The patron saints against illness are:
Alphais
Alphonsa of India
Angela Merici
Angela Truszkowska
Arthelais
Bathild
Bernadette of Lourdes
Camillus of Lellis
Catherine del Ricci
Catherine of Siena
Drogo
Edel Quinn
Elizabeth of the Trinity
Gerard of Villamagna
Germaine Cousin
Gertrude of Nivelles
Gorgonia
Hilary of Poitiers
Hugh of Lincoln
Isabella of France
Jacinta Marto
John of God
Julia Billiart
Julia Falconieri
Juliana of Nicomedia
Louis IX
Louise de Marillac
Lydwina of Schiedam
Maria Bagnesi
Maria Gabriella
Maria Mazzarello
Marie Rose Durocher
Mary Ann de Paredes
Mary Magdalen of Pazzi
Michael the Archangel
Our Lady of Lourdes
Paula Frassinetti
Peregrine Laziosi
Philomena
Rafka Al-Rayes
Raphael the Archangel
Romula
Syncletica
Teresa of Avila
Terese of the Andes
Therese of Lisieux
Saint Teresa of Avila is the patron saint of illness/headache sufferers
Which Saint Francis? There are several.
Saint Dymphna is the patron saint of mental illness in the Greek Orthodox tradition. She is believed to intercede to provide comfort and support to those struggling with mental health issues.
Against Illness
There is no record of any illness that Nicholas of Myra may have had.
Brigid of Ireland is the patron saint of healers.
Saint Dymphna is recognized as the patron saint of mental illness and those afflicted with mental and neurological disorders. She is known for her compassionate nature and is often invoked for strength and comfort in times of mental distress.
There is no patron saint of the mind but there are patron saints against mental illness.
Saint Rita of Cascia. She is also the saint of lost causes, sickness, wounds, illness, and mothers.
She suffered from malaria much of her life.
Saint Michael the Archangel is the patron saint of anyone who serves for the defense of others. Saint Joseph of Cupertino is the patron saint of people traveling by air including pilots, astronauts and other aircrew personnel.
She probably died of complications of old age.
There are several saints named Anthony. Please be specific.