A REACTION–DIFFUSION MODEL FOR THE CONTROL OF CHOLERA EPIDEMIC

2016 ◽  
Vol 24 (04) ◽  
pp. 431-456 ◽  
Author(s):  
A. K. MISRA ◽  
ALOK GUPTA
Keyword(s):  
Temporal Dynamics ◽  
Temporal Distribution ◽  
Reaction Diffusion ◽  
Effective Control ◽  
Lytic Bacteriophage ◽  
Cholera Epidemic ◽  
Reaction Diffusion Model ◽  
Spatially Extended ◽  
Control Procedures ◽  
Spatio Temporal

Understanding the spatio-temporal dynamics of cholera outbreaks may help in devising more effective control procedures. In this paper, we have considered a reaction–diffusion system for biological control of cholera epidemic. Firstly, we have focused on temporal evolution of cholera in a region and its control using lytic bacteriophage in the aquatic reservoirs. Then, we have explored the effect of spatial dispersion of populations on the disease dynamics. We have observed the onset of sustained oscillations via Hopf-bifurcation for the endemic state of temporal system. This onset of fluctuations in populations depends upon the phage adsorption rate. But in the spatially extended setting, all the populations stabilize i.e., the spatio-temporal distribution of all the populations becomes uniform. Some numerical computations have been done to verify analytical results.

scholarly journals From chemical soup to computing circuit: transforming a contiguous chemical medium into a logic gate network by modulating its external conditions

2019 ◽  
Vol 16 (158) ◽  
pp. 20190190
Author(s):  
Matthew Egbert ◽  
Jean-Sébastien Gagnon ◽  
Juan Pérez-Mercader
Keyword(s):  
Logic Gate ◽  
Reaction Diffusion ◽  
Logic Gates ◽  
Full Adder ◽  
Integrated Network ◽  
Lighting Conditions ◽  
Reaction Diffusion Model ◽  
Spatially Extended ◽  
External Conditions ◽  
Spatially Extended Systems

It has been shown that it is possible to transform a well-stirred chemical medium into a logic gate simply by varying the chemistry’s external conditions (feed rates, lighting conditions, etc.). We extend this work, showing that the same method can be generalized to spatially extended systems. We vary the external conditions of a well-known chemical medium (a cubic autocatalytic reaction–diffusion model), so that different regions of the simulated chemistry are operating under particular conditions at particular times. In so doing, we are able to transform the initially uniform chemistry, not just into a single logic gate, but into a functionally integrated network of diverse logic gates that operate as a basic computational circuit known as a full-adder.

scholarly journals IcePAC – a probabilistic tool to study sea ice spatio-temporal dynamics: application to the Hudson Bay area

2019 ◽  
Vol 13 (2) ◽  
pp. 451-468 ◽  
Author(s):  
Charles Gignac ◽  
Monique Bernier ◽  
Karem Chokmani
Keyword(s):  
Sea Ice ◽  
Temporal Dynamics ◽  
Numerical Models ◽  
Temporal Distribution ◽  
Grid Cell ◽  
Hudson Bay ◽  
Sea Ice Concentration ◽  
Temporal Behaviour ◽  
Ice Conditions ◽  
Spatio Temporal

Abstract. A reliable knowledge and assessment of the sea ice conditions and their evolution in time is a priority for numerous decision makers in the domains of coastal and offshore management and engineering as well as in commercial navigation. As of today, countless research projects aimed at both modelling and mapping past, actual and future sea ice conditions were completed using sea ice numerical models, statistical models, educated guesses or remote sensing imagery. From this research, reliable information helping to understand sea ice evolution in space and in time is available to stakeholders. However, no research has, until present, assessed the evolution of sea ice cover with a frequency modelling approach, by identifying the underlying theoretical distribution describing the sea ice behaviour at a given point in space and time. This project suggests the development of a probabilistic tool, named IcePAC, based on frequency modelling of historical 1978–2015 passive microwave sea ice concentrations maps from the EUMETSAT OSI-409 product, to study the sea ice spatio-temporal behaviour in the waters of the Hudson Bay system in northeast Canada. Grid-cell-scale models are based on the generalized beta distribution and generated at a weekly temporal resolution. Results showed coherence with the Canadian Ice Service 1981–2010 Sea Ice Climatic Atlas average freeze-up and melt-out dates for numerous coastal communities in the study area and showed that it is possible to evaluate a range of plausible events, such as the shortest and longest probable ice-free season duration, for any given location in the simulation domain. Results obtained in this project pave the way towards various analyses on sea ice concentration spatio-temporal distribution patterns that would gain in terms of information content and value by relying on the kind of probabilistic information and simulation data available from the IcePAC tool.

