# How many infectious mosquitoes are there?

This is a fun little analysis to work out how many infectious mosquitoes are on the Big Island (Jan 2016).

Bottom line: between five hundred and a thousand infectious mosquitoes right now.

The Dept of Health regularly publishes details of current dengue cases.  They also publish an estimate of how many of those people are infectious to mosquitoes.  Fortunately, this is usually a small number, like 3 or 8 (though there is a bias to lower numbers because often DOH does not complete testing until after the person is no longer infectious).  Unfortunately, this doesn’t really tell us much because we can’t catch dengue from people.  So much more interesting would be how many infectious mosquitoes are there?

You might think this would be impossible to know unless we spent a whole lot of money trapping and testing mozzies.  Fortunately, we can make an estimate with some middle school math.

Here is how a scientist would start to estimate that number. It involves a few assumptions we can argue about, but what matters is the “order of magnitude” result.  Is it 1, or 10, or 100, or 1000, or 10,000??? This kind of analysis is a standard procedure in science.
We’ll assume:
1. for every one confirmed case of dengue in humans there are three more that are not confirmed – ie not sick enough that they go to the doctor. (This number is from DOH, also WHO and numerous research papers). Instead, they go to work, to the beach, the market, to the farms, etc. We’ll conservatively assume the confirmed cases are so sick they stay in bed and don’t get bit.
2. each infectious person is infectious for 5 days only (it could be longer). We’ll say 5 to be conservative.
3. each infectious person who is out and about will get bit just twice per day on average. (some people will be much, much higher than this and some will be zero). Each bite produces one infectious mosquito. You can see that means on average that every asymptomatic infected person goes out and infects ten mosquitoes (order of magnitude) during the time they are infectious.
4. But, these mosquitoes eventually die so we have to figure out how to take that into account by calculating, on average, how many days an infectious mosquito will live.  We’ll assume the average mosquito adult lives about 35 days (lab raised Aedes mosquitoes have survival rate of 50% at 60 days, some live to 100 days). We’ll assume that if they do bite an infected person, it happens half way through their life, ie 18 days. This is a pretty reasonable assumption for randomly occurring events.  Now, after the mosquito bites someone, it takes about 5 – 7 days to become infectious.  So we need to subtract this from 18 days to get the average number of days a mosquito will be infectious.  That leaves about 12.
So here is how we make the estimate:
We’ll call P the number of confirmed cases during the last 12 days.  As of January 14th, I’d estimate (based on DOH numbers of 218 people in 120-ish days, ie about 2 per day) that there were 25 dengue cases in the last 12 days.  So P = 25.
The number of infectious mosquitoes, M is given by:
M = P (confirmed cases) * 3 (infectious humans per confirmed case) * 5 (days a human is infectious) * 2 (mosquitoes that get infected per day per infectious human).
Then M = 25 * 3 * 5 * 2 = 750.  So this is the order of magnitude estimate for how many infectious mosquitoes are out there.  So, it’s reasonable to say, that there are between 500 and 1000 infected mosquitoes on the Big Island today.
Now, before you go into a panic and lather on the DEET, you have to also realize that not all infectious mosquitoes are going to infect someone, especially since they are mostly albopictus which are not as effective as aegypti.  Albopictus get half their meals from animals (DOI: 10.1371/journal.pntd.0003037), mostly pets, and none from birds.  So, there is some thankfully small probability that an infectious mosquito will infect someone, and if we can keep that probability low enough, then dengue will die out!
Mosquito traps (lethal ovitraps) also lower that probability by reducing the average lifetime of an infected mosquito.  If we can cut the 12 days down to 6 days, we just cut the number of infectious mosquitoes by a factor of 2. That’s why health authorities all over the world (but not DOH) respond to a confirmed case by placing 4 to 10 mosquito traps around every house within 200 meters of a confirmed case. In fact, mosquito traps deployed like this have been shown to eliminate 90% of the mosquito population (eg Thursday Island, Australia 2004).
Notes:  I have read dengue shortens the life of mosquitoes but not included it here (and I hope it gives them terrible joint pains, splitting head aches, fever, etc).