An age-structured model for the coupled dynamics of HIV and HSV-2

Georgi Kapitanov; Christina Alvey; Katia Vogt-Geisse; Zhilan Feng; Georgi Kapitanov; Christina Alvey; Katia Vogt-Geisse; Zhilan Feng

doi:10.3934/mbe.2015.12.803

Mathematical Biosciences and Engineering

2015, Volume 12, Issue 4: 803-840. doi: 10.3934/mbe.2015.12.803

Previous Article Next Article

An age-structured model for the coupled dynamics of HIV and HSV-2

1.
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067

Received: 01 March 2014 Accepted: 29 June 2018 Published: 01 April 2015
MSC : Primary: 92B05, 92D30; Secondary: 92D25.

Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation - the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.
- basic reproduction number,
- age-structure,
- partial differential equations,
- co-infection,
- invasion reproduction number,
- HSV-2,
- sexually transmitted diseases.,
- population dynamics,
- mathematical epidemiology,
- HIV,
- sensitivity analysis
Citation: Georgi Kapitanov, Christina Alvey, Katia Vogt-Geisse, Zhilan Feng. An age-structured model for the coupled dynamics of HIV and HSV-2[J]. Mathematical Biosciences and Engineering, 2015, 12(4): 803-840. doi: 10.3934/mbe.2015.12.803

Related Papers:

Abstract

Evidence suggests a strong correlation between the prevalence of HSV-2 (genital herpes) and the perseverance of the HIV epidemic. HSV-2 is an incurable viral infection, characterized by periodic reactivation. We construct a model of the co-infection dynamics between the two diseases by incorporating a time-since-infection variable to track the alternating periods of infectiousness of HSV-2. The model considers only heterosexual relationships and distinguishes three population groups: males, general population females, and female sex workers. We calculate the basic reproduction numbers for each disease that provide threshold conditions, which determine whether a disease dies out or becomes endemic in the absence of the other disease. We also derive the invasion reproduction numbers that determine whether or not a disease can invade into a population in which the other disease is endemic. The calculations of the invasion reproduction numbers suggest a new aspect in their interpretation - the class from which the initial disease carrier arises is important for understanding the invasion dynamics and biological interpretation of the expressions of the reproduction numbers. Sensitivity analysis is conducted to examine the role of model parameters in influencing the model outcomes. The results are discussed in the last section.

