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# Can we spend our way out of the AIDS epidemic? A world halting AIDS model

, 1 , 2 , 3 , 4

BMC Public Health

BioMed Central

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### Abstract

##### Background

There has been a sudden increase in the amount of money donors are willing to spend on the worldwide HIV/AIDS epidemic. Present plans are to hold most of the money in reserve and spend it slowly. However, rapid spending may be the best strategy for halting this disease.

##### Methods

We develop a mathematical model that predicts eradication or persistence of HIV/AIDS on a world scale. Dividing the world into regions (continents, countries etc), we develop a linear differential equation model of infectives which has the same eradication properties as more complex models.

##### Results

We show that, even if HIV/AIDS can be eradicated in each region independently, travel/immigration of infectives could still sustain the epidemic. We use a continent-level example to demonstrate that eradication is possible if preventive intervention methods (such as condoms or education) reduced the infection rate to two fifths of what it is currently. We show that, for HIV/AIDS to be eradicated within five years, the total cost would be ≈ $63 billion, which is within the existing$60 billion (plus interest) amount raised by the donor community. However, if this action is spread over a twenty year period, as currently planned, then eradication is no longer possible, due to population growth, and the costs would exceed \$90 billion.

##### Conclusion

Eradication of AIDS is feasible, using the tools that we have currently to hand, but action needs to occur immediately. If not, then HIV/AIDS will race beyond our ability to afford it.

### Most cited references61

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### Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

(2002)
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### Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

(2015)
A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0 1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
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### Perspectives on the basic reproductive ratio.

(2005)
The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R0. In this paper we give a brief overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R0 from epidemiological data. Finally, we survey the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.
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### Author and article information

###### Journal
BMC Public Health
BMC Public Health
BioMed Central
1471-2458
2009
18 November 2009
: 9
: Suppl 1
: S15
###### Affiliations
[1 ]Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa, Ontario, Canada, K1N 6N5
[2 ]Department of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa, Ontario, Canada, K1N 6N5
[3 ]Department of Radiology, University of Manitoba, Winnipeg, Manitoba, Canada, R3A 1R9
[4 ]Department of Mathematics & Statistics, York University, 4700 Keele St, Toronto, Ontario, Canada, M3J 1P3
###### Article
1471-2458-9-S1-S15
10.1186/1471-2458-9-S1-S15
2779503
19922685

This is an open access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

###### Categories
Research

Public health