Chikungunya: This is a highly likely diagnosis due to the presence of Chikungunya virus in Ecuador and the Galapagos. Chikungunya is known for causing acute polyarthritis, which can be severe and debilitating.

Dengue Fever: Also prevalent in Ecuador and the Galapagos, Dengue can cause severe joint pain and polyarthritis, although it is more commonly associated with a systemic illness including fever and rash.
Zika Virus: Similar to Chikungunya and Dengue, Zika virus is transmitted by the same mosquito vectors and can cause arthritis, although it is less commonly associated with severe polyarthritis compared to Chikungunya.
Osteoarthritis and Rheumatoid Arthritis: While not infectious, these conditions can cause polyarthritis and should be considered in the differential diagnosis, especially if the patient's symptoms do not fully align with an acute infectious etiology.

Septic Arthritis: Although less likely, septic arthritis is a medical emergency that requires prompt diagnosis and treatment to prevent joint destruction and systemic complications. It can present with acute onset of joint pain and swelling.
Lyme Disease: While less common in Ecuador and the Galapagos, Lyme disease can cause arthritis and should be considered, especially in travelers who have visited endemic areas.

Ross River Virus: This virus is more commonly associated with outbreaks in the Pacific Islands and Australia but could potentially be considered in travelers to the region.
Mayaro Virus: Another arthritogenic virus, Mayaro is less commonly reported but could be a consideration in patients with exposure to the vector in endemic areas.
O'nyong-nyong Virus: Similar to Chikungunya, this virus causes severe joint pain but is more commonly found in Africa, making it a rare consideration in Ecuador and the Galapagos unless in a traveler from an endemic area.