References

[1]	Epidemics, 2 (2010), 173-182.
[2]	The journal of infectious diseases, 191 (2005), 546-553.
[3]	Annals of Internal Medicine, 121 (1994), 847-854.
[4]	Annals of Internal Medicine, 131 (1999), 14-20.
[5]	Clin Infect Dis, 39 (2004), S240-S247.
[6]	International Statistical Review/Revue Internationale de Statistique, 62 (1994), 229-243.
[7]	Nature Medicine, 4 (1998), 673-678.
[8]	Proceedings of the National Academy of Sciences, 97 (2000), 12385-12388, URL http://www.pnas.org/content/97/22/12385.abstract.
[9]	Journal of Biosocial Science, 37 (2005), 499-518.
[10]	Sexually Transmitted Infections, 82 (2006), iii26-iii33, URL http://sti.bmj.com/content/82/suppl_3/iii26.abstract.
[11]	The Lancet, 371 (2008), 2109-2119, URL http://www.sciencedirect.com/science/article/pii/S0140673608609204.
[12]	Open Journal of Epidemiology, 3 (2013), 139-148.
[13]	Annals of Internal Medicine, 98 (1983), 958-972.
[14]	J Acquir Immune Defic Syndr, 35 (2004), 435-445.
[15]	PLoS ONE, 8 (2013), e66874.
[16]	Social Science & Medicine, 65 (2007), 1235-1248, URL http://www.sciencedirect.com/science/article/pii/S0277953607002328.
[17]	Social Science & Medicine, 59 (2004), 1581-1592, URL http://www.sciencedirect.com/science/article/pii/S0277953604000504.
[18]	Mathematical Biosciences, 245 (2013), 171-187.
[19]	Bulletin of Mathematical Biology, 71 (2009), 720-749.
[20]	AIDS, 20 (2006), 73-83.
[21]	The Lancet, 373 (2009), 48-57.
[22]	Journal of Infectious Diseases, 205 (2012), 351-352, URL http://jid.oxfordjournals.org/content/205/3/351.short.
[23]	The Lancet, 357 (2001), 1149-1153.
[24]	The Lancet, 370 (2007), 2127-2137.
[25]	Environmental Monitoring and Assessment, 32 (1994), 135-154.
[26]	Reliability Engineering & System Safety, 91 (2006), 1175-1209.
[27]	The Journal of Infectious Diseases, 198 (2008), 687-693, URL http://www.researchgate.net/publication/23132753_HIV-1_transmission_by_stage_of_infection.
[28]	African Studies, 61 (2002), 99-120.
[29]	Poster Presentation: The XIV International AIDS Conference.
[30]	Demographic Research, 21 (2009), 289-340.
[31]	American Journal of Public Health, 85 (1995), 1521-1525.
[32]	Journal of Theoretical Medicine, 1 (1997), 25-34.
[33]	Sexually Transmitted Infections, 89 (2013), A222, URL http://sti.bmj.com/content/89/Suppl_1/A222.2.abstract.
[34]	American Journal of Epidemiology, 141 (1995), 1194-1200, URL http://aje.oxfordjournals.org/content/141/12/1194.abstract.
[35]	New England Journal of Medicine, 341 (1999), 1432-1438, URL http://www.nejm.org/doi/full/10.1056/NEJM199911043411904, PMID: 10547406.
[36]	AIDS, 23 (2009), 377-383, URL http://journals.lww.com/aidsonline/pages/articleviewer.aspx?year=2009&issue=01280&article=00012&type=abstract.
[37]	Annals of Internal Medicine, 116 (1992), 197-202.
[38]	AIDS, 15 (2001), S61-S69.
[39]	URL http://www.cdc.gov/hiv/pdf/statistics_surveillance_Epi-HIV-infection.pdf.
[40]	south africa, 2010.
[41]	Sexually Transmitted Diseases, 26 (1999), 374-380.
[42]	SIAM Journal on Applied Mathematics, 67 (2007), 731-756.
[43]	Nonlinear Analysis: Real World Applications, 14 (2013), 1621-1633, URL http://www.sciencedirect.com/science/article/pii/S1468121812002489.
[44]	Science Translational Medicine, 1 (2009), 7-16, URL http://stm.sciencemag.org/content/1/7/7ra16.abstract.
[45]	Sexually Transmitted Infections, 85 (2009), i72-i80, URL http://sti.bmj.com/content/85/Suppl_1/i72.abstract.
[46]	Sexually Transmitted Infections, 89 (2013), A218, URL http://sti.bmj.com/content/89/Suppl_1/A218.2.abstract.
[47]	URL http://www.unaids.org/sites/default/files/en/media/unaids/contentassets/documents/countryreport/2010/201003_MOT_West_Africa_en.pdf.
[48]	Mathematical Biosciences, 180 (2002), 29-48.
[49]	The Journal of Infectious Diseases, 186 (2002), S34-S39, URL http://www.jstor.org/stable/30085233.
[50]	Journal of Infectious Diseases, 191 (2005), 1403-1409, URL http://jid.oxfordjournals.org/content/191/9/1403.abstract.
[51]	Herpes, 11 (2004), 24A-35A.
[52]	Culture, Medicine and Psychiatry, 26 (2002), 339-370.
[53]	URL http://www.who.int/hiv/data/en/.

Reader Comments

Your name:*

Email:*
© 2015 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Mathematical Biosciences and Engineering

3.9

Metrics

Article views(2989) PDF downloads(582) Cited by(2)

Preview PDF

Download XML

Export Citation

Article outline

Show full outline

Mathematical Biosciences and Engineering

An age-structured model for the coupled dynamics of HIV and HSV-2

Related Papers:

Abstract

References

Reader Comments

通讯作者: 陈斌, bchen63@163.com

Metrics

Other Articles By Authors

Catalog

Mathematical Biosciences and Engineering

An age-structured model for the coupled dynamics of HIV and HSV-2

Related Papers:

Abstract

References

Reader Comments

通讯作者: 陈斌, bchen63@163.com

Metrics

Other Articles By Authors

Related pages

Tools

Export File

Citation

Format

Content

Catalog