Step 1: Understand the problem.
Fatal malaria is transmitted via mosquito bites; the problem is urgent and dangerous.
Step 2: Evaluate Course I.
Fumigation directly reduces mosquito populations, tackling the root cause. This is a preventive and control measure — logically follows.
Step 3: Evaluate Course II.
Advising individuals to avoid bites (using nets, repellents, protective clothing) is also preventive and complements fumigation — logically follows.
Step 4: Combined necessity.
Since both measures address different aspects (environmental control and personal protection), both should follow.
\[
\boxed{\text{(D) Both I and II follow}}
\]