Well when the zombie plague starts there are going to be a lot of other ways to die. Diseases being one. After the San Fransisco earthquake of 1906, there were several outbreaks of bubonic plague caused by rats carrying infected fleas.
The WHO outlines three main factors for how diseases increase after a disaster, dirty drinking water, overcrowding and disease carrying pests.
There are some basic things you can do. Sterilise drinking water, maintain proper hygiene and good sanitation are examples. These simple measures can be very effective. It has been estimated that if everyone in the world washed their hands properly, one million lives would be saved each year, and phone screens would be cleaner.
Bite off more than you can chew