Mathematical Biosciences and Engineering, 2015, 12(1): 23-40. doi: 10.3934/mbe.2015.12.23.

Primary: 92B05, 92D30; Secondary: 92D25.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

A double age-structured model of the co-infection of tuberculosis and HIV

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

After decades on the decline, it is believed that the emergence of HIV is responsible for an increase in the tuberculosis prevalence. The leading infectious disease in the world, tuberculosis is also the leading cause of death among HIV-positive individuals. Each disease progresses through several stages. The current model suggests modeling these stages through a time-since-infection tracking transmission rate function, which, when considering co-infection, introduces a double-age structure in the PDE system. The basic and invasion reproduction numbers for each disease are calculated and the basic ones established as threshold for the disease progression. Numerical results confirm the calculations and a simple treatment scenario suggests the importance of time-since-infection when introducing disease control and treatment in the model.
  Figure/Table
  Supplementary
  Article Metrics

Keywords partial differential equations; tuberculosis; basic reproduction number; co-infection; invasion reproduction number; age-structure.; HIV; population dynamics; mathematical epidemiology

Citation: Georgi Kapitanov. A double age-structured model of the co-infection of tuberculosis and HIV. Mathematical Biosciences and Engineering, 2015, 12(1): 23-40. doi: 10.3934/mbe.2015.12.23

References

  • 1. Math. Model. Nat. Phenom., 3 (2008), 229-266.
  • 2. AIDS, 17 (2003), 2501-2508.
  • 3. Infection and Immunity, 69 (2001), 4195-4201, URL http://iai.asm.org/content/69/7/4195.short.
  • 4. Journal of Infectious Diseases, 198 (2008), 687-693.
  • 5. Theor Popul Biol., 55 (1999), 94-109.
  • 6. BMC Medicine, 11 (2013), p231.
  • 7. Journal of Infectious Diseases, 196 (2007), S5-S14.
  • 8. Global tuberculosis report, 2013.
  • 9. PLoS Pathog, 8 (2012), e1002464.
  • 10. Math Biosci Eng, 6 (2009), 815-837.
  • 11. Math Biosci Eng., 5 (2008), 145-174.
  • 12. Journal of Applied Mathematics, 2013 (2013), Art. ID 429567, 13 pp.
  • 13. Monographs and Textbooks in Pure and Applied Mathematics Series 89. Marcel Dekker Inc., 1985.

 

This article has been cited by

  • 1. Victor Moreno, Baltazar Espinoza, Kamal Barley, Marlio Paredes, Derdei Bichara, Anuj Mubayi, Carlos Castillo-Chavez, The role of mobility and health disparities on the transmission dynamics of Tuberculosis, Theoretical Biology and Medical Modelling, 2017, 14, 1, 10.1186/s12976-017-0049-6
  • 2. Biao Tang, Yanni Xiao, Jianhong Wu, Implication of vaccination against dengue for Zika outbreak, Scientific Reports, 2016, 6, 1, 10.1038/srep35623

Reader Comments

your name: *   your email: *  

Copyright Info: 2015, Georgi Kapitanov, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved