"Of which" does give the meaning of "whose." However, "of which" can be used interchangeably with "whose" only when both phrases refer to the same noun. That would not be the case in your sentence. "Of which" describes "about 30" of the common viruses, but "whose" would have to describe something true about all 100 common viruses.
The complete adjective clause is "about 30 of which are sexually transmitted." "About 30" tells how many out of the hundred common viruses are sexually transmitted. The expression of quantity (30) is really what's being described, not the noun "viruses."
On the other hand, you could use "whose" if the noun itself, "viruses," were being modified. It would describe all hundred viruses:
(a) HPV is a family of 100 common viruses whose behavior is extremely puzzling.
You could also say:
(b) HPV is a family of 100 common viruses of which the behavior is extremely puzzling.
(c) HPV is a family of 100 common viruses, the behavior of which is extremely puzzling.
In all the sentences above, "behavior" is the subject of the adjective clause, not "viruses." The entire adjective clause, though, modifies "viruses."
In the sentences below, "whose" and "of which" both describe the seats. The entire adjective clause modifies "car," and the subject of each of the adjective clauses is "seats."
(d) Martin has an antique car whose seats are made of red leather.
(e) Martin has an antique car of which the seats are made of red leather.
(f) Martin has an antique car, the seats of which are made of red leather.
Compare these sentences:
(g) The police ticketed forty-five cars whose license plates had expired.
(h) The police ticketed forty-five cars, 30 of which had expired license plates.
(i) The United States has fifty states whose senators convene in Washington, D.C.
(j) The United States has fifty states, 48 of which are contiguous.
(k) Our club donated over a hundred bicycles, whose owners were all young people, to a charity for handicapped children.
(l) Our club donated over a hundred bicycles, most of which belonged to young people, to a charity for handicapped children.
In these sentences, the first in each group has an adjective clause that modifies all the units in the main clause (cars, senators, and bicycles). The second sentence in each group has an adjective clause describing only some of the units in the main clause.
The construction of the first sentences in each group would not be appropriate for your sentence. The construction of the second sentence in each group could accurately reflect what your sentence says – that 30 out of the hundred viruses – NOT all hundred – are sexually transmitted.