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A mathematical model for within-host Toxoplasma gondii invasion dynamics
1. | Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, Knoxville, TN 37996, United States, United States |
2. | Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, United States |
3. | National Institute of Mathematical and Biological Synthesis, University of Tennessee, Knoxville, TN 37996, United States |
4. | Department of Microbiology, University of Tennessee, Knoxville, TN 37996, United States |
5. | Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 |
References:
[1] |
Centers for Disease Control and Prevention, Toxoplasmosis, November 2010., Available from: , ().
|
[2] |
F. B. Agusto and A. B. Gumel, Theoretical assessment of avian influenza vaccine, DCDS Series B, 13 (2010), 1-25. |
[3] |
F. B. Agusto and O. R. Ogunye, Avian Influenza optimal seasonal vaccination strategy, ANZIAM Journal, 51 (2010), 394-405. |
[4] |
R. M. Anderson and R. May, "Infectious Diseases of Humans," Oxford University Press, New York, 1991. |
[5] |
A. J. Arenas, G. Gonzalez-Parra and R. V. Mico, Modeling toxoplasmosis spread in cat populations under vaccination, Theoretical Population Biology, 77 (2010), 227-237. |
[6] |
F. Brauer and C. Castillo-Ch\'avez, "Mathematical Models in Population Biology and Epidemiology," Texts in Applied Mathematics, 40, Springer, New York, 2001. |
[7] |
F. Brauer and P. van den Driessche, Models for transmission of disease with immigration of infectives, Math. Biosc., 171 (2001), 143-154.
doi: 10.1016/S0025-5564(01)00057-8. |
[8] |
L. Chen, F. Chen and L. Chen, Analysis of a predator-prey model with holling type II functional response incorporating a constant prey refuge, Nonlinear Analysis: Real World Applications, 11 (2010), 246-252.
doi: 10.1016/j.nonrwa.2009.06.016. |
[9] |
M. da Fonseca, F. da Silva, A. C. Tak\'acs, H. S. Barbosa, U. Gross and C. G L\"uder, Primary skeletal muscle cells trigger spontaneous toxoplasma gondiitachyzoite-to-bradyzoite conversion at higher rates than fibroblasts, International Journal of Medical Microbiology, 299 (2009), 381-388.
doi: 10.1016/j.ijmm.2008.10.002. |
[10] |
R. C. da Silva, A. V. da Silva and H. Langoni, Recrudescence of Toxoplasma gondii infection in chronically infectedrats (Rattus norvegicus), Experimental Parasitology, 125 (2010), 409-412.
doi: 10.1016/j.exppara.2010.04.003. |
[11] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. |
[12] |
J. P. Dubey, D. S. Lindsay and C. A. Speer, Structures of toxoplasma gondii tachyzoites, bradyzoites, andsporozoites and biology and development of tissue cysts, Clin. Microbiol. Rev., 11 (1998), 267-299. |
[13] |
J. P. Dubey, "Toxoplasmosis of Animals and Humans," CRC Press, 2010. |
[14] |
L. Esteva, A. B. Gumel and C. V. de León, Qualitative study of transmission dynamics of drug-resistant malaria, J. Mathematical and Computer Modelling, 50 (2009), 611-630.
doi: 10.1016/j.mcm.2009.02.012. |
[15] |
D. J. Ferguson, Toxoplasma gondii andsex: Essential or optional extra?, Trends Parasitol., 18 (2002), 355-359.
doi: 10.1016/S1471-4922(02)02281-X. |
[16] |
D. Filisetti and E. Candolfi, Immuneresponse to toxoplasma gondii, Ann Ist Super Sanita, 40 (2004), 71-80. |
[17] |
S. M. Garba and A. B. Gumel, Effects of cross-immunity on the transmission dynamics of two strains of dengue, International Journal of Computer Mathematics, 87 (2010), 2361-2384.
doi: 10.1080/00207160802660608. |
[18] |
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Mathematical Biosciences, 215 (2008), 11-25.
