What should a Muslim doctor do if he is the only one who possesses a cure for an epidemic that has spread in a non-Muslim country, and would he be sinful if he deliberately concealed the cure?

There is no harm in showing kindness to disbelievers who are not at war [with Muslims] or who do not support the enemies of the religion. This is based on the Almighty’s saying: "Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly." A Muslim is also commanded to show general kindness to all people, as in His Almighty's saying: "And speak to people good [words]." Such kindness has positive effects in inviting them to Islam, as happened with Thumamah ibn Uthal, may Allah be pleased with him, when he embraced Islam due to the Prophet's kindness towards him. This shows that kindness removes hatred and establishes love.