In this paper, we present a novel method to estimate chemical reaction and diffusion rates for biochemical reaction–diffusion dynamics from time series of observations. Our approach leverages iterated particle filtering as means fit high-dimensional stochastic discrete spatiotemporal model sparse data, often with some species in low copy numbers. We demonstrate the feasibility on three realisti...

Linearly-implicit, approximate factorization methods are used to reduce the solution of multi-dimensional reaction–diffusion equations to a sequence of two-point boundaryvalue problems in ordinary differential equations which are solved analytically in a piecewise manner. It is shown that, depending on the allocation of the transient, diffusion and reaction terms to the second-order ordinary di...

a simple mathematical model of steady state  oxygen distribution subject to diffusive transport and non- linear uptake in a retinal cylinder has been developed. the approximate analytical solution to a reaction- diffusion equation are obtained by using series expansions. the computational results for the scaled variables are presented through graphs. the effect of the important parameters (1) d...

The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. equations consist reaction-diffusion equation for the substrate concentration and fourth-order Cahn–Hilliard-type volume fraction biomass, considered in domain with no-flux boundary conditions. main difficulties are coming from degenerate diffusivity mobility, singular potential arising logar...