In February, the court ruled that Alder Hey Children's Hospital, where Evans is receiving care, could legally stop treatment for Alfie against his parent's wishes, arguing that continuing treatment is not in his best interest, and that his life support should be switched off.
Despite the desire for Alfie's parents, Kate James and Tom Evans, to take their son to Bambino Gesu hospital in Rome, several judges have ruled in the hospital's favor.
The case has drawn international attention, and protesters gathered outside the Liverpool hospital Thursday and Friday to peacefully oppose the decision.
Evans and James recently launched a new legal challenge, asking the Court of Appeal judges to continue life support and treatment for Alfie. The court officials posted their hearing for Monday, saying that a court judge has decided that Alfie could continue treatment, pending the hearing.
In the case of Vincent Lambert, a severely disabled Frenchman without a terminal illness, courts have decided that the Sebastopol Hospital in Reims can remove Lambert's food and water April 19.
Lambert suffered severe head injuries after a tragic car accident in 2008, and as a result has been a quadriplegic and severely disabled for 10 years. Yet despite his injuries, other doctors and his parents have insisted that Lambert is not sick, nor is he in a coma. They argue that he breathes unassisted and his internal organs function normally.
However, despite these arguments, the hospital ruled that continuing to feed and hydrate Lambert constituted "unreasonable obstinacy" toward him, and said that his feeding tubes ought to be taken out.
These and similar cases are "delicate situations, very painful and complex," Francis said, and asked faithful to pray with him that every person who is sick would "always be respected in their dignity and cared for in a way suited to their condition, with the consent of family members, and of other healthcare workers."
He also offered prayers for three Ecuadorean men who were recently kidnapped and killed along the Ecuador-Colombia border, voicing his closeness to their families and praying for peace and unity in the area.
Francis then prayed for areas of the world torn by conflict "despite the instruments available to the international community," and pointed specifically to Syria, where conflict has again flared up in recent days.
A fresh round of threats began when the United States and their allies in France and the UK on Friday ordered a series of bombings on chemical facilities in Syria in retaliation for a chemical attack allegedly carried out last week by Syrian President Bahsar al-Assad which killed more than 40 civilians.
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World leaders immediately reacted supporting both sides, with Syria promising retaliation, and U.S. President Donald Trump threatening further attacks if Assad does not stop using chemical weapons on civilians.
In his Regina Coeli address, Francis said he is "deeply troubled" by ongoing global conflict, and invited all men and women of goodwill to continue to "incessantly pray for peace." He issued a fresh appeal to political leaders, "so that justice and peace will prevail" over violence.