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The Within-Host dynamics of malaria infection with immune response
1. | Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China |
2. | Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250 |
3. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 |
References:
[1] |
P. Adda, J. L. Dimi, A. Iggidr, J. C. Kamgang, G. Sallet and J. J. Tewa, General models of host-parasite systems. Global analysis, Dis. Contin. Dynam. Syst. Ser. B, 8 (2007), 1-17. |
[2] |
Z. Agur, D. Abiri and L. H. T. van der Ploeg, Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates, Proc. Natl. Acad. Sci. USA, 86 (1989), 9626-9630. |
[3] |
R. M. Anderson, Complex dynamic behaviors in the interaction between parasite populations and the host's immune system, Intl. J. Parasitol., 28 (1998), 551-566. |
[4] |
R. M. Anderson, R. M. May and S. Gupta, Non-linear phenomena in host-parasite interactions, Parasitology, 99 (1989), S59-S79. |
[5] |
R. Antia, B. R. Levin and R. M. May, Within-host population dynamics and the evolution and maintenance of microparasite virulence, Am. Nat., 144 (1994), 457-472. |
[6] |
A. D. Augustine, B. F. Hall, W. W. Leitner, A. X. Mo, T. M. Wali and A. S. Fauci, NIAID workshop on immunity to malaria: Addressing immunological challenges, Nature Immunol., 10 (2009), 673-678. |
[7] |
C. Chiyaka, W. Garira and S. Dube, Modelling immune response and drug therapy in human malaria infection, Comput. Math. Meth. Med., 9 (2008), 143-163. |
[8] |
C. Coban, K. J. Ishii, T. Horii and S. Akira, Manipulation of host innate immune responses by the malaria parasite, TRENDS Microbiol., 15 (2007), 271-278. |
[9] |
J. A. Deans and Cohen, Immunology of malaria, Annu. Rev. Microbiol., 37 (1983), 25-49. |
[10] |
R. J. De Boer and A. S. Perelson, Towards a general function describing T cell proliferation, J. Theoret. Biol., 175 (1995), 567-576. |
[11] |
Z. Dong and J.-A. Cui, Dynamical model of vivax malaria intermittence attack in vivo, Intl. J. Biomath., 2 (2009), 507-524. |
[12] |
M. F. Good, H. Xu, M. Wykes and C. R. Engwerda, Development and regulation of cell-mediated immune responses to the blood stages of malaria: Implications from vaccine research, Annu. Rev. Immunol., 23 (2005), 69-99. |
[13] |
M. B. Gravenor and A. L. Lloyd, Reply to: Models for the in-host dynamics of malaria revisited: Errors in some basic models lead to large overestimates of growth rates, Parasitology, 117 (1998), 409-410. |
[14] |
M. B. Gravenor, A. L. Lloyd, P. G. Kremsner, M. A. Missinou, M. English, K. Marsh and D. Kwiatkowski, A model for estimating total parasite load in falciparum malaria patients, J. Theoret. Biol., 217 (2002), 137-148. |
[15] |
M. B. Gravenor, M. B. Van Hensbroek and D. Kwiatkowski, Estimating sequestered parasite population dynamics in cerebral malaria, Proc. Natl. Acad. Sci. USA, 95 (1998), 7620-7624. |
[16] |
C. Hetzel and R. M. Anderson, The within-host cellular dynamics of bloodstage malaria-theoretical and experimental studies, Parasitology, 113 (1996), 25-38. |
[17] |
M. B. Hoshen, R. Heinrich, W. D. Stein and H. Ginsburg, Mathematical modeling of the within-host dynamics of Plasmodium falciparum, Parasitology, 121 (2000), 227-235. |
[18] |
A. Iggidr, J.-C. Kamgang, G. Sallet and J.-J. Tewa, Global analysis of new malaria intrahost models with a competitive exclusion principle, SIAM J. Appl. Math., 67 (2006), 260-278. |
[19] |
