International Journal of Biomathematics

We propose an efficient numerical method for two population models, based on the nonstandard finite difference (NSFD) schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.

The goal of this paper is to investigate the dynamics of a non-autonomous density-dependent predator–prey system with Beddington–DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator–prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. Further, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed-point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, $L^p$-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying $\parallel u_0{\parallel }_{L^1}\le \frac{4}{\chi \alpha C_{GN}}-2^{\frac{1}{\sigma }+1}\sigma {(\sigma +1)}^{-\frac{1}{\sigma }-1}\left|\mathrm{\Omega }\right|$ for $\sigma =1.$ While for $\sigma >1$, there are no restrictions on the initial cell mass and the result still holds.

This paper is concerned with Nicholson’s blowflies difference model with linear harvesting term. We obtain sufficient conditions for the existence of an almost periodic positive solution by using contraction mapping principle. The exponential convergence of almost periodic positive solution is derived by discrete Lyapunov functional.

We consider two DNA sequences and compare both sequences. One of the crucial issues in bioinformatics is to measure the similarity of two DNA sequences. To this purpose one has to consider different alignments between both sequences. The number of alignments grows very rapidly with the length of the sequences. In this paper we give exact, explicit and computable formulas for the number of different possible alignments and for some classes of reduced alignments. We provide a new insight into the theory of DNA sequence alignment.

Researchers hope that establishing a notion of proximity using topology will help to clarify the biological processes underlying the evolution of living organisms. The simple model presented here, using RNA shapes, can carry over to more general and complex genotype–phenotype systems. Proximity is an important component of continuity, in both real-world and topological terms. Consequently, phenotype spaces provide an appropriate setting for modeling and investigating continuous and discontinuous evolutionary change.

Two stochastic models are derived for a susceptible–infectious–susceptible epidemic spreading through a metapopulation: a continuous time Markov chain (CTMC) model and an Itô stochastic differential equation (SDE) model. The stochastic models are numerically compared. Close agreement suggests that computationally intense CTMC simulations can be approximated by simpler SDE simulations. Differential equations for the moments of the SDE probability distribution are also derived, the steady states are solved numerically using a moment closure technique, and these results are compared to simulations. The moment closure technique only coarsely approximates simulation results. The effect of model parameters on stability of the disease-free equilibrium is also numerically investigated.

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson’s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

This work presents a formalized description of information and communicative interactions of individuals on the basis of the communicative field (CF) method. It also contains explication of the possibility to create model of information and communication interactions, which is able to illustrate both interactions between two and more individuals. Methods and approaches which are suggested in this paper can correctly simulate the processes of distortion and generation of information images (IIs) with information and communication social interaction. Expansion and addition of IIs theory in terms of the transmission of information between individuals allows us to speak about the space of IIs. This space helps to explain a number of characteristic phenomena of human thinking.

This paper focuses on the stabilities of the equilibria to a predator–prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.

The purpose of this work is to construct a new crossover operator using the properties of DNA and RNA by using topological concepts in constructing flexible mathematical models in the field of biomathematics. Also, we investigate and study topological properties of the constructed operators and the associated topological spaces of DNA and RNA. Finally we use the process of exchange for sequence of genotypes structures to construct new types of topological concepts to investigate and discuss several examples and some of their properties.

In this paper, we propose a nonlinear virus dynamics model that describes the interactions of the virus, uninfected target cells, multiple stages of infected cells and B cells and includes multiple discrete delays. We assume that the incidence rate of infection and removal rate of infected cells are given by general nonlinear functions. The model can be seen as a generalization of several humoral immunity viral infection model presented in the literature. We derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to establish the existence and global stability of the three equilibria of the model. We study the global asymptotic stability of the equilibria by using Lyapunov method. We perform some numerical simulations for the model with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.

In this paper, we study dynamics in a predator–prey model with delay, in which predator can be infected, with particular attention focused on nonresonant double Hopf bifurcation. By using center manifold reduction methods, we obtain the equivalent normal forms near a double Hopf critical point in this system. Moreover, bifurcations are classified in a two-dimensional parameter space near the critical point. Numerical simulations are presented to demonstrate the applicability of the theoretical results.

It has been certificated that corridors can help giant pandas to keep their habitat from fragmenting. However there are still losses during the process of moving along corridors. In this study, a mathematical model with Allee effect is carried out to describe the diffusion of giant pandas between n patches. Some criteria are obtained to keep the system persisting. It is proved that the system has a unique positive $\omega$-periodic solution which is globally asymptotically stable. The ecological meanings of these findings are discussed following the results. And some numerical simulations in the Qinling Mountain giant panda nature reservation area are also presented in the end.

The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Carreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow are obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weissenberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.

Nutrition diagnosis plays a key role in the crop’s growth, which has mainly been carried out in the field by agricultural workers. Currently, automatic nutrition recognition technologies have been widely used in this field. A procedure is proposed in this paper to diagnose nitrogen nutrition non-destructively for rapeseed qualitatively based on the multifractal theory. Twelve texture parameters are given by the method of multifractal detrended fluctuation (MF-DFA), which contains six generalized Hurst exponents and six relative multifractal parameters that are used as features of the rapeseed leaf images for identifying the two nitrogen levels, namely, the $N$-mezzo and the $N$-wane. For the base leaves, central leaves and top leaves of the rapeseed plant and the three-section mixed samples, three parameters combinations are selected to conduct the work. Five classifiers of Fisher’s linear discriminant algorithm (LDA), extreme learning machine (ELM), support vector machine and kernel method (SVMKM), random decision forests (RF) and $K$-nearest neighbor algorithm (KNN) are employed to calculate the diagnosis accuracy. An interesting finding is that the best diagnose accuracy is from the base leaves of the rapeseed plant. It is explained that the base leaf is the most sensitive to the nitrogen deficiency. The diagnose effect by the base leaves samples is outshining the existing result significantly for the same leaves samples. For the mixed samples, the averaged discriminant accuracy reaches 97.12% and 97.56% by SVMKM and RF methods with the $10$-fold cross-validation respectively. The resulting high accuracy on $N$-levels identification shows the feasibility and efficiency of our method.