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Modeling the role of constant and time varying recycling delay on an ecological food chain

Banibrata Mukhopadhyay, Rakhi Bhattacharyya (2010)

Applications of Mathematics

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the...

Modelling and Mathematical Analysis of the Glass Eel Migration in the Adour River Estuary

M. Odunlami, G. Vallet (2012)

Mathematical Modelling of Natural Phenomena

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

D. Kulasiri, Z. Xie (2008)

Mathematical Modelling of Natural Phenomena

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

Lakshmanan Kuppusamy, Anand Mahendran (2016)

International Journal of Applied Mathematics and Computer Science

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

Y. Sanchez-Dehesa, D. Parsons, J. M. Peña, G. Beslon (2008)

Mathematical Modelling of Natural Phenomena

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 of Cancer Growth, Evolution and Invasion: Bridging Scales and Models

A. R.A. Anderson, K. A. Rejniak, P. Gerlee, V. Quaranta (2010)

Mathematical Modelling of Natural Phenomena

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 the spiders ballooning effect on the vineyard ecology

E. Venturino, M. Isaia, F. Bona, E. Issoglio, V. Triolo, G. Badino (2010)

Mathematical Modelling of Natural Phenomena

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

J. Saldaña (2010)

Mathematical Modelling of Natural Phenomena

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

S. Bowong, J. Kurths (2010)

Mathematical Modelling of Natural Phenomena

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...

Models of interactions between heterotrophic and autotrophic organisms

Urszula Foryś, Zuzanna Szymańska (2009)

Applicationes Mathematicae

We present two simple models describing relations between heterotrophic and autotrophic organisms in the land and water environments. The models are based on the Dawidowicz & Zalasiński models but we assume the boundedness of the oxygen resources. We perform a basic mathematical analysis of the models. The results of the analysis are complemented by numerical illustrations.

Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Noémi Nagy, Péter Simon (2013)

Open Mathematics

Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic...

Multilevel Modeling of the Forest Resource Dynamics

I. N. Vladimirov, A. K. Chudnenko (2009)

Mathematical Modelling of Natural Phenomena

We examine the theoretical and applications-specific issues relating to modeling the temporal and spatial dynamics of forest ecosystems, based on the principles of investigating dynamical models. When developing the predictive dynamical models of forest resources, there is a possibility of achieving uniqueness of the solutions to equations by taking into account the initial and boundary conditions of the solution, and the conditions of the geographical environment. We present the results of a computer...

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