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This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
The Red-face Pox made it across to the mainland and has Gendercided the planet by the time of Chapter 1
The odds of a carrier fleeing the plague making it across the Sea of Japan before the order to seal the borders are pretty good, and once it got going in China/Korea it is a matter of time before all of Eurasia is hosed.
On Blessed Kasuga's orders, the stage management of the VOC's contact with the shogunate has succeeded in concealing the lack of Japanese men from the Dutch sailors. Like the Inner Chambers (which are used for the Kapitan's annual audience with the shogun), Deshima has an unusually high male population to help maintain the facade...but even there many of the men are either past their breeding prime or are actually women in drag like Gondayu.
Certainly, Yoshimune has decreed physicians to find a cure for the Redface Pox. If that is cured then it's a matter of building up the population.
I think I have to amend this WMG: based on reports that the mangaka wanted to end at Volume 10, the front cover (if Amazon is to be believed) has many people instead of just one (which makes me think it's the Grand Finale), and Harusada (daughter of Yoshimune's youngest daughter, and historically will provide Ieharu's heir) has at least one son (that is seen anyway), it's possible that the pox will end right around the time the male Ienari takes power. (Without being able to read Japanese though, I wouldn't be able to confirm or deny it though.)
Which is just as well, really, while it'd have been symbolic to make status quo become God at the Meiji Restoration, as of volume nine we're only two shoguns away from Commodore Perry forcing Japan open at gunpoint. It'd have to be restored by then or else the Americans wouldn't think twice about forcing Manifest Destiny on them and that's too wildly Alternate Timeline, even for Ooku.
Given that "Women's Work" is at this point is "Everything but Dutch Medicine and perhaps soldiery" there is a lot of inertia to overcome if anyone seeks to restore pre-plague-patriarchy. Things will get more egalitarian than the current Lady Land, but the governing classes are not going to conveniently die off.
More to the point, even if the rest of the world dodged the proverbial bullet in terms of the Red-Faced Pox, the opening of Japan will smack the rest of the world with a virgin field epidemic almost tailor made to shatter the Imperial Powers of the age.
Fair points to both. To address the former...perhaps population status quo is restored by the time Perry shows and patriarchy restored by the Meiji Restoration? And as for the latter that does bring to mind something: we only have a Dutch captain's word that the rest of the world is unaffected, and for all we know, he could have left the Netherlands right before the Redface Pox hits. If the pox started in bears that spells trouble cause unless this is a species of bear exclusive to Japan, it could spread to other bears before it hits humans, and all it would take is one bear or infected human to make it to the mainland to spread it. For all we know, ALL of the world got poxed. Which brings me to my new WMG.
Update: There have been reports that there will be a volume 11, but it does indeed look like we're building up to a climax/denouement: Harusada's son Takechiyo/Toyochiyo has been crowned Shogun Ienari.
The manga will end with Commodore Perry arriving...and Perry will be a woman.
Turns out Japan had nothing to worry about regarding conquest: the Redface Pox was a worldwide epidemic and women are the dominant gender around the world.
Spoilers for Basilisk WILL follow. The whole plot is basically 'two ninja clans fight and who wins decides who will be shogun next, the future Iemitsu or his brother'. Kasuga, then known as Lady Ofuku, sided with the Iga and had tried to manipulate events so they would win, despite it being verboten to intervene in the fight. After Oboro, the heiress of the Iga clan, died, Ofuku tried to get her men to kill Gennosuke, the heir to the Koga clan, only for her men to kill themselves due to Gennosuke's special ability. Ofuku suffered a Villainous Breakdown at her belief that she had lost and Takechiyo (Iemitsu) would be displaced as heir. As punishment, Hattori Hanzo never told her that Gennosuke abdicated victory and that Takechiyo would be shogun after all. However, she never recovered from her breakdown and, in her delusion, began to imagine a world where her beloved Takechiyo became shogun after all. In truth though, she wanted power for herself, which is why she started imagining Iemitsu as female. Thus all the later shoguns were female-they are herself. Yes, even after she would be dead, but this is the delusions of an insane woman.