T. Kajiwara and T. Sasaki, A note on the stability analysis of pathogen-immune interaction dynamics, Discret. Contin. Dynam. Syst. Ser. B, 4 (2004), 615-622. |
[20] |
D. Kwiatkowsti and M. Nowak, Periodic and chaotic host-parasite interactions in human malaria, Proc. Natl. Acad. Sci. USA, 88 (1991), 5111-5113. |
[21] |
J. Langhorne, F. M. Ndungu, A.-M. Sponaas and K. Marsh, Immunity to malaria: More questions than answers, Nature Immunol., 9 (2008), 725-732. |
[22] |
W. Liu, Nonlinear oscillation in models of immune responses to persistent viruses, Theoret. Pop. Biol., 52 (1997), 224-230. |
[23] |
L. Malaguarnera and S. Musumeci, The immune response to Plasmodium falciparum malaria, Lancet Infect. Dis., 2 (2002), 472-478. |
[24] |
G. L. Mandell, J. E. Bennett and R. Dolin, "Principles and Practice of Infectious Diseases,'' Churchill Livingstone, New York, 1995. |
[25] |
F. E. McKenzie and H. W. Bossert, An integrated model of Plasmodium falciparum dynamics, J. Theoret. Biol., 232 (2005), 411-426. |
[26] |
P. G. McQueen and F. E. McKenzie, Age-structured red blood cell susceptibility and the dynamics of malaria infections, Proc. Natl. Acad. Sci. USA, 101 (2004), 9161-9166. |
[27] |
P. G. McQueen and F. E. McKenzie, Host control of malaria infections: Constrains on immune and erythropoeitic response kinetics, PLoS Comput. Biol., 4 (2008), 15 pp.
doi: 10.1371/journal.pcbi.1000149. |
[28] |
J. L. Mitchell and T. W. Carr, Oscillations in an intra-host model of plasmodium falciparum malaria due to cross-reactive immune response, Bull. Math. Biol., 72 (2010), 590-610. |
[29] |
L. Molineaux and K. Dietz, Review of intra-host models of malaria, Parassitologia, 41 (1999), 221-231. |
[30] |
A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247-267. |
[31] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Nature, 272 (1996), 74-79. |
[32] |
S. S. Pilyugin and R. Antia, Modeling immune responses with handling time, Bull. Math. Biol., 62 (2000), 869-890. |
[33] |
S. I. Rapaport, "Introduction to Hematology,'' Lippincott, Philadelphia, 1987. |
[34] |
I. M. Rouzine and F. E. McKenzie, Link between immune response and parasite synchronization in malaria, Proc. Natl. Acad. Sci. USA, 100 (2003), 3473-3478. |
[35] |
S. Ruan and G. S. K. Wolkowicz, Bifurcation analysis of a chemostat model with a distributed delay, J. Math. Anal. Appl., 204 (1996), 786-812. |
[36] |
A. Saul, Models for the in-host dynamics of malaria revisited: Errors in some basic models lead to large over-estimates of growth rates, Parasitology, 117 (1998), 405-407. |
[37] |
J. Stark, C. Chan and A. J. T. George, Oscillations in immune system, Immunol. Rev., 216 (2007), 213-231. |
[38] |
M. M. Stevenson and E. M. Riley, Innate immunity to malaria, Nat. Rev. Immunol., 4 (2004), 169-180. |
[39] |
Y. Su, S. Ruan and J. Wei, Periodicity and synchronization in blood-stage malaria infection, J. Math. Biol., 63 (2011), 557-574.
doi: 10.1007/s00285-010-0381-5. |
[40] |
J. Tumwiine, J. Y. T. Mugisha and L. S. Luboobi, On global stability of the intra-host dynamics of malaria and the immune system, J. Math. Anal. Appl., 341 (2008), 855-869. |
[41] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. |
[42] |
, WHO, "Malaria,", 2008. Available from: \url{http://www.who.int/malaria/en}., (2008).
|
[43] |
D. Xiao and H. W. Bossert, An intra-host mathematical model on interaction between HIV and malaria, Bull. Math. Biol., 72 (2010), 1892-1911.
