animal.rb

class Animal < ActiveRecord::Base
  has_many :diseases
  has_many :pets
end

disease.rb

class Disease < ActiveRecord::Base
  belongs_to :animal

  has_and_belongs_to_many :pets
end

pet.rb

class Pet < ActiveRecord::Base
  belongs_to :animal

  has_and_belongs_to_many  :diseases

  accepts_nested_attributes_for :diseases, :allow_destroy => true 
end