The pharmacodynamics of antibiotic treatment.
The Phylogeny Graphs of Doubly Partial Orders
The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph P(D) of a digraph D is the (simple undirected) graph defined by V (P(D)) := V (D) and E(P(D)) := {xy | N+D (x) ∩ N+D(y) ¹ ⊘ } ⋃ {xy | (x,y) ∈ A(D)},...
The population dynamics of conflict and cooperation.
The potential distribution due to a dipole source in the fetal heart: A numerical model of the maternal abdomen.
The power-law formalism as a tool for modeling hormonal systems.
The prognosis of survivance in solid tumor patients based on optimal partitions of immunological parameters ranges.
The rate of satiation in a cooperative system
The resonance phenomenon in the reaction-diffusion systems.
The role of cell motility in metastatic cell dominance phenomenon: Analysis by a mathematical model.
The Role of Cell-Cell Adhesion in the Formation of Multicellular Sprouts
Collective cell motility and its guidance via cell-cell contacts is instrumental in several morphogenetic and pathological processes such as vasculogenesis or tumor growth. Multicellular sprout elongation, one of the simplest cases of collective motility, depends on a continuous supply of cells streaming along the sprout towards its tip. The phenomenon is often explained as leader cells pulling the rest of the sprout forward via cell-cell adhesion. Building on an empirically demonstrated analogy...
The role of delay in digestion of plankton by fish population: A fishery model.
The role of Mechanics in Tumor growth : Modelling and Simulation
A number of biological phenomena are interlaced with classical mechanics. In this review are illustrated two examples from tumor growth, namely the formation of primordial networks of vessels (vasculogenesis) and the avascular phase of solid tumors. In both cases the formalism of continuum mechanics, accompanied by accurate numerical simulations, are able to shed light on biological controversies. The converse is also true: non-standard mechanical problems suggest new challenging mathematical questions....
The role of the incubation period in a disease model.
The Rothe method for the McKendrick-von Foerster equation
We present the Rothe method for the McKendrick-von Foerster equation with initial and boundary conditions. This method is well known as an abstract Euler scheme in extensive literature, e.g. K. Rektorys, The Method of Discretization in Time and Partial Differential Equations, Reidel, Dordrecht, 1982. Various Banach spaces are exploited, the most popular being the space of bounded and continuous functions. We prove the boundedness of approximate solutions and stability of the Rothe method in and...
The Second Half-With a Quarter of a Century Delay
We show how results by Diekmann et al. (2007) on the qualitative behaviour of solutions of delay equations apply directly to a resource-consumer model with age-structured consumer population.
The solution of inverse nonlinear elasticity problems that arise when locating breast tumours.
The solutions of the quasilinear Keller-Segel system with the volume filling effect do not blow up whenever the Lyapunov functional is bounded from below
In [2] we proved two kinds of mechanisms of preventing the blow up in a quasilinear non-uniformly parabolic Keller-Segel systems. One of them was a priori boundedness from below of the Lyapunov functional. In fact, we were able to present a condition under which the Lyapunov functional is bounded from below and a solution exists globally. In the present paper we prove that whenever the Lyapunov functional is bounded from below the solution exists globally.
The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models
A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is considered numerically and analytically. The limiting solutions describing the behaviour of the standard SIR model with a small number of initially infected individuals are derived, and expressions found for the duration of an outbreak. We study a model for a weakly mixed population distributed between the interacting centres. The centres are modelled as SIR nodes with interaction between sites determined by a diffusion-type...
The stability of some chemical systems established by the semi-empirical method.
The transylvanian problem of renewable resources