It has been five days since the tiny plane carrying Vittorio Missoni, his companion Maurizia Castiglioni, and two of their close friends disappeared shortly after take-off from the island of Los Roques off the coast of Venezuela. Despite round-the-clock searches, there is still no trace of the plane or its passengers and two-man crew. But as each day passes, the Missoni family in Italy is actually more secure in their belief that the travelers are still alive. As long as they don’t find debris in the sea, they say there is a growing chance that Missoni was kidnapped.

In an extensive interview with Corriere della Sera newspaper on Wednesday, Missoni’s oldest son, Ottavio, 28, said he believes that his father will soon come back alive. “A plane cannot vanish in this way, on a short route, without leaving any trace,” he said. “I remain convinced that the least plausible reason is that they crashed into the water.”

Missoni and his family’s hopes were bolstered earlier this week when a mysterious message from the cellphone belonging to Guido Foresti, one of Missoni’s fellow passengers on the plane, reached Foresti’s son’s phone late Sunday night—more than 48 hours after the plane disappeared. The message, which said “Call now. We are reachable,” meant that the phone was back in range, which would be impossible if the plane and its contents were submerged. If the phone had somehow floated to the surface, it would likely have been rendered unusable from the water unless it was in an impermeable case, but even that seems far-fetched. No suitcases or other debris have been found on the beach or floating in the sea. The phone is again off and unreachable, meaning investigators cannot trace its location.

Vittorio Missoni’s brother, Luca, who is also a pilot, is currently in Venezuela flying on search missions with the local authorities. On Wednesday the Italian Foreign Ministry sent a specialized team of search-and-rescue divers—some of whom assisted in the Costa Concordia shipwreck last January—to Venezuela to assist in efforts to find the potential wreckage.

The Venezuelan government dismissed the Missoni family’s theory that the plane may have been part of a kidnapping ploy as “gossip,” even though the area is well known as a drug-smuggling haven where kidnapping is not unheard of. They have deployed 385 search-and-rescue specialists to find the missing plane. “The way the plane fell from radar does not correspond with the modus operandi of a kidnapping,” Enrique Martin, spokesman for the Venezuelan civil-protection authority told reporters. “In that type of scenario it happens completely differently.”

Meanwhile, Venezuelan pilot Enrique Rada told La Stampa newspaper that he witnessed Missoni’s plane take off and described how it was “swallowed by an aggregation of clouds” though the plane was on the radar long after it disappeared from sight, calling into question Rada’s eyewitness account. He believes that the plane was hit by a bolt of lightening and went down in deep water. He told the paper that the seas have strong undercurrents that could have pulled the debris out to sea, hindering search-and-rescue officials’ efforts to find the wreckage. Local newspapers in Caracas have also reported that a fishing crew witnessed the plane nosedive into the sea.

The Missoni family has refused to believe the worst. They are searching for any information that might back up the kidnapping theory, reaching out to potential enemies to find out if anyone might have wanted to harm Missoni or the other members of their party. “My father will come back,” Missoni’s son said. “We are all waiting for him.”