International Journal of Biomathematics

The next generation sequencing (NGS) is an important process which assures inexpensive organization of vast size of raw sequence dataset over any traditional sequencing systems or methods. Various aspects of NGS such as template preparation, sequencing imaging and genome alignment and assembly outline the genome sequencing and alignment. Consequently, de Bruijn graph (dBG) is an important mathematical tool that graphically analyzes how the orientations are constructed in groups of nucleotides. Basically, dBG describes the formation of the genome segments in circular iterative fashions. Some pivotal dBG-based de novo algorithms and software packages such as T-IDBA, Oases, IDBA-tran, Euler, Velvet, ABySS, AllPaths, SOAPde novo and SOAPde novo2 are illustrated in this paper. Consequently, overlap layout consensus (OLC) graph-based algorithms also play vital role in NGS assembly. Some important OLC-based algorithms such as MIRA3, CABOG, Newbler, Edena, Mosaik and SHORTY are portrayed in this paper. It has been experimented that greedy graph-based algorithms and software packages are also vital for proper genome dataset assembly. A few algorithms named SSAKE, SHARCGS and VCAKE help to perform proper genome sequencing.

The system of two-dimensional nonlinear partial differential equations is considered. This system describes the vein formation in meristematic tissues of young leaves. Variable directions difference scheme is constructed and investigated. Absolute stability regarding space and time steps of scheme is shown. The convergence statement for the constructed scheme is proved. Rate of convergence is given. Various numerical experiments are carried out and results of some of them are considered in this paper. Comparison of numerical experiments with the results of the theoretical investigation is given too.

In this paper, we consider two nonlinear models for viral infection with humoral immunity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The second model is a modification of the first one by including the latently infected cells. The incidence rate, removal rate of infected cells, production rate of viruses and the latent-to-active conversion rate are given by more general nonlinear functions. We have established a set of conditions on these general functions and determined two threshold parameters for each model which are sufficient to determine the global dynamics of the models. The global asymptotic stability of all equilibria of the models has been proven by using Lyapunov theory and applying LaSalle's invariance principle. We have performed some numerical simulations for the models with specific forms of the general functions. We have shown that, the numerical results are consistent with the theoretical results.

Ever since HIV was first diagnosed in human, a great number of scientific works have been undertaken to explore the biological mechanisms involved in the infection and progression of the disease. This paper deals with stability and bifurcation analyses of mathematical model that represents the dynamics of HIV infection of thymus. The existence and stability of the equilibria are investigated. The model is described by a system of delay differential equations with logistic growth term, cure rate and discrete type of time delay. Choosing the time delay as a bifurcation parameter, the analysis is mainly focused on the Hopf bifurcation problem to predict the existence of a limit cycle bifurcating from the infected steady state. Further, using center manifold theory and normal form method we derive explicit formulae to determine the stability and direction of the limit cycles. Moreover the mitosis rate r also plays a vital role in the model, so we fix it as second bifurcation parameter in the incidence of viral infection. Our analysis shows that, while both the bifurcation parameters can destabilize the equilibrium E* and cause limit cycles. Numerical simulations are performed to investigate the qualitative behaviors of the inherent model.

Statistical models using stochastic differential equations (SDEs) to describe dynamically evolving natural systems are appearing in the scientific literature with some regularity in recent years. In this study, the SDE mixed-effects parameter models based on a Vasicek non-homogeneous diffusion process are formulated. The breast height diameter-dependent drift function additionally depends on deterministic function that describes the dynamic of certain exogenous stand variables (crown height, c_h, crown width, c_w, mean breast height diameter, d₀, mean height, h₀, age, A, soil fertility index, SFI, stocking level, S) versus breast height diameter. The mixed-effects parameters SDE models included a random parameter that affected the models asymptote. The parameter estimators are evaluated by maximum likelihood procedure. The objective of the research was to develop a generalized mixed-effects parameters SDE height–diameter models and to illustrate issues using dataset of Scots pine trees (Pinus sylvestris L.) in Lithuania with the breast height diameter outside the bark larger than 0 cm. The parameters of all used models were estimated using an estimation dataset and were evaluated using a validation dataset. The new developed height–diameter models are an improvement over exogenous stand variables, in that it can be calibrated to a new stand with observed height–diameter pairs, thus improving height prediction.

The objective of this communication is to examine the effect of rotation on the peristaltic motion of non-Newtonian fluid. Constitutive relationship of Jeffrey fluid is employed in the mathematical formulation and related analysis. The thermal radiation and Joule heating effects are also considered. An electrically conducting fluid in a channel with compliant boundaries is taken. Solution expressions are established through assumptions of large wavelength and low Reynolds number. Impact of Taylor and Hartman numbers on the axial velocity is similar in a qualitative sense. There is reverse effect of Taylor number on the secondary velocity when compared with the axial velocity. Temperature and heat transfer coefficients are increasing functions of Taylor number.

