American Institute of Mathematical Sciences

Advanced
2010, 7(4): 765-777. doi: 10.3934/mbe.2010.7.765

A model of varicella-zoster reactivation

Jonathan E. Forde 1, and  Bailey Meeker 2,

1. 

Department of Mathematics and Computer Science, Hobart and William Smith Colleges, Geneva, NY 14456, United States
2. 

Department of Mathematics, University of California, Davis, CA 95616, United States

Received  January 2010 Revised  August 2010 Published  October 2010

Mathematical models have been used to study the dynamic interaction of many infectious diseases with the host's immune system. In this paper, we study Varicella Zoster Virus, which is responsible for chicken pox (varicella), and after a long period of latency, herpes zoster (shingles). After developing the model and demonstrating that is exhibits the type of periodic behavior necessary for long term latency and reactivation, we examine the implications of the model for vaccine booster programs aimed at preventing herpes zoster.
Keywords: mathematical model., periodic solutions, latency, vaccine booster, VZV, chronic infection.
Mathematics Subject Classification: Primary: 92C99; Secondary: 34C25, 34C2.
Citation: Jonathan E. Forde, Bailey Meeker. A model of varicella-zoster reactivation. Mathematical Biosciences & Engineering, 2010, 7 (4) : 765-777. doi: 10.3934/mbe.2010.7.765
References:
[1]

A. Abendroth and A. M. Arvin, Immune evasion as a pathogenic mechanism of varicella zoster virus, Seminars in Immunology, 13 (2001), 27-39. doi: doi:10.1006/smim.2001.0293.

[2]

Centers for Disease Control and Prevention, Prevention of varicella: Updated recommendations of the Advisory Committee on Immunization Practices (ACIP), Morbidity and Mortality Weekly Report, 48, 1999.

[3]

Centers for Disease Control and Prevention, Prevention of herpes zoster, Morbidity and Mortality Weekly Report, 57, 2008.

[4]

J. I. Cohen, S. E. Straus and A. M. Arvin, Varicella-zoster virus replication, pathogenesis and management, in "Field's Virology" (eds. D. M. Knipe and P. M. Howley), Wolters Kluwer Health/Lippincott Williams and Wilkins, (2007), 2773-2818.

[5]

D. H. Gilden, R. J. Cohrs and R. Mahalingam, Clinical and molecular pathogenesis of varicella virus infection, Viral Immunology, 16 (2003), 243-258.

[6]

R. E. Hope-Simpson, The nature of herpes zoster: A long-term study and a new hypothesis, Proc. R. Soc. Med., 58 (1965), 9-20.

[7]

R. E. Hope-Simpson, Post-herpetic neuralgia, Journal of the Royal College of General Practitioners, 25 (1975), 571-575.

[8]

M. J. Levin, D Barber, E. Goldblatt, M. Jones, B. LaFleur, C. Chan, D. Stinson, G. O. Zerbe and A. R. Hayward, Use of a live attenuated varicella vaccine to boost varicella-specific immune responses in seropositive people 55 years of age or older: Duration of booster effect, The Journal of Infectious Diseases, 178 (suppl. 1) (1998), S109-S112.

[9]

M. J. Levin, J. G. Smith, R. M. Kaufhold, D. Barber, A. R. Hayward, C. Y. Chan, I. S. F. Chan, D. J. J. Li, W. Wang, P. M. Keller, A. Shaw, J. L. Silber, K. Schlienger, I. Chalikonda, S. J. R. Vessey and M. J. Caulfield, Decline of varicella zoster virus (VZV)-specific cell mediated immunity with increasing age and boosting with a high-dose VZV vaccine, The Journal of Infectious Diseases, 188 (2003), 1336-1344.

[10]

M. Reichelt, L. Zerboni and A.M. Arvin, Mechansisms of varicella-zoster virus neuropathogenesis in human dorsal root ganglia, Journal of Virology, 82 (2008), 3971-3983. doi: doi:10.1128/JVI.02592-07.

[11]

K. E. Schmader and R. H. Dworkin, Natural history and treatment of herpes zoster, The Journal of Pain, 9 (suppl. 1) (2008), 53-59. doi: doi:10.1016/j.jpain.2007.10.002.

