Step 1: Define a propagated epidemic. A propagated (progressive) epidemic spreads by serial person-to-person transmission. Its epidemic curve shows a series of progressively taller peaks, each separated from the next by roughly one incubation period, as successive generations of cases occur.
Step 2: Match to the disease type. This pattern requires direct human-to-human spread. Measles is a highly contagious, directly transmitted (respiratory droplet) viral infection, so it produces the classic multiple-peaked propagated epidemic curve with peaks one incubation period apart.
Step 3: Select the answer. Measles (option 1) is the textbook example of a propagated, person-to-person epidemic.
Step 4: Why the others are wrong. Staphylococcal food poisoning (option 2) and Salmonella food poisoning (option 4) are common-source, point-source outbreaks from contaminated food — a single sharp peak, no serial generations. Typhoid (option 3) is typically a common-source (water/food-borne) outbreak as well; although secondary spread can occur, it is not the classic example of a multiple-peaked propagated epidemic in the way measles is.
Key fact: A propagated epidemic with peaks one incubation period apart is characteristic of directly transmitted infections like measles.