People (Crime), Diseases, Animals, Roads .....
These issues will be addressed by the PH/Outfitter, your Doctor/Travel Clinic, the PH/Outfitter, the PH/Outfitter.
You are not heading to downtown Chicago, etc.
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This is where you are headed.
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You are in the care of a PH during your entire safari. It's their job to keep you safe no matter where you are headed.
Namibia, South Africa, Botswana, Zambia, Mocambique, Zimbabwe, Tanzania, Ethiopia, Uganda will all have issues of some fashion.
Everyone has a different risk tolerance. I have no trouble driving myself through South Africa, Namibia, or Botswana. If I had the time I'd give Zambia and Zimbabwe a go. The others, not on my radar.
Hunting in any of them with a professional, no problem. Get a trusted outfit and go hunting.
Skip the countries that are actually having large scale internal wars or whatevers:
Burkina Faso, Cameroon, the Central African Republic (CAR), the Democratic Republic of the Congo.
Ethiopia, Mozambique have some localized conflicts. AH Members have hunted both and been just fine. I felt just fine in Mozambique and would go into Ethiopia in a heart beat.
Blah Blah stats. (You are not heading into high crime areas so grain of salt.)
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Good luck with your research.