Does immunity disprove the fall?

16 To the woman he said,
"I will greatly increase your pains in childbearing;
with pain you will give birth to children.
Your desire will be for your husband,
and he will rule over you."17 To Adam he said, "Because you listened to your wife and ate from the tree about which I commanded you, 'You must not eat of it,'
"Cursed is the ground because of you;
through painful toil you will eat of it
all the days of your life.18 It will produce thorns and thistles for you,
and you will eat the plants of the field.19 By the sweat of your brow
you will eat your food
until you return to the ground,
since from it you were taken;
for dust you are
and to dust you will return."

But this is the whole story of creation told (twice) in less than a page.

Just because details are in short supply, are we to understand that there were no details to provide?

Given this, perhaps the immune system was the agent of god's punishment that brings suffering and death.

16Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children; and thy desire shall be to thy husband, and he shall rule over thee.17And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life;18Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field;19In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.