You should be quoting violent crime rates rather than murder rates. The articles premise is that violent crime is infectious but the infection does not spread if the patients all die.
David Simon (The Wire, Tremane) notes that murder stats are hard to game: there's a corpse, and the determination is made by the coroner, not chief of police or sherrif.
Othe crime stats can be easily and massively gamed.
The game just shifts to one of attribution rather than what the rates are. A lot of physical violence would have resulted in death not too long ago, but thanks to medical technology like washing wounds, getting looked at by a doctor, ambulances, surgery, drugs, etc. it's much harder to die. The lack of as many deaths is then attributed to whatever cause is expedient (democracy, authoritarian crackdown, etc.) when technology and access to it is probably the best explanatory factor.
You can control for that by looking at the rate of treatment for gunshot wounds and similar, which in some countries show a similar decrease as in the overall deadly violence.
The inverse can also be true:
the famous French paradox (The French drink more red wine, but are healthier than the rest of Europe) might be caused lazy French coroners.
Even if "patients" die, their friends and brothers don't, and the violence spreads.
When looking at trends, murder rate is a better metric than counting violent crimes, because statistics for other violence are quite easily impacted by changes in policies of how to record reports.
A dead person is a dead person, it's a very consistent metric. Of course, it is also a changing metric as emergency care improves - wounds that used to be deadly can now be treated. For instance, Swedish cities are reporting a vastly improved care for shooting wounds, as hospitals have gained experience and developed methods in treating them.
Also murder rates have a confounding factor in that they can go down simply due to better medical technology allowing more people to survive murder attempts.