doi: 10.1016/j.mbs.2008.05.002. |
[19] |
G. C. Gonzalez-Parra, A. J. Arenas, D. F. Aranda, R. J. Villanueva, L. Jódar, Dynamics of a model of Toxoplasmosis disease in human and cat populations, Computers and Mathematics with Applications, 57 (2009), 1692-1700.
doi: 10.1016/j.camwa.2008.09.012. |
[20] |
A. B. Gumel, Global dynamics of atwo-strain avian influenza model, International Journal of Computer Mathematics, 86 (2009), 85-108.
doi: 10.1080/00207160701769625. |
[21] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[22] |
C. Jeffries, V. Klee And P. van den Driessche, When is a matrix sign stable?, Can. J. Math., (1977) 29, 315-326. |
[23] |
M. E. Jerome, J. R. Radke, W. Bohne, D. S. Roos and M. W. White, Toxoplasma gondii bradyzoites form spontaneously during sporozoite-initiated development, Infection and Immunity, 66 (1998), 4838-4844. |
[24] |
W. Jiang, A. Sullivan, C. Su and X. Zhao, An agent-based model for the transmission dynamics of toxoplasma gondii, Journal of Theoretical Biology, 293 (2012), 15-26.
doi: 10.1016/j.jtbi.2011.10.006. |
[25] |
M. Lélu, M. Langlais, M.-L. Poulle and E. Gilot-Fromont, Transmission dynamics of toxoplasma gondii along an urban-rural gradient, Theoretical Population Biology, (2010), 139-147. |
[26] |
B. Kafsack, V. B. Carruthers and F. J. Pineda, Kinetic modeling of toxoplasma gondii invasion, Journal of Theoretical Biology, 249 (2007), 817-825.
doi: 10.1016/j.jtbi.2007.09.008. |
[27] |
M. J. Keeling and P. Rohani, "Modeling Infectious Diseases in Humans and Animals," Princeton University Press, Princeton, NJ, 2008. |
[28] |
M. Kot, "Elements of Mathematical Ecology," Cambridge University Press, 2003. |
[29] |
S. Leela, V. Lakshmikantham and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Monographs and Textbooks in Pure and Applied Mathematics, 125, Marcel Dekker, Inc., New York, 1989. |
[30] |
J. D. Murray, "Mathematical Biology. I. An Introduction," Third edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2002. |
[31] |
M. A. Nowak and R. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology," Oxford University Press, Oxford, 2000. |
[32] |
J. R. Radke, R. G. Donald, A. Eibs, M. E. Jerome, M. S. Behnke, P. Liberator and W. W. White, Changes in the expression of the human cell division autoantigen-1 influence toxoplasma gondii growth and development, PLoS Pathog., 2 (2006), 105. |
[33] |
Z. Qiu, J. Yu and Y. Zou, The asymptotic behaviour of a chemostat model, Discr. Cont. Dynam. Syst. Ser. B, 4 (2004), 721-727. |
[34] |
O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment, Mathematical Biosciences and Engineering, 5 (2008), 145-174. |
[35] |
O. Sharomi and A. B. Gumel, Re-infection-induced backward bifurcation in the transmission dynamics of Chlamydia trachomatis, Journal of Mathematical Analysis and Applications, 356 (2009), 96-18.
doi: 10.1016/j.jmaa.2009.02.032. |
[36] |
G. Skalski and J. Gilliam, Functional responses with predator interference: Viable alternatives to the holling type II model, Ecology, 82 (2001), 3083-3092. |
[37] |
H. L. Smith and P. Waltman, "The Theory of the Chemostat. Dynamics of Microbial Competition," Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995. |
[38] |
M. Turner, S. Lenhart, B. Rosenthal, A. Sullivan and X. Zhao, Modeling effective transmission strategies and control of the world's most successful parasite,, submitted., ().
|
[39] |
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.
doi: 10.1016/S0025-5564(02)00108-6. |
[40] |
L. Weiss and K. Kim, "Toxoplasma Gondii," Academic Press, 2007. |
[41] |
D. Wodnarz, "Killer Cell Dynamics. Mathematical and Computational Approaches to Immunology," Springer-Verlag, New York, 2007. |
show all references
References:
[1] |
Centers for Disease Control and Prevention, Toxoplasmosis, November 2010., Available from: , ().
