There are fungicides on the market that are recommended for Fusarium control. They can be helpful when applied correctly. Other than that, it's recommended that you rake out the dead areas, topdress with soil and seed with a premium mixture. Patching with sod is adding insult to injury. Even though Fusarium is a problem, sod may be the best way to go if the area gets a lot of foot traffic.
Sod is also less work than seed, requiring less watering and weeding.
Be sure to water those Fusarium-repaired areas regularly. Seeding generally produces a stronger and more disease resistant lawn over the long term. Although seeding the lawn usually bypasses the Fusarium problem, it will require more maintenance. You have to be more vigilant about watering. Water twice each day for the first month in hot weather.