Journal of Mathematical Biology

, Volume 43, Issue 1, pp 69–80

The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission

  • Ying-Hen Hsieh
  • Shin-Pyng Sheu

DOI: 10.1007/s002850100087

Cite this article as:
Hsieh, YH. & Sheu, SP. J Math Biol (2001) 43: 69. doi:10.1007/s002850100087

Abstract.

In this work, we propose a model for heterosexual transmission of HIV/AIDS in a population of varying size with an intervention program in which treatment and/or behavior change of the infecteds occur as an increasing function of the density of the infected class in the population. This assumption has socio-economic implications which is important for public health considerations since density-dependent treatment/behavior change may be more cost-saving than a program where treatment/behavior change occurs linearly with respect to the number of infecteds. We will make use of the conservation law of total sexual contacts which enables us to reduce the two-sex model to a simpler one-sex formulation. Analytical results will be given. Unlike a similar model with linear treatment/behavior change in Hsieh (1996) where conditions were obtained for the eradication of disease, we will show that density-dependent treatment/behavior change cannot eradicate the disease if the disease is able to persist without any treatment/behavior change. This work demonstrates the need to further understand how treatment/behavior change occurs in a society with varying population.

Key words or phrases: Epidemiological models – HIV transmission – Population with varying size – Density-dependent treatment/behavior change – Global analysis – Existence and uniqueness of endemic steady state

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ying-Hen Hsieh
    • 1
  • Shin-Pyng Sheu
    • 1
  1. 1.Department of Applied Mathematics, National Chung-Hsing University, Taichung, Taiwan 402. e-mail: yhhsieh@dragon.nchu.edu.twTW