|
[2] |
F. B. Agusto and A. B. Gumel, Theoretical assessment of avian influenza vaccine, DCDS Series B, 13 (2010), 1-25. |
[3] |
F. B. Agusto and O. R. Ogunye, Avian Influenza optimal seasonal vaccination strategy, ANZIAM Journal, 51 (2010), 394-405. |
[4] |
R. M. Anderson and R. May, "Infectious Diseases of Humans," Oxford University Press, New York, 1991. |
[5] |
A. J. Arenas, G. Gonzalez-Parra and R. V. Mico, Modeling toxoplasmosis spread in cat populations under vaccination, Theoretical Population Biology, 77 (2010), 227-237. |
[6] |
F. Brauer and C. Castillo-Ch\'avez, "Mathematical Models in Population Biology and Epidemiology," Texts in Applied Mathematics, 40, Springer, New York, 2001. |
[7] |
F. Brauer and P. van den Driessche, Models for transmission of disease with immigration of infectives, Math. Biosc., 171 (2001), 143-154.
doi: 10.1016/S0025-5564(01)00057-8. |
[8] |
L. Chen, F. Chen and L. Chen, Analysis of a predator-prey model with holling type II functional response incorporating a constant prey refuge, Nonlinear Analysis: Real World Applications, 11 (2010), 246-252.
doi: 10.1016/j.nonrwa.2009.06.016. |
[9] |
M. da Fonseca, F. da Silva, A. C. Tak\'acs, H. S. Barbosa, U. Gross and C. G L\"uder, Primary skeletal muscle cells trigger spontaneous toxoplasma gondiitachyzoite-to-bradyzoite conversion at higher rates than fibroblasts, International Journal of Medical Microbiology, 299 (2009), 381-388.
doi: 10.1016/j.ijmm.2008.10.002. |
[10] |
R. C. da Silva, A. V. da Silva and H. Langoni, Recrudescence of Toxoplasma gondii infection in chronically infectedrats (Rattus norvegicus), Experimental Parasitology, 125 (2010), 409-412.
doi: 10.1016/j.exppara.2010.04.003. |
[11] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. |
[12] |
J. P. Dubey, D. S. Lindsay and C. A. Speer, Structures of toxoplasma gondii tachyzoites, bradyzoites, andsporozoites and biology and development of tissue cysts, Clin. Microbiol. Rev., 11 (1998), 267-299. |
[13] |
J. P. Dubey, "Toxoplasmosis of Animals and Humans," CRC Press, 2010. |
[14] |
L. Esteva, A. B. Gumel and C. V. de León, Qualitative study of transmission dynamics of drug-resistant malaria, J. Mathematical and Computer Modelling, 50 (2009), 611-630.
doi: 10.1016/j.mcm.2009.02.012. |
[15] |
D. J. Ferguson, Toxoplasma gondii andsex: Essential or optional extra?, Trends Parasitol., 18 (2002), 355-359.
doi: 10.1016/S1471-4922(02)02281-X. |
[16] |
D. Filisetti and E. Candolfi, Immuneresponse to toxoplasma gondii, Ann Ist Super Sanita, 40 (2004), 71-80. |
[17] |
S. M. Garba and A. B. Gumel, Effects of cross-immunity on the transmission dynamics of two strains of dengue, International Journal of Computer Mathematics, 87 (2010), 2361-2384.
doi: 10.1080/00207160802660608. |
[18] |
S. M. Garba, A. B. Gumel and M. R. Abu Bakar, Backward bifurcations in dengue transmission dynamics, Mathematical Biosciences, 215 (2008), 11-25.
doi: 10.1016/j.mbs.2008.05.002. |
[19] |
G. C. Gonzalez-Parra, A. J. Arenas, D. F. Aranda, R. J. Villanueva, L. Jódar, Dynamics of a model of Toxoplasmosis disease in human and cat populations, Computers and Mathematics with Applications, 57 (2009), 1692-1700.
