More Words, Deeper Hole

Any of the influenzas (there are theoretically 198 possible strains of influenza A based on surface proteins alone, not even counting the as-yet unknown strains circulating in bats and the like; also flu B and C) are plausible, but have fairly short incubation times so you'd have to get the ship back home within a couple of weeks or so. Measles also has the short incubation time problem, compounded by its incredible transmissibility (at least flu you could argue takes some time to spread through a ship's population). Yersinia pestis has a strong precedent. Tuberculosis and leprosy have long incubations and could spread widely before being recognized, and there are significant genetic components to susceptibility for each. Diseases like norovirus and rotavirus aren't usually fatal in modern humans, but are very contagious and especially norovirus has a strong genetic component to susceptibility too. Obvious other possibilities include mumps, rubella, diphtheria, pertussis, and polio (though that has a low symptomatic rate that isn't obviously influenced by genetics).