Outils mathématiques pour modéliser les systèmes complexes
Pathway complexity of model virus capsid assembly systems.
Patterns of Zooplankton Functional Response in Communities with Vertical Heterogeneity: a Model Study
Parameterization of zooplankton functional response is crucial for constructing plankton models. Theoretical studies predict enhancing of system stability in case the response is of sigmoid type. Experiments on feeding in laboratories tell us in favor of non-sigmoid types for most herbivorous zooplankton species. However, recent field observations show that the overall functional response of zooplankton in the whole euphotic zone can exhibit a sigmoid behavior even when the response for the same...
Positive and Negative Feedback in Engineering and Biology
No other concepts have shaken so deeply the bases of engineering like those of positive and negative feedback. They have played a most prominent role in engineering since the beginning of the previous century. The birth certificate of positive feedback can be traced back to a pair of patents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is already lost in time. We present in this paper a short review on the feedback's origins in the fields of engineering and biology....
Positive periodic solutions of functional differential equations and population models.
Possibly Longest Food Chain: Analysis of a Mathematical Model
We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases,...
Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)
Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate clinical attack rates in children much higher than in adults. Non-medical interventions such as school closings are constrained by their large socio-economic costs. Here we develop a mathematical model to ascertain the roles of pre-symptomatic influenza transmission as well as symptoms surveillance of children to assess the utility of school closures. Our model analysis...
Reaction-Diffusion Modelling of Interferon Distribution in Secondary Lymphoid Organs
This paper proposes a quantitative model of the reaction-diffusion type to examine the distribution of interferon-α (IFNα) in a lymph node (LN). The numerical treatment of the model is based on using an original unstructured mesh generation software Ani3D and nonlinear finite volume method for diffusion equations. The study results in suggestion that due to the variations in hydraulic conductivity of various zones of the secondary lymphoid organs...
Reflections on the Origin, Meaning, and Future of Systems Biology
Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics
In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton...
Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach
An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the...
Simulating Kinetic Processes in Time and Space on a Lattice
We have developed a chemical kinetics simulation that can be used as both an educational and research tool. The simulator is designed as an accessible, open-source project that can be run on a laptop with a student-friendly interface. The application can potentially be scaled to run in parallel for large simulations. The simulation has been successfully used in a classroom setting for teaching basic electrochemical properties. We have shown that...
Some Parameter Estimation Issues in Functional-Structural Plant Modelling
The development of functional-structural plant models has opened interesting perspectives for a better understanding of plant growth as well as for potential applications in breeding or decision aid in farm management. Parameterization of such models is however a difficult issue due to the complexity of the involved biological processes and the interactions between these processes. The estimation of parameters from experimental data by inverse methods...
Stabilization and control of some microbial populations
Support vector machine skin lesion classification in Clifford algebra subspaces
The present study develops the Clifford algebra within a dermatological task to diagnose skin melanoma using images of skin lesions, which are modeled here by means of 5D lesion feature vectors (LFVs). The LFV is a numerical approximation of the most used clinical rule for melanoma diagnosis - ABCD. To generate the we develop a new formula that uses the entries of a 5D vector to calculate the entries of a 32D multivector. This vector provides a natural mapping of the original 5D vector onto...
Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space
With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the spatial coexistence,...
The Effect of Bacteria on Epidermal Wound Healing
Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...
The formation of a tree leaf
In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...
The generalized Turner-Bradley-Kirk-Pruitt equation.
The Immune System – Complexity Exemplified