Improper disposal of garbage and human waste leads to disease. In fact, the two greatest factors in increasing human longevity have been improved nutrition and improved sanitation. Improvements in medical treatment come in third.
So let's talk about sewage disposal. What happens when the sewage and water plants shut down? Well, you better be ready to do something about it yourself. If you have a septic tank system you can continue to use an indoor toilet, but you will have to haul buckets of water to flush the toilet. When we have a power outage my water well only works if I have my generator going. I don't like to run the generator all the time, so I fill up a five gallon plastic bucket with water and set it in the bathroom. One bucket of water will serve to flush the toilet two or three times. Another alternative is to buy a portable, chemical toilet; but I find the bucket of water to be easier. In the city, if the water goes out you will have to use a chemical toilet. You wouldn't want to waste any of the water that you have to flush a toilet. If the problem is long-term you're going to need to leave the city anyway, so I wouldn't bother trying to put together an elaborate waste disposal system
For us country folks the old timey outhouse is a long-time tradition. You still see outhouses in the country, and I just happen to have a working model on my farm. I'll grant you that it doesn't get used very often, but I have one, and it works!
An outhouse should be located a good distance away from your house. It should be at least a hundred feet from your home and I would recommend that it be at least two hundred feet from your water well or garden. An outhouse is basically just a hole in the ground with a seat over the top of it. The fecal matter falls into the hole where it can decompose. It is important to treat the waste after each use so that it will not attract flies. You can do this by sprinkling powdered lime in the hole, or you can do it the old timey way and use hardwood ashes. I keep a five gallon bucket of lime and a coffee can in my outhouse. After use you just dip up a little lime and sprinkle away.
I keep toilet tissue in my out house, but back in the day they used pages torn from an old Sear's catalogue or even corn cobs. Trust me, corn cobs are not the route to go.
One caution about outhouses. Beware of spiders. It is a good idea to hang one of those plastic no-pest-strips down under the toilet seat to discourage spiders and other bugs from making a home in your outhouse.
One final word on human waste disposal. Please do not try and compost human waste to use on your garden. The human digestive tract contains e. coli bacteria, and if any of these bacteria survive the composting process you could have serious problems. Many of the e. coli outbreaks that you hear about on the news are the result of agricultural workers defecating in the fields as they work. You can get deadly sick from this bacterium, so be safe and don't fertilize with human waste.