International Journal of Biomathematics

In this paper, spatial patterns of a diffusive predator–prey model with sigmoid (Holling type III) ratio-dependent functional response which concerns the influence of logistic population growth in prey and intra-species competition among predators are investigated. The (local and global) asymptotic stability behavior of the corresponding non-spatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. In addition, we derive the conditions for Turing instability and the consequent parametric Turing space in spatial domain. The results of spatial pattern analysis through numerical simulations are depicted and analyzed. Furthermore, we perform a series of numerical simulations and find that the proposed model dynamics exhibits complex pattern replication. The feasible results obtained in this paper indicate that the effect of diffusion in Turing instability plays an important role to understand better the pattern formation in ecosystem.

In recent years, the popular multifractal detrended fluctuation analysis (MF-DFA) is extended to two-dimensional (2D) version, which has been applied in some field of image processing. In this paper, based on the 2D MF-DFA, a novel multifractal estimation method for images, which we called the local multifractal detrended fluctuation analysis (LMF-DFA), is proposed to recognize and distinguish 20 types of tea breeds. A set of new multifractal descriptors, namely the local multifractal fluctuation exponents is defined to portray the local scaling properties of a surface. After collecting 10 tea leaves for each breed and photographing them to standard images, the LMF-DFA method is used to extract characteristic parameters for the images. Our analysis finds that there are significant differences among the different tea breeds' characteristic parameters by analysis of variance. Both the proposed LMF-DFA exponents and another classic parameter, namely the exponent based on capacity measure method have been used as features to distinguish the 20 tea breeds. The comparison results illustrate that the LMF-DFA estimation can differentiate the tea breeds more effectively and provide more satisfactory accuracy.

The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the consideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave c. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.

In this paper, we use a dynamical systems approach to prove the existence of traveling waves solutions for the Fisher–Kolmogorov density-dependent equation. Moreover, we prove the existence of upper and lower bounds for these traveling wave solutions found previously. Finally, we present a particular example which has several applications in the mathematical biology field.

In biological development, morphogens are locally produced and spread to other regions in organs, forming gradients that control the inter-related pattern and growth of developing organs. Mechanisms of morphogen transport were built and investigated by numerical simulations in [A. D. Lander, Q. Nie and F. Y. M. Wan, Do morphogen gradients arise by diffusion? Developmental Cell2 (2002) 785–796]. In that paper, model C, which considers endocytosis, exocytosis and receptor synthesis and degradation, is in a one-dimensional spatial region and couples a partial differential equation with ordinary differential equations. Here, this model is promoted to an arbitrary dimension bounded region. We prove existence, uniqueness and non-negativity of a global solution for this advanced model, of its steady-state solution and linear stability of steady state by operator semigroup, the Schauder theorem and local perturbation method. Our results improve previous results for this model in a one dimension region.

In this paper, we first combine tetra-peptide structural words with contact number for protein secondary structure prediction. We used the method of increment of diversity combined with quadratic discriminant analysis to predict the structure of central residue for a sequence fragment. The method is used tetra-peptide structural words and long-range contact number as information resources. The accuracy of Q₃ is over 83% in 194 proteins. The accuracies of predicted secondary structures for 20 amino acid residues are ranged from 81% to 88%. Moreover, we have introduced the residue long-range contact, which directly indicates the separation of contacting residue in terms of the position in the sequence, and examined the negative influence of long-range residue interactions on predicting secondary structure in a protein. The method is also compared with existing prediction methods. The results show that our method is more effective in protein secondary structures prediction.

Ongoing improvements in Computational Biology research have generated massive amounts of Protein–Protein Interactions (PPIs) dataset. In this regard, the availability of PPI data for several organisms provoke the discovery of computational methods for measurements, analysis, modeling, comparisons, clustering and alignments of biological data networks. Nevertheless, fixed network comparison is computationally stubborn and as a result several methods have been used instead. We illustrate a probabilistic approach among proteins nodes that are part of various networks by using Chapman–Kolmogorov (CK) formula. We have compared CK formula with semi-Markov random method, SMETANA. We significantly noticed that CK outperforms the SMETANA in all respects such as efficiency, speed, space and complexity. We have modified the SMETANA source codes available in MATLAB in the light of CK formula. Discriminant-Expectation Maximization (D-EM) accesses the parameters of a protein network datasets and determines a linear transformation to simplify the assumption of probabilistic format of data distributions and find good features dynamically. Our implementation finds that D-EM has a satisfactory performance in protein network alignment applications.

This paper presents a nonlinear sex-structured mathematical model to study the spread of HIV/AIDS by considering transmission of disease by heterosexual contact. The epidemic threshold and equilibria for the model are determined, local stability and global stability of both the "Disease-Free Equilibrium" (DFE) and "Endemic Equilibrium" (EE) are discussed in detail. The DFE is shown to be locally and globally stable when the basic reproductive number ℛ₀ is less than unity. We also prove that the EE is locally and globally asymptotically stable under some conditions. Finally, numerical simulations are reported to support the analytical findings.

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4⁺ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R₀ and the immune response activation number . We have proven that if R₀ ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if , then the infected steady state without CTL immune response is GAS, and if , then the infected steady state with CTL immune response is GAS.

Aedes aegypti is known as the responsible vector in transmitting dengue flavivirus. Unavailability of medication to cure the transmission in human blood becomes a global health issue in recent decades. World epidemiologists are encouraged to focus on investigation toward an effective and inexpensive way to prevent dengue transmission, i.e. mosquito control. In this paper, we present a model depicting the dynamics of mosquito population based on indoor–outdoor life cycle classification. The basic mosquito offspring number is obtained and analysis of equilibria is shown. We bring along a discussion on application of optimal control model which engineers two simultaneous schemes. The first scheme is done by disseminating chemical like Temephos in spots where eggs and larvae develop, meanwhile the second scheme is done by conducting fumigation through areas where adult mosquitoes prevalently nest, indoor as well as outdoor. A version of gradient-based method is presented to set down a workflow in minimizing the objective functional with respect to control variable. Numerical results from analysis of the basic mosquito offspring number with constant control and from optimal control suggest that one has to enhance the usage of fumigation rather than Temephos. It is also suggested that applying both control schemes simultaneously gives the most significant reduction to the population.

Effect of Hall current on peristaltic transport of couple stress fluid in an inclined asymmetric channel is investigated. An incompressible fluid is conducting in the presence of inclined magnetic field. Problem formulation is developed through heat and mass transfer aspects. Soret and Dufour effects are present. Long wavelength and low Reynolds number approaches are adopted. Closed form expression for longitudinal velocity, pressure gradient, temperature and concentration are presented. Important results reflecting the influence of embedded parameters in the problems have been pointed out. Pumping and trapping phenomena are especially focused.

This paper is retracted from IJB due to misconduct.

In real-world applications, some systems are composed of independent production units that use different inputs to produce outputs. The conventional data envelopment analysis model measures the relative efficiencies of a set of decision-making units with exact values of both inputs and outputs. In this paper, we propose an approach to assess parallel production systems with shared sources and bounded interval data, and also we provide a model that focuses on calculating the efficiency of the whole of a system along with the efficiencies of its components.