The figures were all very specific and very frightening. "Two thousand bugs taking a ride in every train compartment," said the Daily Mail. "Cockroaches cluster on trains," groaned the Telegraph. "Commuters share trains with 1,000 cockroaches, 200 bedbugs and 200 fleas," said the Evening Standard.

These figures all sound a little bit on the high side. Where did they come from? "Staff at Rentokil sprayed insecticide throughout the carriages of a train and a bus and then counted the bodies of insects," said the Standard. It quoted a Rentokil spokesman: "The bus we studied was within the M25."

But Transport for London says it has had no contact with Rentokil, and that no such study has been done on its vehicles. I asked Rentokil for more details.

After a bit of prodding, its PR company, Brands2Life, explained: no buses or trains were studied.

How did people get the wrong end of the stick? I have no way of knowing, as Brands2Life and Rentokil both declined to show me what they had sent to journalists but, in any case, contrary to what was said earlier, these numbers did not come from measurements and counts – they are based on a "theoretical model".

Models are handy. They're a simulation of reality, based on a series of assumptions. Rentokil's model for the number of bugs on trains and buses made some interesting assumptions, and you will have your own view on whether they make for a reasonable approximation of the real world.

It assumed, for example, that the railway carriage or bus was left in isolation. It assumed this carriage was helpfully furnished with a plentiful food supply. It assumed that the ratio of male to female bugs was perfectly optimal for breeding.

It assumed (surprisingly for anyone involved in modelling populations – surprisingly for anyone, really) that the population of bugs would be left entirely unchecked, with no external factors to control the mortality rate.

It assumed that the siding or garage was controlled at a constant temperature all day and night, with no extremes. It assumed there were no trampling commuters, no cruel vacuum cleaners, no anything. In fact, it assumed there was no cleaning, ever, and no passengers, ever. This was its model of insect populations on commuter vehicles.

You will have your own view on whether you could trust an organisation that makes assumptions like these in estimating the average population of bugs. But it's somehow unseemly that Rentokil, a company with £2.36bn in revenue and a 54% increase in profits in 2009 to £166m, and poised to pay £90m in bonuses to its top three executives, feels the need to make everyone afraid of public transport on a PR whim. There is also the ugly thought that Rentokil will do more business if it can make everyone scared of bugs on the bus.

And on 2 March, the day before the cockroach press release, Rentokil announced the single biggest ever contract in the history of its business: £200m over five years with London Underground.