A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion which depends upon the way the specific disease is communicated among different populations or subpopulations. Compartmental models describing a finite number of subpopulations can be described mathematically via systems of ordinary differ...

This dissenation introduces a new method of creating computer graphics textures that is based on simulaling a biological model of pa11em formation known as reaction-diffusion. Applied mathematicians and biologistli have shown how simple reaction-diffusion systems can create pan ems of spots or stripes. Here we demonstr.lte that the range of patterns created by reaction-dtffusion can be greatly ...

Diffusion mechanism models the movement of many individuals in an environment or media. The individuals can be very small such as basic particles in physics, bacteria, molecules, or cells, or very large objects such as animals, plants, or certain kind of events like epidemics, or rumors. The particles reside in a region, which we call Ω, and we assume that Ω is open subset of Rn (the n-th dimen...

Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may ex...

Any computer consists of processor and memory elements. Patterns and waves in excitable or oscillatory reaction– diffusion media are able to perform such processor tasks as counting, logical operations, signal transformation, and finding the shortest path through a maze. Since the brain may be thought of as a reaction–diffusion system, these capabilities are perhaps not so remarkable, though th...