International Journal of Biomathematics

In the last 60 years, great progress has been made in controlling and preventing tuberculosis in China. However, the number of tuberculosis cases has increased dramatically in the last 25 years, mainly due to the lack of effective control measures of immigrating populations with tuberculosis. In order to explore the effective control and prevention measures we propose a deterministic model to study the transmission dynamics of tuberculosis in Guangdong province of China in this paper. The model consists of susceptible, exposed and infectious recovered subpopulations of immigrating populations from other provinces and the local population of Guangdong. We obtain the effective reproduction number. Based on the analysis, we also establish an optimal immune programming model, and get the optimal proportion of vaccine coverage with control of the effective reproduction number. Simulation is used to determine the validation and reliability. Our study demonstrates that the immigrating population from different provinces needs to be vaccinated according to the incidence rate of TB in their original provinces, and it is an effective way to prevent the outbreak of tuberculosis in Guangdong.

The effect of laser, as a heat source, on a one-dimensional finite living tissue was studied in this paper. The dual phase lagging (DPL) non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature-dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method (ADM). It was concluded that the nonlinear analysis was important in non-Fourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.

Ebola virus (EBOV) is the causative agent of a severe hemorrhagic fever disease associated with high mortality rates in humans. This virus has five strains of which Zaire Ebola virus (ZEBOV) is the first and most important strain. It can be transmitted through contact with contaminated surfaces and objects. The genome of EBOV codes one non-structural and seven structural proteins consisting of two forms of glycoprotein (GP): soluble glycoprotein (sGP) and GP (spike). In this paper, we attempted to characterize and predict physicochemical properties, B-cell epitopes, mutation sites, phosphorylation sites, glycosylation sites, and different protein structures of EBOV GP to provide comprehensive data about changes of this GP during a 40-years course (1976–2015). GP sequences were obtained from NCBI gene bank from 1976–2015. Expasy’sProtParam, PROTSCALE, immuneepitope, Bepipred, BcePred, ABCpred, VaxiJen, DISPHOS, NetPhos, and numerous programs were used to predict and analyze all sequences. More variety of mutations were found in 2015 sequences and mutations were related to huge changes in B-cell epitopes, phosphorylation and glycosylation sites. In addition, our results determined different sites of disulfide bonds and an important mutation related to IgE epitope as well as four potent B-cell epitopes (380–387, 318–338, 405–438 and 434–475). In this study, we suggested the effect of mutations on GP properties, six positions for disulfide bonds and four phosphorylation sites for protein kinase C enzyme. Selected sequences were shown different sites for O-link and N-link glycosylation. A mutation that changed GP to an allergen protein and has a significant role in vaccine designing as well as four potent B-cell epitopes in GP protein were found.

We introduce the class-age-dependent rates of the infected and vaccinated class in the compartmental model of dengue transmission. An age-structured host-vector interaction model incorporating vaccination effects is formulated and analyzed for the spread of dengue. Moreover, the basic reproduction number is derived, which serves as a threshold value determining the stability of the equilibrium points. By constructing suitable Lyapunov functional, the global asymptotic stability of the equilibria of the model is established in terms of the basic reproduction number. In particular, the disease-free equilibrium of the model is globally asymptotically stable if the basic reproduction number is less than one, while the disease persists and the unique endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one. The analysis of our model indicates that our model is realistic to give a hint to control the transmission of dengue. Furthermore, it follows from the formulation of the infection-free equilibrium of susceptible humans $S_h^0$ and the basic reproduction number $R_0$ that both of them are decreasing with respect to the vaccination parameter ${\psi }_h$, which indicates that appropriate vaccinating program may contribute to prevent the transmission of Dengue disease.

This paper is concerned with a diffusive West Nile virus model (WNv) in a heterogeneous environment. The basic reproduction number $R_0$ for spatially homogeneous model is first introduced. We then define a threshold parameter $R_0^N$ for the corresponding diffusive WNv model in a heterogeneous environment. It is shown that if $R_0^N>1$, the model admits at least one nontrivial T-periodic solution, whereas if $R_0^N<1$, the model has no nontrivial T-periodic solution. By means of monotone iterative schemes, the true solution can be obtained and the asymptotic behavior of periodic solutions is presented. The paper is closed with some numerical simulations to illustrate our theoretical results.

