Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic
-
1.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3
-
Received:
01 August 2007
Accepted:
29 June 2018
Published:
01 March 2009
-
-
MSC :
92D30.
-
-
Since the discovery of HIV/AIDS there have been numerous mathematical models
proposed to explain the epidemic of the disease and to evaluate possible
control measures. In particular, several recent studies have looked at the
potential impact of condom usage on the epidemic
[1, 2, 3, 4]. We develop a simple
model for HIV/AIDS, and investigate the effectiveness of condoms as a
possible control strategy. We show that condoms can greatly reduce the number
of outbreaks and the size of the epidemic. However, the necessary condom usage
levels are much higher than the current estimates. We conclude that condoms
alone will not be sufficient to halt the epidemic in most populations
unless current estimates of the transmission probabilities are high.
Our model has only five independent
parameters, which allows for a complete analysis. We show that the assumptions
of mass action and standard incidence provide similar results, which implies
that the results of the simpler mass action model can be used as a good first
approximation to the peak of the epidemic.
Citation: Jeff Musgrave, James Watmough. Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic[J]. Mathematical Biosciences and Engineering, 2009, 6(2): 363-376. doi: 10.3934/mbe.2009.6.363
-
Abstract
Since the discovery of HIV/AIDS there have been numerous mathematical models
proposed to explain the epidemic of the disease and to evaluate possible
control measures. In particular, several recent studies have looked at the
potential impact of condom usage on the epidemic
[1, 2, 3, 4]. We develop a simple
model for HIV/AIDS, and investigate the effectiveness of condoms as a
possible control strategy. We show that condoms can greatly reduce the number
of outbreaks and the size of the epidemic. However, the necessary condom usage
levels are much higher than the current estimates. We conclude that condoms
alone will not be sufficient to halt the epidemic in most populations
unless current estimates of the transmission probabilities are high.
Our model has only five independent
parameters, which allows for a complete analysis. We show that the assumptions
of mass action and standard incidence provide similar results, which implies
that the results of the simpler mass action model can be used as a good first
approximation to the peak of the epidemic.
-
-
-
-