I'm almost sure it will be the case but not directly due to supply demand

Define “global”, “famine”, and “soon”.

Intense food shortages in some regions? Reportedly already happening due to the closure of the strait of Hormuz.

Absolutely every region experiencing food shortages to the point of widespread starvation everywhere? Not entirely unlikely within the next 50 years, but doubtful within 5.

The wars in Ukraine, 4+ years, and Afghanistan, 20+ years, took food production off the suppy chain and you can see the knockon effects from there. People in the know say one third of fertilizer has been taken off the supply chain in the latest war expansion to the Hormuz chokepoint and, due to price rises, lower social classes in Italy, for example, have enough to buy three of four weeks a month to keep their family in shape.

Famine and disease always follows wars. The more wars, the more famines. It's not just supply chains. Very often things are delayed - shortage of fertilizer will impact things a year later.