Modelling and analysis of a pest-control pollution model with integrated control tactics.
Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary
In this paper we are interested in a mathematical model of migration of grass eels in an estuary. We first revisit a previous model proposed by O. Arino and based on a degenerate convection-diffusion equation of parabolic-hyperbolic type with time-varying subdomains. Then, we propose an adapted mathematical framework for this model, we prove a result of existence of a weak solution and we propose some numerical simulations.
Modelling Circadian Rhythms in Drosophila and Investigation of VRI and PDP1 Feedback Loops Using a New Mathematical Model
We present a brief review of molecular biological basis and mathematical modelling of circadian rhythms in Drosophila. We discuss pertinent aspects of a new model that incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are probabilistically...
Modelling DNA and RNA secondary structures using matrix insertion-deletion systems
Insertion and deletion are operations that occur commonly in DNA processing and RNA editing. Since biological macromolecules can be viewed as symbols, gene sequences can be represented as strings and structures can be interpreted as languages. This suggests that the bio-molecular structures that occur at different levels can be theoretically studied by formal languages. In the literature, there is no unique grammar formalism that captures various bio-molecular structures. To overcome this deficiency,...
Modelling Evolution of Regulatory Networks in Artificial Bacteria
Studying the evolutive and adaptative machanisms of prokayotes is a complicated task. As these machanisms cannot be easily studied "in vivo", it is necessary to consider other methods. We have therefore developed the RAevol model, a model designed to study the evolution of bacteria and their adaptationto the environment. Our model simulates the evolution of a population of artificial bacteria in a changing environment, providing us with an insight into the strategies that digital organisms develop...
Modelling immune response and drug therapy in human malaria infection.
Modelling macrophage infiltration into avascular tumours.
Modelling of Cancer Growth, Evolution and Invasion: Bridging Scales and Models
Since cancer is a complex phenomenon that incorporates events occurring on different length and time scales, therefore multiscale models are needed if we hope to adequately address cancer specific questions. In this paper we present three different multiscale individual-cell-based models, each motivated by cancer-related problems emerging from each of the spatial scales: extracellular, cellular or subcellular, but also incorporating relevant information from other levels. We apply these hybrid...
Modelling of Dynamic Problems in Biomechanics
This paper is devoted to solving of dynamic problems in biomechanics that require detailed study of fast processes. Numerical method of characteristics is used to model the temporal development of the processes with high accuracy.
Modelling of peripheral fluid accumulation after a crystalloid bolus in female volunteers. A mathematical study.
Modelling of Plant Growth with Apical or Basal Meristem
Plant growth occurs due to cell proliferation in the meristem. We model the case of apical meristem specific for branch growth and the case of basal meristem specific for bulbous plants and grass. In the case of apical growth, our model allows us to describe the variety of plant forms and lifetimes, endogenous rhythms and apical domination. In the case of basal growth, the spatial structure, which corresponds to the appearance of leaves, results...
Modelling Physiological and Pharmacological Control on Cell Proliferation to Optimise Cancer Treatments
This review aims at presenting a synoptic, if not exhaustive, point of view on some of the problems encountered by biologists and physicians who deal with natural cell proliferation and disruptions of its physiological control in cancer disease. It also aims at suggesting how mathematicians are naturally challenged by these questions and how they might help, not only biologists to deal theoretically with biological complexity, but also physicians to optimise therapeutics, on which last point the...
Modelling the effect of cell shedding on avascular tumour growth.
Modelling the effects of Paclitaxel and Cisplatin on breast and ovarian cancer.
Modelling the hepatitis C with different types of virus genome.
Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents
Over the past decade or so, there have been a large number of modelling approaches aimed at elucidating the most important mechanisms affecting the formation of new capillaries from parent blood vessels — a process known as angiogenesis. Most studies have focussed upon the way in which capillary sprouts are initiated and migrate in response to diffusible chemical stimuli supplied by hypoxic stromal cells and leukocytes in the contexts of solid tumour...
Modelling the interactions of mixtures of organophosphorus insecticides with cholinesterase.
Modelling the spiders ballooning effect on the vineyard ecology
We consider an ecosystem in which spiders may be transported by the wind from vineyards into the surrounding woods and vice versa. The model takes into account this tranport phenomenon without building space explicitly into the governing equations. The equilibria of the dynamical system are analyzed together with their stability, showing that bifurcations may occur. Then the effects of indiscriminated spraying to keep pests under control is also investigated via suitable simulations.
Modelling the Spread of Infectious Diseases in Complex Metapopulations
Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially,...
Modelling Tuberculosis and Hepatitis B Co-infections
Tuberculosis (TB) is the leading cause of death among individuals infected with the hepatitis B virus (HBV). The study of the joint dynamics of HBV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. We formulate and analyze a deterministic mathematical model which incorporates of the co-dynamics of hepatitis B and tuberculosis. Two sub-models, namely: HBV-only and TB-only sub-models...