**Core Concept**
Malaria's communicability is determined by the presence and density of gametocytes in the bloodstream. Gametocytes are the sexual stage of the parasite responsible for transmitting the disease to mosquitoes. Understanding the dynamics of gametocyte production and appearance is crucial for assessing the risk of malaria transmission.

**Why the Correct Answer is Right**
The number of gametocytes in the blood does not increase with time. In fact, the gametocyte density typically peaks within 2-3 days after the appearance of the asexual parasite and then declines. This is because the parasite's energy is primarily devoted to producing asexual forms, which multiply rapidly. The production of gametocytes is a secondary process, and their numbers decrease as the infection progresses. In vivax and falciparum infections, gametocytes appear in the blood 4-5 days and 10-12 days after the appearance of asexual parasites, respectively.

**Why Each Wrong Option is Incorrect**
**Option B:** This statement is true for vivax malaria, where gametocytes appear in the blood 4-5 days after the appearance of asexual parasites. However, it is not the correct answer because option A is the statement that is false.

**Option C:** This statement is true for falciparum malaria, where gametocytes appear in the blood 10-12 days after the appearance of asexual parasites.

**Option D:** This statement is true, as in the early stage of infection, the density of gametocytes can exceed 1000 per cmm of blood.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the communicability of malaria is highest during the early stage of infection, when gametocyte density is high. However, this period is also when the parasite is most likely to be detected by microscopy or rapid diagnostic tests, allowing for early treatment and reduction of transmission risk.

**✓ Correct Answer: A. The number of gametocytes in blood increases with time**