doi: 10.1016/j.camwa.2008.09.012. |
[20] |
A. B. Gumel, Global dynamics of atwo-strain avian influenza model, International Journal of Computer Mathematics, 86 (2009), 85-108.
doi: 10.1080/00207160701769625. |
[21] |
H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[22] |
C. Jeffries, V. Klee And P. van den Driessche, When is a matrix sign stable?, Can. J. Math., (1977) 29, 315-326. |
[23] |
M. E. Jerome, J. R. Radke, W. Bohne, D. S. Roos and M. W. White, Toxoplasma gondii bradyzoites form spontaneously during sporozoite-initiated development, Infection and Immunity, 66 (1998), 4838-4844. |
[24] |
W. Jiang, A. Sullivan, C. Su and X. Zhao, An agent-based model for the transmission dynamics of toxoplasma gondii, Journal of Theoretical Biology, 293 (2012), 15-26.
doi: 10.1016/j.jtbi.2011.10.006. |
[25] |
M. Lélu, M. Langlais, M.-L. Poulle and E. Gilot-Fromont, Transmission dynamics of toxoplasma gondii along an urban-rural gradient, Theoretical Population Biology, (2010), 139-147. |
[26] |
B. Kafsack, V. B. Carruthers and F. J. Pineda, Kinetic modeling of toxoplasma gondii invasion, Journal of Theoretical Biology, 249 (2007), 817-825.
doi: 10.1016/j.jtbi.2007.09.008. |
[27] |
M. J. Keeling and P. Rohani, "Modeling Infectious Diseases in Humans and Animals," Princeton University Press, Princeton, NJ, 2008. |
[28] |
M. Kot, "Elements of Mathematical Ecology," Cambridge University Press, 2003. |
[29] |
S. Leela, V. Lakshmikantham and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Monographs and Textbooks in Pure and Applied Mathematics, 125, Marcel Dekker, Inc., New York, 1989. |
[30] |
J. D. Murray, "Mathematical Biology. I. An Introduction," Third edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2002. |
[31] |
M. A. Nowak and R. May, "Virus Dynamics: Mathematical Principles of Immunology and Virology," Oxford University Press, Oxford, 2000. |
[32] |
J. R. Radke, R. G. Donald, A. Eibs, M. E. Jerome, M. S. Behnke, P. Liberator and W. W. White, Changes in the expression of the human cell division autoantigen-1 influence toxoplasma gondii growth and development, PLoS Pathog., 2 (2006), 105. |
[33] |
Z. Qiu, J. Yu and Y. Zou, The asymptotic behaviour of a chemostat model, Discr. Cont. Dynam. Syst. Ser. B, 4 (2004), 721-727. |
[34] |
O. Sharomi, C. N. Podder, A. B. Gumel and B. Song, Mathematical analysis of the transmission dynamics of HIV/TB co-infection in the presence of treatment, Mathematical Biosciences and Engineering, 5 (2008), 145-174. |
[35] |
O. Sharomi and A. B. Gumel, Re-infection-induced backward bifurcation in the transmission dynamics of Chlamydia trachomatis, Journal of Mathematical Analysis and Applications, 356 (2009), 96-18.
doi: 10.1016/j.jmaa.2009.02.032. |
[36] |
G. Skalski and J. Gilliam, Functional responses with predator interference: Viable alternatives to the holling type II model, Ecology, 82 (2001), 3083-3092. |
[37] |
H. L. Smith and P. Waltman, "The Theory of the Chemostat. Dynamics of Microbial Competition," Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995. |
[38] |
M. Turner, S. Lenhart, B. Rosenthal, A. Sullivan and X. Zhao, Modeling effective transmission strategies and control of the world's most successful parasite,, submitted., ().
|
[39] |
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.
doi: 10.1016/S0025-5564(02)00108-6. |
[40] |
L. Weiss and K. Kim, "Toxoplasma Gondii," Academic Press, 2007. |
[41] |
D. Wodnarz, "Killer Cell Dynamics. Mathematical and Computational Approaches to Immunology," Springer-Verlag, New York, 2007. |
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