Pharmaceutical compositions are described comprising fucoidan for use in a method for the treatment or the prevention, by intranasal administration, of coronavirus infection in a human. Particularly, the viral infection is OC43 or SARS-CoV-1 or SARS-CoV-2 infection. There are also described Pharmaceutical compositions comprising fucoidan for use in a method for prevention coronavirus spread in a human population, wherein subjects of the population are tested for infection with OC43 or SARS-CoV-1 or SARS-CoV-2 and infected subjects are treated with intranasal administration of the Pharmaceutical composition.