Involve: A Journal of Mathematics

  • Involve
  • Volume 4, Number 1 (2011), 13-26.

Vertical transmission in epidemic models of sexually transmitted diseases with isolation from reproduction

Daniel Maxin, Timothy Olson, and Adam Shull

Full-text: Open access

Abstract

We describe a population logistic model exposed to a mild life-long sexually transmitted disease, that is, without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify this model to include groups isolated from sexual contact and analyze their potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels. In particular, we analyze the connection between vertical transmission and isolation from reproduction on the long term behavior of the disease. A comparison with similar effects caused by vaccination and quarantine is also provided.

Article information

Source
Involve, Volume 4, Number 1 (2011), 13-26.

Dates
Received: 10 September 2009
Revised: 16 December 2010
Accepted: 4 March 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733359

Digital Object Identifier
doi:10.2140/involve.2011.4.13

Mathematical Reviews number (MathSciNet)
MR2838258

Zentralblatt MATH identifier
1230.92030

Subjects
Primary: 92D30: Epidemiology
Secondary: 92D25: Population dynamics (general)

Keywords
sexually transmitted diseases abstaining individuals vertical transmission isolation from reproduction

Citation

Maxin, Daniel; Olson, Timothy; Shull, Adam. Vertical transmission in epidemic models of sexually transmitted diseases with isolation from reproduction. Involve 4 (2011), no. 1, 13--26. doi:10.2140/involve.2011.4.13. https://projecteuclid.org/euclid.involve/1513733359


Export citation

References

  • D. Maxin, “The influence of sexually active non-reproductive groups on persistent sexually transmitted diseases”, J. Biol. Dyn. 3:5 (2009), 532–550.
  • D. Maxin and F. A. Milner, “The effect of nonreproductive groups on persistent sexually transmitted diseases”, Math. Biosci. Eng. 4:3 (2007), 505–522.
  • D. Maxin and F. A. Milner, “The role of sexually abstained groups in two-sex demographic and epidemic logistic models with non-linear mortality”, J. Theor. Biol. 258:3 (2009), 389–402.
  • F. A. Milner, “How do nonreproductive groups affect population growth?”, Math. Biosci. Eng. 2:3 (2005), 579–590.