Is a patient with a spinal disc condition and a foul odor sinful if he prays in his home instead of going to the mosque?

If you are sick and would be harmed by going to the mosque, there is no sin upon you for missing the congregational prayer. The mosque is not a condition for performing the congregational prayer. If you are able to pray in congregation at home with some of your family, then the obligation, which is performing the prayer in congregation, is fulfilled by that, and you will receive the reward of the congregation.