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In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…

Motivated by biological applications on tumour invasion through thin membranes, we study a porous-medium type equation where the density of the cell population evolves under Darcy's law, assuming continuity of both the density and flux…

Migration of animal cells is based on the interplay between actin polymerization at the front, adhesion along the cell-substrate interface, and actomyosin contractility at the back. Active gel theory has been used before to demonstrate that…

This paper presents an analytical comparison of active and passive receiver models in diffusive molecular communication. In the active model, molecules are absorbed when they collide with the receiver surface. In the passive model, the…

Adhesion bonds between membranes and surfaces are attracted to each other via effective interactions whose origin the entropy loss due to the reduction in the amplitude of the membrane thermal fluctuations in the vicinity of the adhesion…

How individual dispersal patterns and human intervention behaviours affect the spread of infectious diseases constitutes a central problem in epidemiological research. This paper develops an impulsive nonlocal faecal-oral model with free…

Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our computer simulations are based on a Langevin…

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of P\'eclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these…

In this work, receiver diversity in advection-dominated diffusion-advection channels is investigated. Strong directed flow fundamentally alters the communication-theoretic properties of molecular communication systems (MC). Specifically,…

Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…

A simple multiscale approach to the diffusion-driven adsorption from a solution to a solid surface is presented. The model combines two important features of the adsorption process: (i) the kinetics of the chemical reaction between…

In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always…

The ability of eukaryotic cells to squeeze through constrictions is limited by the stiffness of their large and rigid nucleus. However, migrating cells are often able to overcome this limitation and pass through constrictions much smaller…

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear.…

We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…

This paper analyzes the channel impulse response of an absorbing receiver (RX) covered by multiple non-overlapping heterogeneous receptors with different sizes and arbitrary locations in a molecular communication system. In this system, a…

We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of…

We investigate a stochastic process consisting of a two-dimensional particle with anisotropic diffusion, mortality rate and a drift velocity, in the presence of an absorbing boundary. After the particle has encountered the boundary, the…

We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…

This paper considers the scenario of a targeted drug delivery system, which consists of deploying a number of biological nanomachines close to a biological target (e.g. a tumor), able to deliver drug molecules in the diseased area. Suitably…