  We model hypothetical bio-dispersal within a single Galactic region using the
stochastic infection dynamics process, which is inspired by these local
properties of life dispersal on Earth. We split the population of stellar
systems into different categories regarding habitability and evolved them
through time using probabilistic cellular automata rules analogous to the
model. As a dynamic effect, we include the existence of natural dispersal
vectors (e.g., dust, asteroids) in a way that avoids assumptions about their
agency. By assuming that dispersal vectors have a finite velocity and range,
the model includes the parameter of 'optical depth of life spreading'. The
effect of the oscillatory infection rate on the long-term behavior of the
dispersal flux, which adds a diffusive component to its progression, is also
taken into account. We found that phase space is separated into subregions of
long-lasting transmission, rapidly terminated transmission, and a transition
region between the two. We observed that depending on the amplitude of the
oscillatory life spreading rate, life-transmission in the Galactic patch might
take on different geometrical shapes. Even if some host systems are
uninhabited, life transmission has a certain threshold, allowing a patch to be
saturated with viable material over a long period. Although stochastic
fluctuations in the local density of habitable systems allow for clusters that
can continuously infect one another, the spatial pattern disappears when life
transmission is below the observed threshold, so that transmission process is
not permanent in time. Both findings suggest that a habitable planet in a
densely populated region may remain uninfected.
