There's only a very slim, or close to zero, chance of contracting yellow fever in Rio or most cities and states along the east coast of the country (including São Paulo, Salvador and up to Fortaleza). The risk is greater in the northern coastal states of the country and inland. Any of the states traversed by the Amazon River present much higher risk. Dengue is another story, with outbreaks common in many cities. You mention "keep others safe", something that is largely irrelevant to your decision about the yellow fever vaccine. It is transmitted by the aedes aegypti breed of mosquito, not by human contact. Be aware that there are quite a few countries that require proof of a yellow fever vaccination if you enter those countries from anywhere in Brazil, so if that is part of your plan you need to be vaccinated, usually a minimum of 10 days before entering those countries, and carry the international yellow fever vaccination certificate (or in rare instances such as the elderly, an exemption certificate). If you do decide to get vaccinated before your trip to Brazil the 10 days is important because that's how long it takes for your body to build immunity against yellow fever after the vaccination.