(CNN) Without a heart transplant, three-week-old Carter Cookson has just days to live.

The baby boy, from South Shields in the northeast of England, suffered three cardiac arrests after his birth on December 26, and a subsequent operation to fit a pacemaker revealed dead tissue in the left ventricle of his heart.

Parents Sarah and Chris Cookson have launched a social media campaign, #findaheartforcarter , in the hope of finding a donor for their son.

In 2013, they lost their first child, two-year-old Charlie , to a progressive disease doctors could not identify. The toddler couldn't breathe, eat, or sit up unassisted, and suffered frequent seizures. "It took five years after that for us to try again," Chris Cookson told CNN. "Now we're very much in the same situation again."

Carter is being treated at the Freeman Hospital in the English city of Newcastle, where an ECMO machine -- a life-support apparatus that performs the functions of the heart and lungs -- is keeping him alive. While doctors initially predicted the baby boy had five weeks to live in the absence of a transplant, issues with blood clots in the machine reduced his life expectancy further.

Read More