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In this work, we study some characteristics of sigmoidal growth/decay functions that are solutions of dynamical systems. In addition, the studied dynamical systems have a realization in terms of reaction networks that are closely related to the Gompertzian and logistic type growth models. Apart from the growing species, the studied reaction networks involve an additional species interpreted as an environmental resource. The reaction network formulationВ of the proposed models hints forВ the intrinsic mechanism of the modeled growthВ process and can be used for analyzing evolutionaryВ measured data when testing various appropriateВ models, especially when studying growth processesВ in life sciences. TheВ proposed reaction network realization of GompertzВ growth model can be interpreted from the perspectiveВ of demographic and socio-economic sciences.В The reaction network approachВ clearly explains the intimate links between the GompertzВ model and the Verhulst logistic model.В There are shown reversible reactions which complete the already known non-reversible ones. It is also demonstrated that the proposed approach can be applied in oscillating processes and social-science events.В The paper is richly illustrated with numericalВ computations andВ computer simulations performed by algorithmsВ using the computer algebra systemВ Mathematica.

Schistosomiasis, a health challenge in many communities, is prevalent as the rate of infection is one in every thirty individuals. In this work, a deterministic model for schistosomiasis transmission dynamics is studied. The stability properties of equilibrium states, disease-free and endemic equilibria are established in terms of the basic reproduction number, R_0. The sensitivity analysis of R_0 with respect to the model parameters is carried out using Partial rank correlation coefficients (PRCCs). The optimal control model with control measures, public health education, diagnosis and treatment and snail control, is formulated and its optimality system is derived using Pontragyin's maximum Principle. Simulation results showed that simultaneous implementation of public health education, diagnosis and treatment and snail control will reduce the burden of the schistosomiasis infection in the population. However due to toxicity of some snail controls to other aquatic bodies and difficulty to single out the chemical control that will focus only on the snail population even though snails are special food in Africa, it is preferable to implement public health education and diagnosis and treatment simultaneously in order to eradicate schistosomiasis transmission in the affected regions.

In this note we construct a family of recurrence generated sigmoidal functions based on the Log--logistic function. The study of some biochemical reactions is linked to a precise Log--logistic function analysis.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given. The plots are prepared using CAS Mathematica.

The PSP modelling approach allows you to model biological/pharmaceutical behaviour by combining micro-scale ordinary differential equation (ODE) models with macro-scale ODE models and their bi-directional interaction. E.g.: based on the model of a single cell, billions of cells can be simulated to get the response of an entire organ (also incorporating the organ to cell reaction). The PSP approach allows to simulate this in a mathematically efficient way by characterising different cells by a set of physiologically relevant quantities [2], [3]. Our framework is capable of taking into account up to 3 physiological parameters resulting in a 3D structure for which a partial differential equation (PDE) should be solved. We achieve considerable speed-up by using a semi-Lagrangian PDE solver that allows big stable time stepping. Combining this with a low level C-language implementation, we achieve exceptional efficient usage of the computing processing unit (CPU). Furthermore we accelerate the computation of the steady-state by using a Newton-Krylov method. For ease of use, a PSP description language is constructed to allow straightforward input of different models. The simulator should empower future computational/mathematical biologists to create and evaluate more detailed models than currently is common practice.

The enzyme kinetics reaction scheme of single enzyme-sub-strate dynamics, originally proposed by V. Henri, is considered. The system of ODEs induced by the reaction scheme is compared to two approximate models, namely the Michaelis-Menten model and the model of exponential decay. Validity conditions for the Michaelis-Menten model are briefly reviewed. A case specific for ``superefficient enzymes'' is used as a setting for a comparison between the three models via computational experiments. The case study proves the importance of validating the applicability of the approximate model.A novel cell growth model is proposed and analyzed. The approach of model development is to make use of the original Henri enzyme kinetics law in the context of metabolic processes in living cells, namely cell growth. Two approximations corresponding to different cell growth phases are introduced in order to study the model analytically.

Proposed are some modifications of bio-economic models with stage structure [3]-[8]. The proposed modifications aim at a better description and understanding of the underlying bio-economic mechanisms. This is achieved by formulating the model in terms of chemical-type reaction steps. Several new modules in the Computer Algebra System MATHEMATICA are proposed, offering a possibility for visualization of the resulting solutions and sensitive analysis of the model.

he Kumaraswamy-Dagum distribution is a flexible and simple model with applications to income and lifetime data.We prove upper and lower estimates for the Hausdorff approximation of the shifted Heaviside function by a class of Kumaraswamy-Dagum-Log-Logistic cumulative distribution function - (KD-CDF). Numerical examples, illustrating our results are given.

In this paper we find application of some new cumulative distribution functions transformations to construct a family of sigmoidal functions based on the Gompertz logistic function.We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of these families.Numerical examples, illustrating our results are given.

In this note we find application of a new class cumulative distribution function transformations to construct a family of sigmoidal functions based on the Verhulst logistic function. We prove estimates for the Hausdorff approximation of the shifted Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

This review paper surveys results on branching stochastic models with and without immigration published during the past nine years. Studies of this class of stochastic models were motivated by the quantitative analysis of the dynamics of population of cells of the central nervous system, called the terminally differentiated oligodendrocytes, and their progenitor cells. We focus on original ideasspecifically developed for Sevastyanov branching processes allowing the contribution of an external cellular compartment (e.g., stem cells) via anonhomogeneous Poisson immigration process. Limiting distributions are discribed in the subcritical, critical and supercritical cases for various immigration rates.