Okay, I might be reaching a bit on this one. The opening of John’s gospel says that ‘the Word became flesh and dwelt among us.’ The teaching of the New Testament is that the son of God became fully human (whilst also remaining fully divine, but we can puzzle over that another time). There’s a good article on Jesus’ humanity over at Desiring God if you’d like to read a bit more on that.
Now if he’s fully human, he will for his time on Earth have been just as susceptible to disease and illness as we are. On the other hand, the Bible never records him getting ill (other than the ordeal of the cross). Also, almost whenever Jesus encounters ill health he prays for the patient and they are miraculously healed – the notable exceptions seeming to be those who lack faith, for instance in Nazareth in Mark 6:4-6. Would Jesus have suffered through head colds and tummy bugs to better understand and sympathise with humanity, or would he have prayed to his Father in heaven with complete faith for healing and be shot of them? I don’t know. The Bible doesn’t tell us, but for the purposes of this comic, I’m going to go ahead and say that he was a manly dude and he didn’t take a whole lot of sick leave.