Critical Slowing-Down of Spatially Nonhomogeneous Patterns in a Reaction–Diffusion Model

1997 ◽  
Vol 11 (14) ◽  
pp. 1717-1730 ◽  
Author(s):  
Fernando Castelpoggi ◽  
Horacio S. Wio ◽  
Damian H. Zanette
Keyword(s):  
Diffusion Model ◽  
Lyapunov Functional ◽  
Reaction Diffusion ◽  
Critical Slowing Down ◽  
Threshold Parameter ◽  
Extended System ◽  
Slowing Down ◽  
Reaction Diffusion Model ◽  
Spatially Extended ◽  
Nonequilibrium Potential

We exploit the concept of the nonequilibrium potential in order to analize the approach to stationary homogeneous and nonhomogeneous equilibrium states in a bounded bistable reaction-diffusion model. The analysis proceeds through the study of the Lyapunov functional, in terms of a control parameter -the threshold parameter ϕc-in the neighbourghood of a critical point (where a stable and an unstable pattern coalesce), that clearly shows the phenomenon of critical slowing-down in a spatially extended system.

SPATIO-TEMPORAL PATTERNS IN A CHOLERA TRANSMISSION MODEL

2015 ◽  
Vol 23 (03) ◽  
pp. 471-484 ◽  
Author(s):  
A. K. MISRA ◽  
MILAN TIWARI ◽  
ANUPAMA SHARMA
Keyword(s):  
Spatial Patterns ◽  
Dimensional Space ◽  
Spatial Dynamics ◽  
Transmission Model ◽  
Cholera Epidemic ◽  
Temporal System ◽  
Spatially Extended ◽  
Variable Population ◽  
Spatio Temporal ◽  
Variable Population Size

Cholera has been a public health threat for centuries. Unlike the biological characteristics, relatively less effort has been paid to comprehend the spatial dynamics of this disease. Therefore, in this paper, we have proposed a cholera epidemic model for variable population size and studied the spatial patterns in two-dimensional space. First, we have performed the equilibrium and local stability analysis of steady states obtained for temporal system. Afterwards, the local and global stability behavior of the endemic steady state in a spatially extended setting has been investigated. The numerical simulations have been done to investigate the spatial patterns. They show that dynamics of the cholera epidemic varies with time and space.

scholarly journals Stochastic simulation of the spatio-temporal dynamics of reaction-diffusion systems: the case for the bicoid gradient

2010 ◽  
Vol 7 (1) ◽  
Author(s):  
Paola Lecca ◽  
Adaoha E. C. Ihekwaba ◽  
Lorenzo Dematté ◽  
Corrado Priami
Keyword(s):  
Diffusion Coefficient ◽  
Stochastic Simulation ◽  
Diffusion Coefficients ◽  
Temporal Dynamics ◽  
Concentration Field ◽  
Reaction Diffusion ◽  
Local Concentration ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatio Temporal

SummaryReaction-diffusion systems are mathematical models that describe how the concentrations of substances distributed in space change under the influence of local chemical reactions, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose solution predicts how diffusion causes the concentration field to change with time. This change is proportional to the diffusion coefficient. If the solute moves in a homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and solute. However, in nonhomogeneous and structured media the assumption of constant intracellular diffusion coefficient is not necessarily valid, and, consequently, the diffusion coefficient is a function of the local concentration of solvent and solutes. In this paper we propose a stochastic model of reaction-diffusion systems, in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces. We then describe the software tool Redi (REaction-DIffusion simulator) which we have developed in order to implement this model into a Gillespie-like stochastic simulation algorithm. Finally, we show the ability of our model implemented in the Redi tool to reproduce the observed gradient of the bicoid protein in the Drosophila Melanogaster embryo. With Redi, we were able to simulate with an accuracy of 1% the experimental spatio-temporal dynamics of the bicoid protein, as recorded in time-lapse experiments obtained by direct measurements of transgenic bicoidenhanced green fluorescent protein.

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