doi: p10.1007/s11538-010-9515-6. |
show all references
References:
[1] |
P. Adda, J. L. Dimi, A. Iggidr, J. C. Kamgang, G. Sallet and J. J. Tewa, General models of host-parasite systems. Global analysis, Dis. Contin. Dynam. Syst. Ser. B, 8 (2007), 1-17. |
[2] |
Z. Agur, D. Abiri and L. H. T. van der Ploeg, Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates, Proc. Natl. Acad. Sci. USA, 86 (1989), 9626-9630. |
[3] |
R. M. Anderson, Complex dynamic behaviors in the interaction between parasite populations and the host's immune system, Intl. J. Parasitol., 28 (1998), 551-566. |
[4] |
R. M. Anderson, R. M. May and S. Gupta, Non-linear phenomena in host-parasite interactions, Parasitology, 99 (1989), S59-S79. |
[5] |
R. Antia, B. R. Levin and R. M. May, Within-host population dynamics and the evolution and maintenance of microparasite virulence, Am. Nat., 144 (1994), 457-472. |
[6] |
A. D. Augustine, B. F. Hall, W. W. Leitner, A. X. Mo, T. M. Wali and A. S. Fauci, NIAID workshop on immunity to malaria: Addressing immunological challenges, Nature Immunol., 10 (2009), 673-678. |
[7] |
C. Chiyaka, W. Garira and S. Dube, Modelling immune response and drug therapy in human malaria infection, Comput. Math. Meth. Med., 9 (2008), 143-163. |
[8] |
C. Coban, K. J. Ishii, T. Horii and S. Akira, Manipulation of host innate immune responses by the malaria parasite, TRENDS Microbiol., 15 (2007), 271-278. |
[9] |
J. A. Deans and Cohen, Immunology of malaria, Annu. Rev. Microbiol., 37 (1983), 25-49. |
[10] |
R. J. De Boer and A. S. Perelson, Towards a general function describing T cell proliferation, J. Theoret. Biol., 175 (1995), 567-576. |
[11] |
Z. Dong and J.-A. Cui, Dynamical model of vivax malaria intermittence attack in vivo, Intl. J. Biomath., 2 (2009), 507-524. |
[12] |
M. F. Good, H. Xu, M. Wykes and C. R. Engwerda, Development and regulation of cell-mediated immune responses to the blood stages of malaria: Implications from vaccine research, Annu. Rev. Immunol., 23 (2005), 69-99. |
[13] |
M. B. Gravenor and A. L. Lloyd, Reply to: Models for the in-host dynamics of malaria revisited: Errors in some basic models lead to large overestimates of growth rates, Parasitology, 117 (1998), 409-410. |
[14] |
M. B. Gravenor, A. L. Lloyd, P. G. Kremsner, M. A. Missinou, M. English, K. Marsh and D. Kwiatkowski, A model for estimating total parasite load in falciparum malaria patients, J. Theoret. Biol., 217 (2002), 137-148. |
[15] |
M. B. Gravenor, M. B. Van Hensbroek and D. Kwiatkowski, Estimating sequestered parasite population dynamics in cerebral malaria, Proc. Natl. Acad. Sci. USA, 95 (1998), 7620-7624. |
[16] |
C. Hetzel and R. M. Anderson, The within-host cellular dynamics of bloodstage malaria-theoretical and experimental studies, Parasitology, 113 (1996), 25-38. |
[17] |
M. B. Hoshen, R. Heinrich, W. D. Stein and H. Ginsburg, Mathematical modeling of the within-host dynamics of Plasmodium falciparum, Parasitology, 121 (2000), 227-235. |
[18] |
A. Iggidr, J.-C. Kamgang, G. Sallet and J.-J. Tewa, Global analysis of new malaria intrahost models with a competitive exclusion principle, SIAM J. Appl. Math., 67 (2006), 260-278. |
[19] |
T. Kajiwara and T. Sasaki, A note on the stability analysis of pathogen-immune interaction dynamics, Discret. Contin. Dynam. Syst. Ser. B, 4 (2004), 615-622. |
[20] |
