Tuesday, January 02, 2007

How fast can bedbugs multiply? - Part 1

I started caulking my parent's place in late September, and my new apartment in November, now the work is nearing the end. Looking back, I probably should have stayed in the old apartment, just to prove that I can defeat the bedbugs, and to make my strategy more convincing. But the place had cracks everywhere and would have taken too much effort to seal them all, and I had two infestations to take care of at the same time, a damaged ceiling to repair, a scratched car to fix (I was thinking about how to fight the bedbugs while I was driving). I was physically and mentally exhausted and just wanted to get out. However, my parents did stay and the battle there is still going on.

Back to the main topic.

Suppose you accidentally brought home two bedbugs, one male and one female, how fast can they multiply with unlimited blood meals? Without using complicated mathematics, the result can be obtained easily with spreadsheet.

There are different data on bedbug's life cycle on the Internet. I tried to use the average and made the following assumptions:

- sex ratio is 1:1

- 10 months of life span

- eggs hatch in 10 days

- nympal development time is 60 days

- female lay 4 eggs per day

click the image to enlarge

Based on these assumptions, the spreadsheet was then setup and a graph was plotted, which contained three periods:

Period I: from day 1 to day 10, eggs are laid daily, number of bedbugs remains constant at 2.

Period II: from day 11 to day 70, eggs start to hatch, number of bedbugs starts to increase, but growth is linear at the rate of 4 per day, and reaches 242 on day 70.

Period III: From day 71 and on, nymphs start to mature, number of bedbugs increases exponentially, total number quadrupled in 20 days to more than 1000 on day 93, or in 3 months.

Just for your information, the number reaches 5000 on day 114, and 10000 on day 129. Stephen Doggett, an entomologist at the institute of clinical pathology and medical research at Westmead hospital in Sydney, said he once found 5,000 bugs in one woman's bed. So it is realistic to have a few thousand of bedbugs in one residence, provided that there are enough food supply and harborage places.

Here's how I set up the spreadsheet:


A: number of days

B: number of total adults

C: number of female adults

D: number of newly hatched 1st instars on this day

E: number of eggs laid on this day

F: total number of nymphs

G: total number of bedbugs

Formulas for each column:

A: From day 1 to day 365

B: It's 2 in period I and II. Starting day 71, the formula becomes B71 = B70 + D11, meaning the number of adults on day 71 is the sum of the number of adults on the previous day and the number of 1st instar hatched 60 days ago (and matures on this day).

C: C1=B1*(1/(1+1)), where B1 is the number of total adults, and 1/(1+1) is the female percentage of the population.

D: It's zero in period I. Starting period II, the formula is C11 = D1, meaning the number of newly hatched 1st instar is equal to the number of eggs laid 10 days ago (eggs hatch in 10 days).

E: E1 = C1*4, eggs laid on this day is the number of eggs laid per day by each female multiplied by the total number of female adults.

F: Total number of nymphs is equal to the sum of 1st instar hatched in the last 60 days, the ones born earlier already matured and are added to column B instead. Since we can't use zero or negative numbers as the row number, we enter this formula on cell F60: F60 = SUM(D1:D60), and then copy it downwards. For row 1 to 59, we alter the formula to F60=SUM(D$1:D60) and copy it upwards. The dollar sign makes the summation always start from row 1, otherwise you will get error.

G: G1 = B1 + F1, total number of bedbugs is the sum of total adults and total nymphs.

After 10 months, another event will kick in, which is that the bedbugs will start to die. However, the number is negligible compared with the huge base, so this wasn't taken into consideration.

Also, 100% survival rate was assumed for all stages of life cycle, hence the result might differ a little in reality.

(Revised on Feb 25, 2007) From what I have researched so far, female adults lay 200 to 500 eggs over a period of two months. Therefore, in my calculations, the number of eggs laid should be reduced accordingly after day 130. But this will not affect the results that we have obtained above, because we were only looking at a period of about three months.

The conclusion is that it only takes a few months to have a heavy infestation, you need to catch it early and take care of it as soon as possible, once the number increases exponentially, it will be out of control. Next time we'll examine how the numbers change if the food supply is limited.


Blogger uniteddetection.com said...

Great calculation Frank, with permission I would like to post the information on our website. Even if you cut all numbers by 75% the message is clear: find and treat your bed bug problem as soon as possible. The faster you detect a problem, the quicker you stop the growth.

Certified K9 Handler

1:14 PM  
Blogger Frank said...

John, thanks for reading my Blog. You may use the information, I would be grateful if it can be helpful to anyone.


7:04 AM  
Anonymous Stacey said...

This is great info to know.

4:17 AM  
Blogger N E Biddle, aka The Roach Lady said...

I have written a similar article from the perspective of what it would appear like for the "Blood Buffet" (you) from the first to the 30th day of infestation from one bedbug couple. It starts with one or two bites (the adult needs only 1 meal every ten days) that come, irritate and go away over the course of one week, and you may even have already disregarded it as an allergy to something. By the eleventh day the four eggs the mom laid on day one hatch and the nymphs and the mom herself partake of the blood buffet. And the Next day the next 4 nymphs and so on for the next ten days so that by day twenty you have about (considering 3 bites each) 60 or more itchy spots in various stages of healing. I will be publishing the article shortly. I needed an interval stat for how often nymphs need a blood meal which is how I found your blog. Nice work, great articles Frank!

6:57 PM  
Anonymous Anonymous said...

I found one green solution for killing these suckers.

0.)reduce all the clutter in home

1.) use tape to catch and seal all the visible beadbugs and their eggs / littleones. from matress and box spring and where ever they are found. ensure that you kill them all physically.

2.) I have also tried to sanitise the entire matress & springbox by gently waxing all the spring box so that any invisible eggs or little ones are plucked out from your matress and box spring on the surface.

Use steam Iron to iron your matress and box spring (after you have waxed the matress and box spring with tape. excercise caution when you do this. Then put both items in encasements.

4.) use pillow encacements.

5.)Vaccum your entire home carpet and corners with the vaccume attachments given.

6.) if you have super steamer vaccum use it to sanitise your carpet (I am yet to find this)

7.) clean all shelfs.

8.) Use dryer in FULL HOT setting to clean your clothes just to kill the bugs in case they exist there

9) Spot heating of 120F also helps in sanitising your small wooden furniture. Ensure care when you do this. Probably some where outside.

10) properly bin your infected stuff if you cant sanitise it. One needs to be unattached to the materialistic things in this world once these aliens attack

11.) thoroughly vaccume your entire home every 2 days entire surface and corners need to be covered. do this religiously

12.) Persistance pays off. This is a long drawn battle and we must win.

14) I have also tried to use the summer heat to my advantage by storing all the sealed sanitised stuff in my car cabin and boot where the summer heat of 80F makes the internal temperature of closed car to 120F plus

I did all this and found that I have to some extent contained the blowout of infestation but i think I did it just in time or else i would have ended up with thousands of these in my home.

I will keep you posted on my progress and i make.

Tango the Indian

12:20 AM  

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