In the real world, the population systems are often subject to white noises and a system with such stochastic perturbations tends to be suitably modeled by stochastic differential equations. This paper is concerned with the dynamic behaviors of a delay stochastic competitive system. We first obtain the global existence of a unique positive solution of system. Later, we show that the solution of system will be stochastically ultimate boundedness. However, large noises may make the system extinct exponentially with probability one. Also, sufficient conditions for the global attractivity of system are established. Finally, illustrated examples are given to show the effectiveness of the proposed criteria.

Graphical representation is a very efficient tool for visual analysis of protein sequences. In this paper, a novel 2D graphical representation scheme is proposed on the basis of a newly introduced concept, named characteristic model of the protein sequences. After obtaining the 2D graphics of protein sequences, two numerical characterizations of them is designed as descriptors to analyze the nine DN5 protein sequences, simulation and analysis results show that, comparing with existing methods, our method is not only visible, intuitional, and simple, but also has no circuit or degeneracy, and even more important, since the storage space required by our method is constant and has nothing to do with the length of protein sequences, then it can keep excellent visual inspection for long protein sequences.

In the present paper, we have studied the blood flow through tapered artery with a stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Phan-Thien–Tanner fluid. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shearing stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Exact solutions have been evaluated for velocity, resistance impedance, wall shear stress and shearing stress at the stenosis throat. The graphical results of different type of tapered arteries (i.e. converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.

Optimal control theory is applied to a system of ordinary differential equations modeling banana Xanthomonas wilt within plantations. The objective is to reduce the proportion of infected plants by use of controls representing two types of preventive methods: vector and contaminated tool prevention. The optimal controls are characterized in terms of the optimality system, which is solved analytically and numerically for several scenarios.

The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a graph. In this paper we investigate Wiener and terminal Wiener for graphs derived from certain operations.

In this paper, we consider three species harvesting model and develop a solution procedure which is able to calculate the equilibrium points of the model where some biological parameters of the model are interval numbers. A parametric mathematical program is formulated to find the biological equilibrium of the model for different values of parameters. This interval-valued problem is converted into equivalent crisp model using interval operations. The main advantage of the proposed procedure is that we can present different characteristics of the model in a single framework. Analytically, the existence of steady state and stabilities are looked into. Using mathematical software, the model is illustrated and the results are obtained and presented in tabular and graphical forms.

In this paper, a HTLV-I infection model with two delays is considered. It is found that the dynamics of this model are determined by two threshold parameters R₀ and R₁, basic reproduction numbers for viral infection and for CTL response, respectively. If R₀ < 1, the infection-free equilibrium P₀ is globally asymptotically stable. If R₁ < 1 < R₀, the asymptomatic-carrier equilibrium P₁ is globally asymptotically stable. If R₁ > 1, there exists a unique HAM/TSP equilibrium P₂. The stability of P₂ is changed when the second delay τ₂ varies, that is there exist stability switches for P₂.

In this paper, the tumor-immune dynamics are simulated by solving a nonlinear system of differential equations. The fractional-order mathematical model incorporated with three Michaelis–Menten terms to indicate the saturated effect of immune response, the limited immune response to the tumor and to account the self-limiting production of cytokine interleukin-2. Two types of treatments were considered in the mathematical model to demonstrate the importance of immunotherapy. The limiting values of these treatments were considered, satisfying the stability criteria for fractional differential system. A graphical analysis is made to highlight the effects of antigenicity of the tumor and the fractional-order derivative on the tumor mass.

Genetic diversity of 51 oil-tea camellia germplasms was analyzed using the optimized inter-simple sequence repeat (ISSR)–PCR reaction system with 22 primers screened from a set of 100 ISSR primers. The results showed that 493 discernible loci with distinct electrophoretic bands were obtained, of which, 478 loci (96.78%) were polymorphic. This indicated that oil-tea germplasms possess abundant genetic diversities. By clustering analysis performed using softwares of NTSYS 2.10 and Winboot, 51 oil-tea germplasms were divided into two groups: Group I had 48 lines of Camellia oleifera Abel, while Group II had three C. oleifera Abel related species and their similarity coefficient was 0.62. Group I was further divided into Group I-1 and Group I-2, and their similarity coefficient (Gs) was 0.634. All members of Group I-1 originated from Hunan Province, while Group I-2 included the rest of Hunan lines and those originated from other regions of China. Analyzed by software POPGENE 1.32, the Shannon's information index (I*) of genetic polymorphism was 0.3852, the genetic diversity among different region populations (Ht) was 0.2537, the genetic diversity within populations (Hs) was 0.15545, the differentiation coefficient of genetic diversity among populations (Gst) was 0.3967, and the gene flow among populations (Nm*) was 0.8262. The Nei's genetic distances between the Hunan population and the populations originated from other regions of China implied that geographic isolation strongly influenced genetic differentiation among populations. Meanwhile, seedling rootstock grafting and high grafting for tree crown produced genetic variations among clonal offsprings.