D. Kwiatkowsti and M. Nowak, Periodic and chaotic host-parasite interactions in human malaria, Proc. Natl. Acad. Sci. USA, 88 (1991), 5111-5113. |
[21] |
J. Langhorne, F. M. Ndungu, A.-M. Sponaas and K. Marsh, Immunity to malaria: More questions than answers, Nature Immunol., 9 (2008), 725-732. |
[22] |
W. Liu, Nonlinear oscillation in models of immune responses to persistent viruses, Theoret. Pop. Biol., 52 (1997), 224-230. |
[23] |
L. Malaguarnera and S. Musumeci, The immune response to Plasmodium falciparum malaria, Lancet Infect. Dis., 2 (2002), 472-478. |
[24] |
G. L. Mandell, J. E. Bennett and R. Dolin, "Principles and Practice of Infectious Diseases,'' Churchill Livingstone, New York, 1995. |
[25] |
F. E. McKenzie and H. W. Bossert, An integrated model of Plasmodium falciparum dynamics, J. Theoret. Biol., 232 (2005), 411-426. |
[26] |
P. G. McQueen and F. E. McKenzie, Age-structured red blood cell susceptibility and the dynamics of malaria infections, Proc. Natl. Acad. Sci. USA, 101 (2004), 9161-9166. |
[27] |
P. G. McQueen and F. E. McKenzie, Host control of malaria infections: Constrains on immune and erythropoeitic response kinetics, PLoS Comput. Biol., 4 (2008), 15 pp.
doi: 10.1371/journal.pcbi.1000149. |
[28] |
J. L. Mitchell and T. W. Carr, Oscillations in an intra-host model of plasmodium falciparum malaria due to cross-reactive immune response, Bull. Math. Biol., 72 (2010), 590-610. |
[29] |
L. Molineaux and K. Dietz, Review of intra-host models of malaria, Parassitologia, 41 (1999), 221-231. |
[30] |
A. Murase, T. Sasaki and T. Kajiwara, Stability analysis of pathogen-immune interaction dynamics, J. Math. Biol., 51 (2005), 247-267. |
[31] |
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent viruses, Nature, 272 (1996), 74-79. |
[32] |
S. S. Pilyugin and R. Antia, Modeling immune responses with handling time, Bull. Math. Biol., 62 (2000), 869-890. |
[33] |
S. I. Rapaport, "Introduction to Hematology,'' Lippincott, Philadelphia, 1987. |
[34] |
I. M. Rouzine and F. E. McKenzie, Link between immune response and parasite synchronization in malaria, Proc. Natl. Acad. Sci. USA, 100 (2003), 3473-3478. |
[35] |
S. Ruan and G. S. K. Wolkowicz, Bifurcation analysis of a chemostat model with a distributed delay, J. Math. Anal. Appl., 204 (1996), 786-812. |
[36] |
A. Saul, Models for the in-host dynamics of malaria revisited: Errors in some basic models lead to large over-estimates of growth rates, Parasitology, 117 (1998), 405-407. |
[37] |
J. Stark, C. Chan and A. J. T. George, Oscillations in immune system, Immunol. Rev., 216 (2007), 213-231. |
[38] |
M. M. Stevenson and E. M. Riley, Innate immunity to malaria, Nat. Rev. Immunol., 4 (2004), 169-180. |
[39] |
Y. Su, S. Ruan and J. Wei, Periodicity and synchronization in blood-stage malaria infection, J. Math. Biol., 63 (2011), 557-574.
doi: 10.1007/s00285-010-0381-5. |
[40] |
J. Tumwiine, J. Y. T. Mugisha and L. S. Luboobi, On global stability of the intra-host dynamics of malaria and the immune system, J. Math. Anal. Appl., 341 (2008), 855-869. |
[41] |
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. |
[42] |
, WHO, "Malaria,", 2008. Available from: \url{http://www.who.int/malaria/en}., (2008).
|
[43] |
D. Xiao and H. W. Bossert, An intra-host mathematical model on interaction between HIV and malaria, Bull. Math. Biol., 72 (2010), 1892-1911.
doi: p10.1007/s11538-010-9515-6. |
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