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.

- 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.
- each infectious person is infectious for 5 days only (it could be longer). We’ll say 5 to be conservative.
- 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.
- 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.