This is a most interesting question but also impossible to answer without knowing the species of the cockroach. Different cockroaches, often from different countries function extremely differently, from how many eggs they lay to where they prefer to live and even their size can vary dramatically. Oddly enough the size of the cockroach is inversely related to the number of eggs. So the bigger the cockroach, the bigger the eggs and the less room for each egg in the cockroach’s ootheca. For this reason, your house, if infested by an American or brown-banded cockroach is likely not to be too high a population and may be handled with a domestic treatment. Oriental cockroaches make more eggs but are still too large to make a massive impact on your home. The real danger and the worst cockroach infestation you can have are German cockroaches. These tiny greenish cockroaches are baby-making machines. They can have up to sixty eggs in a single ootheca meaning you will likely see the babies more often than the adults. They are not like other insects in that they are closer to arachnids in how they grow. The egg hatches to reveal a full-grown but tiny cockroach. There are physical distinctions that changeover growth, like the brown-banded cockroach is born with one band but matures with two. This process is called moulting. The cockroaches shed their carapace as they grow to leave behind a very light piece of material that can float in the air. This old skin is coated in dangerous bacteria and inhaling it can cause respiratory problems and worse already existing ones. Asthma sufferers are often the worst hit by a cockroach infestation.
If you have cockroaches it is important to act fast. You can try a domestic treatment first but if that does not work without a month then you will need to call in the big guns. The professionals do use insecticide dust which is a domestic product but everything else that is used is a commercial product that requires a pest control license to even hold. Do not try to get ahold of these chemicals you will end up harming yourself much more than the cockroaches ever could have. The best treatment is a multi chemical with crack and crevis treatments, ultra-light insecticide mist to fill hard-to-reach areas, a baseboard spray of a neural agent and other processes that will get rid of your cockroaches faster and easier. SO call the professionals to get rid of your cockroach infestation, they are ready to help at a moment’s notice.