Bruce Monkhouse said:
Next!!!
[in a different thread of course]
MATH actually, a little outside your lane.
Model
Naturally, not all crime can be stopped; that would not be economically
desirable. This model seeks to optimize interventions so that crime is reasonably controlled and so that the cost is minimal. The two interventions considered are , the rate of converting those in poverty to recovered, and
, the rate of incarceration. In the model, the population is divided into
five sub-classes: the non-impoverished class N, the poverty class P, the
criminal class C, the jailed class J, and recovered class (from jail or from
impoverished class) R. The total population is T = N + P + C + J + R.
Let denote the rate of the flow from the non-impoverished class to the
impoverished class. It is assumed that sigma is omnipresent and dependent
upon the unemployment rate because of the nature of unemployment and
because of the dependency of poverty on unemployment. denote the conversion
rate from the P class to the R class due to government interventions;
the rate at which criminals is captured; denote the rate at which individuals
get out jails; µ is the death rate, and since T is constant (dT/dt = 0),
µ is also the birth rate. All rates are per capita.
We assume that there is a certain probability that a person in the P class
will resort to crime after coming into contact with a criminal. The term
PC/T is the conversion of impoverished individuals to criminals due to
contact over a certain period of time. represents the “transmission” rate.
A recovered individual may also become criminal again but at a reduced
rate RC/T where 0 1 is the reduction fraction that accounts
for recidivism. The known rate of recidivisim is around 50% (Bureau of
Justice Statistics, 2005). The assumption is that those who have already
gone to jail flow immediately into the R class, and then, due to contact with
criminals, revert back to criminality at some reduced rate . The rate
is reduced because these people have a greater cost to commit their next
crime, according to Becker’s theory (1968). All parameters are assumed
non-negative. Under these assumptions the interaction between poverty
and crime is governed by the following system:
http://mtbi.asu.edu/downloads/Document8.pdf