Did the apostles have the same authority over unclean spirits, disease and affliction that Jesus had?
The apostles had the same authority over unclean spirits, disease and affliction as Jesus had (Matthew 9:35)—authority given by Jesus himself. The first act of the apostle mentioned in Matthew 10:1, the casting out of unclean spirits, directly confronted the power of Satan, and so could not be conquered without the power of God granted by the authority given by Jesus. However, it is not a magical power, because it must be accompanied by the continual prayer of Matthew 9:38. This gift of healing various kinds of illness, must be grounded in faith in Christ (Matthew 17:20), imitate his work (see Matthew 4:23, Matthew 8:17 ,Matthew 9:35; John 14:12), and be carried out in his name.
Yes, for Jesus, having called the apostles himself, also gives them his authority over demons and illnesses. The authority given to the apostles here in Matthew 10:1, Matthew 10:7, Matthew 10:8 is equal to that of the Master (Matthew 9:35).1
With the assent of the Lord of the harvest, he therefore confers his own authority on his disciples. In his name they now also have power over unclean spirits just like Jesus. This is not a magical power, however, for the competence that Jesus confers on them must be accompanied by the continual prayer of Matthew 9:38. God thereby grants these twelve people the powers of the kingdom of heaven. They harvest that which God gives, and distribute that harvest of the kingdom to all.2
The nature of this gift of healing various kinds of illnesses is clearly outlined in Matthew 8:17. Gifts such as these could, of course, only be employed in faith (Matthew 17:20). Jesus’ command to the apostles reminds of his own work (see Matthew 4:23, Matthew 9:35; John 14:12). The apostles thereby continued the work done by Jesus, and did so in his name3
The first act of the apostles mentioned in Matthew 10:1 is the casting out of unclean spirits. The activities of these spirits were conducted by the power of Satan, and as such they could not be conquered without the power of God. The fact that the apostles were equipped to do this testifies to the fact that their authority comes from Jesus himself, and by their authority over unclean spirits the apostles then in turn reveal his majesty.4
1 Puis, ayant appelé ses douze disciples, il leur donna le pouvoir de chasser les esprits impurs, et de guérir toute maladie et toute infirmité.