For a class of time inhomogenous distribution dependent birth-death processes, we derive the well-posedness, Wp-estimate, exponential ergodicity, and uniform in time propagation of chaos. These extend the corresponding results derived for distribution dependent stochastic differential equations and mean field particle systems. As preparation, a criterion on the well-posedness of inhomogenous jump process is presented in the end of the paper, which should be interesting by itself.
Wang et al. (2026) studied this question.