I'm not sure that disaster response and public health are mutually exclusive, or how far non-specialists can get with this. In any case, the disaster response consists of getting Wikipedia-based knowledge into areas without internet, either as an offline resource via Wiki Project Med/App, or a local internet connection, so, in any case, they can only provide as much information as is already in Wikipedia.
Doing a spot check on children's health, individual articles that have been adopted by WikiProject Medicine, like chickenpox and rubella, seem to be well developed, but the navigation is hard to follow. There is a category for "pediatrics" also for "children's health", but where is the navbox to tie everything together? What if you want to know something about standard vaccines, for example, or psycho-social issues, or the reemergence of polio in war zones. What if you want to work on or evaluate a series of articles around a central theme, or you want information to care for your own children?
Compare the extensive connection of articles at "Women's health" with navigation templates at both the right sidebar and footer areas. Compare also the pitiful coverage of "Men's heath", which a google search resolves to an article about a Rodale publication of that name. A note at the top of that article says "For health issues that apply specifically to men, see men's health", which links to a pitiful start-class article with a somewhat promotional tone, rated "low-importance" by Wikproject Medicine, that has sported an incomplete tag since 2015. The "men's health" article only has a navigation template for "reproductive health". There is a Rodale magazine called Women's Health, but Wikipedia does not consider the magazine to be the "primary topic"
(WP:PRIMARYTOPIC) according to Wikipedia's naming conventions. It has the secondary topic title format of "Women's Health (magazine)" and an additional note at the top: "It is not to be confused with the academic journals, Women's Health Issues (journal), or Journal of Women's Health."
And where is "domestic violence" or "sexual assault" in the men's health roster? Are these women's topics only? For that matter, where is "prostate-specific antigen blood test". You can find more information about these topics on reddit than on Wikipedia.
https://en.wikipedia.org/wiki/Category:Pediatricshttps://en.wikipedia.org/wiki/Category:Children%27s_healthhttps://en.wikipedia.org/wiki/Women%27s_healthhttps://en.wikipedia.org/wiki/Men%27s_Healthhttps://en.wikipedia.org/wiki/Men%27s_healthhttps://en.wikipedia.org/wiki/Women%27s_Health_(magazine)