[12]

S. L. Thomas, J. G. Wheeler and A. J. Hall, Contacts with varicella or with children and protection against herpes zoster in adults: A case-control study, The Lancet, 360 (2002), 678-682.

[13]

J. M. Weinberg., Herpes zoster: Epidemiology, natural history and common complications, Journal of the American Academy of Dermatology, 57 (2007), S130-S135. doi: doi:10.1016/j.jaad.2007.08.046.

[14]

A. Wilson, M. Sharp, C. M. Koropchak, S. F. Ting and A. M. Arvin, Subclinical varicella-zoster virus viremia, herpes zoster, and T lymphocyte immunity to varicella-zoster viral antigens after bone marrow transplants, Journal of Infectious Diseases, 165 (1992), 119-126.

show all references

References:
[1]

A. Abendroth and A. M. Arvin, Immune evasion as a pathogenic mechanism of varicella zoster virus, Seminars in Immunology, 13 (2001), 27-39. doi: doi:10.1006/smim.2001.0293.

[2]

Centers for Disease Control and Prevention, Prevention of varicella: Updated recommendations of the Advisory Committee on Immunization Practices (ACIP), Morbidity and Mortality Weekly Report, 48, 1999.

[3]

Centers for Disease Control and Prevention, Prevention of herpes zoster, Morbidity and Mortality Weekly Report, 57, 2008.

[4]

J. I. Cohen, S. E. Straus and A. M. Arvin, Varicella-zoster virus replication, pathogenesis and management, in "Field's Virology" (eds. D. M. Knipe and P. M. Howley), Wolters Kluwer Health/Lippincott Williams and Wilkins, (2007), 2773-2818.

[5]

D. H. Gilden, R. J. Cohrs and R. Mahalingam, Clinical and molecular pathogenesis of varicella virus infection, Viral Immunology, 16 (2003), 243-258.

[6]

R. E. Hope-Simpson, The nature of herpes zoster: A long-term study and a new hypothesis, Proc. R. Soc. Med., 58 (1965), 9-20.

[7]

R. E. Hope-Simpson, Post-herpetic neuralgia, Journal of the Royal College of General Practitioners, 25 (1975), 571-575.

[8]

M. J. Levin, D Barber, E. Goldblatt, M. Jones, B. LaFleur, C. Chan, D. Stinson, G. O. Zerbe and A. R. Hayward, Use of a live attenuated varicella vaccine to boost varicella-specific immune responses in seropositive people 55 years of age or older: Duration of booster effect, The Journal of Infectious Diseases, 178 (suppl. 1) (1998), S109-S112.

[9]

M. J. Levin, J. G. Smith, R. M. Kaufhold, D. Barber, A. R. Hayward, C. Y. Chan, I. S. F. Chan, D. J. J. Li, W. Wang, P. M. Keller, A. Shaw, J. L. Silber, K. Schlienger, I. Chalikonda, S. J. R. Vessey and M. J. Caulfield, Decline of varicella zoster virus (VZV)-specific cell mediated immunity with increasing age and boosting with a high-dose VZV vaccine, The Journal of Infectious Diseases, 188 (2003), 1336-1344.

[10]

M. Reichelt, L. Zerboni and A.M. Arvin, Mechansisms of varicella-zoster virus neuropathogenesis in human dorsal root ganglia, Journal of Virology, 82 (2008), 3971-3983. doi: doi:10.1128/JVI.02592-07.

[11]

K. E. Schmader and R. H. Dworkin, Natural history and treatment of herpes zoster, The Journal of Pain, 9 (suppl. 1) (2008), 53-59. doi: doi:10.1016/j.jpain.2007.10.002.

[12]

S. L. Thomas, J. G. Wheeler and A. J. Hall, Contacts with varicella or with children and protection against herpes zoster in adults: A case-control study, The Lancet, 360 (2002), 678-682.

[13]

J. M. Weinberg., Herpes zoster: Epidemiology, natural history and common complications, Journal of the American Academy of Dermatology, 57 (2007), S130-S135. doi: doi:10.1016/j.jaad.2007.08.046.

[14]

A. Wilson, M. Sharp, C. M. Koropchak, S. F. Ting and A. M. Arvin, Subclinical varicella-zoster virus viremia, herpes zoster, and T lymphocyte immunity to varicella-zoster viral antigens after bone marrow transplants, Journal of Infectious Diseases, 165 (1992), 119-126.

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