Abstract: In this paper we introduce a bacteria-leukocyte model
with bacteria chemotaxsis. We assume that bacteria develop a tactic
defence mechanism as a response to Leukocyte phagocytosis. We
explore the effect of this tactic motion on Turing space in two
parameter spaces. A fine tuning of bacterial chemotaxis shows a
significant effect on developing a non-uniform steady state.
Abstract: In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain.
Here, the susceptible phytoplankton is growing logistically and the
growth of infected phytoplankton is due to the instantaneous Holling
type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further
explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain.
It is also observe that the reaction diffusion system exhibits spatiotemporal
chaos and pattern formation in phytoplankton dynamics,
which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient
on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis
of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern
formation.
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