  We study a nonlocal balance equation that describes the evolution of a system
consisting of infinitely many identical particles those move along a
deterministic dynamics and can also either disappear or give a spring. In this
case, the solution of the balance equation is considered in the space of
nonnegative measures. We prove the superposition principle for the examined
nonlocal balance equation. Furthermore, we interpret the source/sink term as a
probability rate of jumps from/to a remote point. Using this idea and replacing
the deterministic dynamics of each particle by a nonlinear Markov chain, we
approximate the solution of the balance equation by a solution of a system of
ODEs and evaluate the corresponding approximation rate. This result can be used
for construction of numerical solutions of the nonlocal balance equation.
