Department of Mathematics and Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa, Ontario, Canada, K1N 6N5.
BMC Public Health. 2009 Nov 18;9 Suppl 1(Suppl 1):S15. doi: 10.1186/1471-2458-9-S1-S15.
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.
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.
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 asymptotically equal to $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.
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.
愿意用于全球艾滋病/艾滋病疫情的捐款数额突然增加。目前的计划是将大部分资金储备起来并缓慢支出。然而,快速支出可能是阻止这种疾病的最佳策略。
我们开发了一种数学模型,用于预测全球范围内艾滋病/艾滋病的消除或持续。我们将世界划分为区域(大陆、国家等),并开发了一种具有相同消除特性的线性微分方程感染者模型,比更复杂的模型更简单。
我们表明,即使可以在每个地区独立消除艾滋病/艾滋病,感染者的旅行/移民仍可能维持该疾病的流行。我们使用大陆级别的示例来说明,如果预防干预措施(如避孕套或教育)将感染率降低到当前水平的五分之二,那么消除是可能的。我们表明,要在五年内消除艾滋病/艾滋病,总成本将渐近等于 630 亿美元,这在捐赠社区筹集的 600 亿美元(加上利息)范围内。但是,如果按照目前的计划将此行动延长 20 年,那么由于人口增长,消除将不再可能,并且成本将超过 900 亿美元。
使用我们目前掌握的工具,艾滋病的消除是可行的,但需要立即采取行动。否则,艾滋病/艾滋病将超出我们的承受能力。