djb, none of the mosquito-born diseases you brought up are deemed to be significant issues in Mexico by any health authorities that I'm aware of. I wouldn't mention a disease unless it's known to be an actual issue for where someone is going. Lots of people, not just Denis, will read it and then have incorrect ideas in their heads about diseases found in Mexico.
I've traveled to the Gulf coast of Mexico myself, as well as to the Yucatan. This is the dry season in most of the area where he'll be biking. Tabasco state and southeastern Veracruz state will likely have some rain, though it's still drier during the winter than from June-November. I don't recall any issues with mosquitos during my travels in Veracruz state or in the Yucatan. My travels were between December and February, i.e. the dry season. During the North American summer months, the Yucatan sounds awful with high temperatures, high humidity, high rainfall, and lots of bugs.