And the toll of waiting for him to be well enough to leave a foreign hospital is clearly taking its toll on new mother Katie Price.
The mother-of-four, 35, took to Twitter on Wednesday and revealed her little boy is suffering from breathing problems during his stay in a special care baby unit.
Loved up: Katie Price shares a kiss with husband Kieran Hayler in a candid Twitter photo following the birth of their son last week
Stressful times: Katie admitted her newborn son was struggling to breathe
Katie and husband Kieran Hayler, 25, welcomed their first child together in a hospital on the continent earlier this month, although a birthdate hasn't been formally announced.
Jett's arrival eight weeks early via Caeserean section came after Katie was admitted to hospital while on holiday after suffering complications in her pregnancy.
She tweeted on Wednesday: 'Me & @kieran0322 miss home soo much & miss our family & friends its been 5 weeks now! Jett still in baby unit with breathing problems :((.'
Her latest message comes two days after she tweeted about her hopes that Jett, who weighed 5lbs 2oz, would soon be strong enough to be discharged so they could return to England.
Hiding out: Katie and Kieran have spent the past few weeks on the continentKatie has been missing her two other children Princess Tiaamii and Junior, who are believed to be with their father Peter Andre.
She wrote on Monday: 'Me & my hubby @kieran0322 still abroad with our baby Jett in hospital praying he will be ok and out soon #homesick.'
It is unknown whether her eldest son Harvey is with Katie and Kieran, who are staying in a villa near the hospital.
Last week, Katie was photographed for the first time since giving birth, in a candid Twitter image with her husband Kieran.
Uploading a photo of them kissing on his Twitter page, Kieran wrote: 'Its been a tough 3 weeks but we are closer and more in love than ever before. I love my wife @MissKatiePrice xxx.'
Forever: Kieran tweeted a photo of him and his wife's wedding rings
He then uploaded a photo of themselves holding hands, writing: 'In sickness and in health!!! We can get through anything.... #strongerthanever #vows.'
Katie and Kieran wed in front of just a few people in the Bahamas on January 16 after getting engaged after Christmas - just two months after she ended her 20 month on/off romance with Argentine model Leandro Penna.
In February, Katie announced she was pregnant with her fourth child.
Her surprise pregnancy comes after failed IVF attempts to start a family with Leandro and second ex-husband Alex Reid.
She started dating Alex just a few months after splitting from first husband Peter Andre, but left him in January 2011 after 11 months of marriage.
She also had a 20 month on/off romance and subsequent engagement with Leandro, but they never made it down the aisle.