Crime is societal, it is a product of the construct of the particular society in which it is occurring. 
Crime generally thrives in situations in which people are denied the basic amenities of everyday living.  Usually when they are unable to work or source jobs which pay a livable wage.
On the other hand, crime thrives when people have jobs, homes and are really not too badly off but society makes it easy for those with the predisposition to commit crimes to do so.

View of parts of downtown Chicago

With the most sophisticated policing techniques available to law enforcement officers, crimes, including violent crimes will persist and grow if certain components of the mix are left unaddressed.
The city of Chicago police department in the state of  Illinois is the second-largest municipal police department in the United States. It has about 12,244 officers behind only the New York City Police Department.  Chicago has a population of 2,716,450.

Despite having the largest police department in the mid-west and all of the sophisticated accouterments of the trade, the city of Chicago has one of the highest homicide rates and violent crime in the nation.
This is not unique to the city of Chicago, the same is true of Detroit Michigan, and many other cities the length and breadth of the United States

So you ask, “If the police departments across the country are so well equipped and staffed why are there so many killings in the United States each year”?
If you ask that question it means you are thinking so I will try to address two factors which I believe are contributing to the over 33,000 gun killings which occur in the US each and every year.

Poverty and the lack of opportunities and a strident refusal to accept that there are far too many guns in the hands of far too many people who should ‘t have them have seriously influenced the continuation of violent crimes in the United States.
During the 1970’s to early 1980’s New York City was allowed to slide into depression, violent crime was rampant.  Many businesses fled to other areas more conducive to their bottom line.

New York City

After Mayor David Dinkins took over, he initiated something called “safe cities, safe streets”, this was a multi-faceted approach aimed at increasing the number of cops on the streets while improving police-community relations.
The other was prosecuting minor offenses thereby limiting the process of smaller criminals graduating to larger more violent crimes.

A cleanup of the city began and businesses started to return. Rudolph Guliani succeeded David Dinkins, he not only continued Dinkins’ policy he put them on steroids.
Getting caught with a gun in New York City meant mandatory prison time, on the gun charge as well as for the ammunition.
Violent crimes plummetted in NYC, as businesses returned so did the jobs.
Today NYC is one of the world’s safest big city.

It seems that the takeaway, at least to me, is that when we tackle the issues of poverty by providing jobs to people, ensure that we keep unregistered guns out of the hands of people, and most of all ensure that offenders are duly penalized the outcomes are positive.

Kingston, Jamaica – Aerial view to Kingston’s uptown area, called New Kingston.

If we co-opt the foregone and apply them to Jamaica, a country with the population of Chicago Illinois, we may be able to garner the results which were accomplished in New York City.
Today Chicago Illinois remains one of America’s most dangerous and violent cities because those who run the city failed to learn from the principles applied in New York City.
In Jamaica’s case, there is an (a) seeming lack of understanding of what it takes to reduce and ultimately eliminate violent crimes, and (b) an absence of will to get the job started.
So, instead, they blame the police for something which is far outside the scope of what the police can accomplish without executive input.