200140)
-
(2002)
Journal of Mathematical Biology
, vol.44
, Issue.1
, pp. 31-48
-
-
Billings, L.1
Schwartz, I.B.2
-
32
-
-
41149102542
-
Seasonal dynamics and thresholds governing recurrent epidemics
-
Olinky R, Huppert A, Stone L, Seasonal dynamics and thresholds governing recurrent epidemics, J Math Biol 56:827-839, 2008.
-
(2008)
J Math Biol
, vol.56
, pp. 827-839
-
-
Olinky, R.1
Huppert, A.2
Stone, L.3
-
33
-
-
27144554272
-
SIRS epidemic model and simulations using different types of seasonal contact rate
-
DOI 10.1080/023929021000008813, PII LW7HAJNM0JXD4UKD
-
Greenhalgh D, Moneim IA, SIRS epidemic model and simulations using different types of seasonal contact rate, Syst Anal Modelling Simul 43:573-600, 2003. (Pubitemid 44112309)
-
(2003)
Systems Analysis Modelling Simulation
, vol.43
, Issue.5
, pp. 573-600
-
-
Greenhalgh, D.1
Moneim, I.A.2
-
34
-
-
34548404314
-
The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study
-
DOI 10.1016/j.compbiomed.2007.02.007, PII S0010482507000376
-
Moneim IA, The effect of using different types of periodic contact rate on the behaviour of infectious diseases: A simulation study, Comp Biol Med 37:1582-1590, 2007. (Pubitemid 47362101)
-
(2007)
Computers in Biology and Medicine
, vol.37
, Issue.11
, pp. 1582-1590
-
-
Moneim, I.A.1
-
35
-
-
33847663496
-
Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate
-
Moneim IA, Greenhalgh D, Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate, Math Biosci Eng 2:599-611, 2005.
-
(2005)
Math Biosci Eng
, vol.2
, pp. 599-611
-
-
Moneim, I.A.1
Greenhalgh, D.2
-
36
-
-
19344365285
-
Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy
-
DOI 10.1142/S0218339005001446
-
Moneim IA, Greenhalgh D, Threshold and stability results for an SIRS epidemic model with a general periodic vaccination strategy, J Biol Syst 13:131-150, 2005. (Pubitemid 40717617)
-
(2005)
Journal of Biological Systems
, vol.13
, Issue.2
, pp. 131-150
-
-
Moneim, I.A.1
Greenhalgh, D.2
-
37
-
-
77952669726
-
A tuberculosis model with seasonality
-
Liu L, Zhao XQ, Zhou Y, A tuberculosis model with seasonality, Bull Math Biol 72:931-952, 2010.
-
(2010)
Bull Math Biol
, vol.72
, pp. 931-952
-
-
Liu, L.1
Zhao, X.Q.2
Zhou, Y.3
-
38
-
-
35648967095
-
On a nonautonomous SEIRS model in epidemiology
-
DOI 10.1007/s11538-007-9231-z
-
Zhang T, Teng Z, On a Nonautonomous SEIRS model in epidemiology, Bull Math Biol 69:2537-2559, 2007. (Pubitemid 350029419)
-
(2007)
Bulletin of Mathematical Biology
, vol.69
, Issue.8
, pp. 2537-2559
-
-
Zhang, T.1
Teng, Z.2
-
39
-
-
79960370612
-
-
MATLAB The Mathworks Inc., Natich, MA
-
MATLAB, Matlab release 12, The Mathworks Inc., Natich, MA, 2000.
-
(2000)
Matlab Release
, vol.12
-
-
-
40
-
-
33746870044
-
Simulations of rubella vaccination strategies in China
-
DOI 10.1016/j.jmmm.2005.07.010, PII S0025556406000320
-
Gao L, Hethcote H, Simulations of rubella vaccination strategies in China, Math Biosci 202:371-385, 2006. (Pubitemid 44188800)
-
(2006)
Mathematical Biosciences
, vol.202
, Issue.2
, pp. 371-385
-
-
Gao, L.1
Hethcote, H.2
-
41
-
-
0347663530
-
Seasonally forced disease dynamics explored as switching between attractors
-
DOI 10.1016/S0167-2789(00)00187-1, PII S0167278900001871
-
Keeling M, Rohani P, Greenfell BT, Seasonality forced disease dynamics explored as switching between attractors, Physica C 148:317-335, 2001. (Pubitemid 33651593)
-
(2001)
Physica D: Nonlinear Phenomena
, vol.148
, Issue.3-4
, pp. 317-335
-
-
Keeling, M.J.1
Rohani, P.2
Grenfell, B.T.3
-
42
-
-
0021690803
-
Seasonality and period-doubling bifurcations in an epidemic model
-
Aron JL, Schwartz IB, Seasonality and period-doubling bifurcation in an epidemic model, J Theor Biol 110:665-679, 1984. (Pubitemid 15185682)
-
(1984)
Journal of Theoretical Biology
, vol.110
, Issue.4
, pp. 665-679
-
-
Aron, J.L.1
Schwartz, I.B.2
-
43
-
-
34047120681
-
Seasonal dynamics of recurrent epidemics
-
DOI 10.1038/nature05638, PII NATURE05638
-
Stone L, Olinky R, Huppert A, Seasonal dynamics of recurrent epidemics, Nature 446:533-536, 2007. (Pubitemid 46514727)
-
(2007)
Nature
, vol.446
, Issue.7135
, pp. 533-536
-
-
Stone, L.1
Olinky, R.2
Huppert, A.3
-
44
-
-
0006835685
-
-
Wiley & Sons, Inc., New York-London
-
Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mishchenko EF, The Mathematical Theory of Optimal Processes, Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962.
-
(1962)
The Mathematical Theory of Optimal Processes, Interscience Publishers John
-
-
Pontryagin, L.S.1
Boltyanskii, V.G.2
Gamkrelidze, R.V.3
Mishchenko, E.F.4
|