Smita Dick, Clare MacRae, Claire McFaul, Usman Rasul, Philip Wilson, Stephen W Turner
Interventions to reduce acute paediatric hospital admissions: a systematic review
Archives of disease in childhood
time delays modelling process intracellular gene expression shown important impacts dynamics pattern formation reactiondiffusion systems particular past work shown time delays shrink turing space thereby inhibiting patterns forming across large ranges parameters delays also increase time taken pattern formation even turing instabilities occur consider reactiondiffusion models incorporating fixed distributed time delays modelling underlying stochastic nature gene expression dynamics analyse systematic linear instability analysis numerical simulations several sets different reaction kinetics find even complicated distribution kernels skewed gaussian probability density functions little impact reactiondiffusion dynamics compared fixed delays mean delay show location delay terms model lead changes size turing space increasing decreasing mean time delay formula see text increased show time pattern formation perturbation homogeneous steady state scales linearly formula see text conjecture general impact time delay reactiondiffusion dynamics independent form kinetics location delayed terms finally show initial boundary conditions influence dynamics particularly timetopattern effects delay appear robust variations initial boundary data overall results help clarify role gene expression time delays reactiondiffusion patterning suggest clear directions work studying realistic models pattern formation