A search of the word “HEALED” in the Gospel According to Matthew New King James Version (NKJV). Key phrase: “and He healed them.” Note the action the sick or their families did before the word “and“. What did they do? They came to Jesus. They brought the sick to Him. They sought Him out. They followed Him. They believed in His compassion. They believed in His power to heal. In the cases of the two foreigners (a Roman centurion and a woman of Canaan), Jesus specifically commended their faith in action. “And He healed them (the sick-regardless what diseases or causes thereof).”
4:24 Then His fame went throughout all Syria; and they brought to Him all sick people who were afflicted with various diseases and torments, and those who were demon-possessed, epileptics, and paralytics; and He healed them.
8:8 The centurion answered and said, “Lord, I am not worthy that You should come under my roof. But only speak a word, and my servant will be healed. 8:13 Then Jesus said to the centurion, “Go your way; and as you have believed, so let it be done for you.” And his servant was healed that same hour.
8:16 When evening had come, they brought to Him many who were demon-possessed. And He cast out the spirits with a word, and healed all who were sick,
12:15 But when Jesus knew it, He withdrew from there. And great multitudes followed Him, and He healed them all. 12:22 Then one was brought to Him who was demon-possessed, blind and mute; and He healed him, so that the blind and mute man both spoke and saw.
14:14 And when Jesus went out He saw a great multitude; and He was moved with compassion for them, and healed their sick.
15:28 Then Jesus answered and said to her, “O woman, great is your faith! Let it be to you as you desire.” And her daughter was healed from that very hour.
15:30 Then great multitudes came to Him, having with them the lame, blind, mute, maimed, and many others; and they laid them down at Jesus’ feet, and He healed them.
19:2 And great multitudes followed Him, and He healed them there.
21:14 Then the blind and the lame came to Him in the temple, and He healed them.