Some simple mathematical thoughts about epidemics. An epidemic is a disease that spreads rapidly or expands into a large population. A bit of thought will show that for a disease outbreak to become an epidemic, each person with the disease needs to pass it on to more than one other person on average. Suppose 100 people have the disease but on average each one has only a 50% chance of passing it on to another person before the disease runs its course. In that situation an epidemic is impossible; the original 100 will pass it on to only 50 new sufferers, who will pass it on to only 25 new cases, and so on until the disease stops with only 200 (approximately) having been affected. Not an epidemic.
If on the other hand, each person on average passes the disease on to two others, then there will be exponential growth and a real epidemic unless it is contained by some intervention. In that case, the original 100 sick people will infect 200, who will pass it on to 400 new cases, and so on. Thus, it is useful to think in terms of a "infection ratio" being the average number of people each affected person infects before the disease has run its course.
Clearly various factors will affect this infection ratio for different populations, subgroups or even individuals. Things like the weather, the population density, living conditions, sources of food and water, etc. can all change the circumstances of infection and hence the likelihood of transmitting the disease. Perhaps the most obvious factor is vaccination. In a population where almost everyone has been vaccinated against measles, there is little danger of one case of measles causing an outbreak. On the other hand, as the unvaccinated fraction of people increases, the danger of an outbreak will rise, until the infection ratio exceeds unity. Then an outbreak will occur, which could turn into an epidemic unless measures are taken to reduce the infection ratio, by vaccinating all the unvaccinated people, or perhaps just by isolating the sick people from contact with unvaccinated ones.
One interesting application of this concept is HIV infections in North America. Under typical conditions, faithful monogamous heterosexual people who do not inject drugs with shared needles have a very low chance of contracting HIV, and if they do contract it by some means, they have a low probability of passing it on to anyone else, or perhaps at most, to only one person. Thus, HIV/AIDS in such a population would never have become an epidemic.
In contrast, there are at least two groups in North America with demonstrated HIV infection ratios above unity. These are injection drug users (IDU's) who share needles, and men who have sex with other men (MSM). In both cases, the behaviours of people in these groups raise their infection ratio above unity, and the virus infects others in those groups. Indeed, these two groups remain the two where HIV/AIDS is most prevalent, and most of the new infections (on a per capita basis) occur.
For IDU's, sharing needles transmits the virus from one individual directly into the bloodstream of another. Since such people shoot up often, and sometimes change who they do it with, the risk of infection can be very high and the disease can spread rapidly in that population. Therefore preventive measures like needle exchanges, or bleach washing of used needles can be important to reduce the risk and stop the epidemic.
With MSM, the combination of anal sex and multiple partners make HIV transmission much more likely than for single-partner, heterosexual intercourse. Thus, here too, the infection ratio can be quite high and the virus can spread quickly through an unprotected population. For example, recall "patient zero" and the rapid increase in AIDS among homosexual men before the virus was identified. Here too, limiting partners, and using some form of protection can presumably reduce the risk.
Notwithstanding attempts to prevent transmission and limit the risk of infection, these two populations remain centres for HIV transmission in the North American population. Indeed, these two sub-populations may be considered as "reservoirs" for the disease and act to maintain it at significant levels within the wider population. How that works can be explained by the relative infection ratios of these two groups compared to the rest of the people. Within these sub groups, the infection ratio is high (more than one), so the disease does not die out.
However, these groups also interact in risky ways with people outside their groups, and thus may pass on the infection to those people. For example, bisexual, or secretly homosexual men may infect their female partners, even if the chance for that is relatively low. In the past, IDU's might give blood to earn money to pay for their drugs, children might be pricked by used needles left in parks, or health care workers might accidentally get infected blood on them.
In such ways, HIV/AIDS can "leak" out of the reservoirs where it is sustained, and into the broader population. But once there, it does not become epidemic, because the subsequent infection ratio outside the reservoirs is less than unity. A few other unfortunates will contract the disease, but for most of us the risk is low, although given the nature of the disease, taking precautions in uncertain situations is still a good idea.
This analysis suggests that efforts to combat the spread of HIV/AIDS should focus almost entirely on the reservoir sub-populations of IDU's and MSM. This is happening to some extent, but misplaced political correctness (e.g. "everyone is at risk" campaigns), and the tendency of these two groups not to adopt the recommended precautions (any needle for a fix?) allow the reservoirs to maintain the disease at low but stable levels, condemning many more each year to the AIDS disease.
Stronger methods (recall the "Typhoid Mary" quarantine rules) could be applied if health care agencies had the will and political clout to apply them. Mandatory HIV testing for some groups, tightly focused educational campaigns, backed up by strong laws against knowingly transmitting the virus, enforced and coupled with aggressive treatment regimes, could presumably reduce the infection ratio even within these reservoirs, thereby winding down the disease, at least to some significant degree.
Given the cost of lifelong anti-HIV treatments and the poor health associated with the disease and ongoing treatments, it seems that we would be well advised to pursue such measures, to protect these sub groups and the population at large from this scourge. There are good reasons for being sexually faithful to one partner, and for not injecting yourself with drugs, and North America would do well to promote truly healthy behaviour and stop pretending otherwise. I expect an unbiased professional epidemiologist would agree.
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