Next post in category based on menu order

I have a couple of categories book titles with the posts being chapters within the book. I’ve used a plugin to reorder the chapters so they’re in the right order on my category.php page, but if I add “next” and “previous” links to each chapter page, they will take me to the next or previous post based on the date they were originally entered into WP. Is there a way to overcome that so the links will take me from one chapter to the next?

Thanks.