  This paper presents a model for active particles in two dimensions with
time-dependent self-propulsion speed undergoing both translational and
rotational diffusion. Usually, for modeling the motion of active particles, the
self-propulsion speed is assumed to be constant as in the famous model of
active Brownian motion. This assumption is far from what may happen in reality.
Here, we generalize active Brownian motion by considering stochastic
self-propulsion speed $v(t)$. In particular, we assume that $v(t)$ is a
two-state process with $v=0$ (passive state) and $v=s$ (active state). The
transition between the two states is also modeled using the random telegraph
process. It is expected that the presented two-state model where we call it
active-passive Brownian particle has the characteristics of both pure active-
and pure passive-Brownian particle. The analytical results for the first two
moments of displacement and the effective diffusion coefficient confirm this
expectation. We also show that a run-and-tumble particle (such as a motile
bacterium) can be mapped to our model so that their diffusivities at large
scales are equal.
