Abstract: We present analysis of spatial patterns of generic
disease spread simulated by a stochastic long-range correlation SIR
model, where individuals can be infected at long distance in a power
law distribution. We integrated various tools, namely perimeter,
circularity, fractal dimension, and aggregation index to characterize
and investigate spatial pattern formations. Our primary goal was to
understand for a given model of interest which tool has an advantage
over the other and to what extent. We found that perimeter and
circularity give information only for a case of strong correlation–
while the fractal dimension and aggregation index exhibit the growth
rule of pattern formation, depending on the degree of the correlation
exponent (β). The aggregation index method used as an alternative
method to describe the degree of pathogenic ratio (α). This study may
provide a useful approach to characterize and analyze the pattern
formation of epidemic spreading
Abstract: The dynamics of Min proteins plays a center role in
accurate cell division. Although the nucleoids may presumably play
an important role in prokaryotic cell division, there is a lack of
models to account for its participation. In this work, we apply the
lattice Boltzmann method to investigate protein oscillation based on a
mesoscopic model that takes into account the nucleoid-s role. We
found that our numerical results are in reasonably good agreement
with the previous experimental results On comparing with the other
computational models without the presence of nucleoids, the
highlight of our finding is that the local densities of MinD and MinE
on the cytoplasmic membrane increases, especially along the cell
width, when the size of the obstacle increases, leading to a more
distinct cap-like structure at the poles. This feature indicated the
realistic pattern and reflected the combination of Min protein
dynamics and nucleoid-s role.