Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit

Optimal Screening in Structured SIR Epidemics

We present a model for describing the spread of an infectious disease with public screening measures to control the spread. We want to address the problem of determining an optimal screening strategy for a disease characterized by appreciable duration of the infectiveness period and by variability of the transmission risk. The specific disease we have in mind is the HIV infection. However the model will apply to a disease for which class-age structure is significant and should not be disregarded

Large-time behavior of matured population in an age-structured model

International audienc

An adaptative model for a multistage structured population under fluctuating environment

International audienc