In this paper, we study a fractional-order model with time-delay to describe the dynamics of Ebola virus infection with cytotoxic T-lymphocyte (CTL) response in vivo. The time-delay is introduced in the CTL response term to represent time required to stimulate the immune system. Based on fractional Laplace transform, some conditions on stability and Hopf bifurcation are derived for the model. The analysis shows that the fractional-order with time-delay can effectively enrich the dynamics and strengthen the stability condition of fractional-order infection model. Finally, the derived theoretical results are justified by some numerical simulations.

The identification of protein-coding regions in DNA sequence using digital signal processing methods is one of the central issues in bioinformatics. In this paper, a multirate structure is proposed for the identification of protein-coding regions whose input sampling rate is same as output sampling rate. The multirate structure consists of cascade combination of decimation filter, kernel filter and interpolation filter. The decimation filter is a complex filter, the kernel filter is an FIR lowpass filter and the interpolation filter isa moving average filter. Polyphase decomposition is applied on both decimation filter and interpolation filter for computationally efficient implementation. The potential of the proposed method is evaluated in comparison with existing methods using standard datasets. The results show that the proposed method improves the identification accuracy of protein-coding regions to a great extent compared to its counterparts.

In this paper, we investigate the effects on prey of two predators which are also related in terms of prey–predator relationship. Different types of functional responses are considered to formulate the mathematical model for predator and generalist predator of our proposed model. Harvesting effort for the generalist predator is considered and the density-dependent mortality rate for predator and generalist predator is incorporated in our proposed model. Local stability as well as global stability for the system is discussed. We analyze the different bifurcation parameters to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Finally, some numerical simulations and graphical figures are provided to verify our analytical results with the help of different sets of parameters.

In this study, Haar wavelet method is implemented for solving the nonlinear age-structured population model which is the nonclassic type of partial differential equation associated with boundary integral equation. This paper develops the flexibility of Haar wavelet method for reduction of the partial differential equation with nonlocal boundary conditions to an algebraic system. In fact, the simple structure of piecewise orthogonal Haar basis functions which leads to sparse matrices causes the convergence and computational efficiency. Some illustrative results show the reliability and accuracy of the presented method.

In this paper, a two-species harvesting model has been considered and developed 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 an equivalent crisp model using interval mathematics. The main advantage of the proposed procedure is that different characteristics of the model can be presented 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.

The basic theme of this work is to identify the optimal measurement locations for pressure and flow in the systemic circulation to detect aortic stenoses and aneurysms in early stages of a disease. For this purpose, a linear elastic lumped parameter model of the fluid dynamical simulator, major arterial cardiovascular simulator (MACSim), is considered and global sensitivity analysis is applied to identify the better measurement locations for pressure and flow in the systemic circulation. The obtained results of sensitivity analysis provide insight that enable the experimentalists to optimize their experimental setups for detecting aortic stenoses and aneurysms using parameter estimation process. From the results, it is observed that the stenosis in the thoracic aorta can be identified from both pressure and flow at the location itself, nearby nodes, aorta ascendens, arcus aorta, arteria subclavia and arteria axillaris. On the other hand, the preferable measurement locations for abdominal aneurysms are locations themselves, nearby nodes and left/right leg of the body.

We investigate the global exponential stability of Cohen–Grossberg neural networks (CGNNs) with variable moments of impulses using B-equivalence method. Under certain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.

In this paper, we consider an application of hyperstructure theory in biological inheritance in which we deal with $n$-ary hyperstructures associated to the genotypes of the second generation $F_2$ for $n=2,3,4$. First, we define a hyperoperation × (mating) on $F_2$ and prove that it is a cyclic $H_v$-semigroup under the defined hyperoperation. Then we define a ternary hyperstructure $f$ associated to the genotypes of $F_2$ and prove that $(F_2,f)$ is a ternary $H_v$-semigroup. Finally, we define a $4$-ary hyperstructure $g$ associated to the genotypes of $F_2$ and prove that $(F_2,g)$ is a $4$-ary $H_v$-semigroup.

The dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.

Paddy growth is influenced by the amount of inorganic fertilizer in paddy ecosystem in fallow season. To discover the interaction among weed, inorganic fertilizer and herbivore in the system, we put forward a differential equation model and investigate its properties. Results show that the system has a weed and herbivore extinct equilibrium and a herbivore extinct equilibrium. The two equilibria are proven to be unstable using the center manifold method. Under certain conditions, the system also has a positive equilibrium point. We give the stable region and the unstable region of the positive equilibrium point, which are determined by some parameters. We find that the system has the Hopf bifurcation phenomenon, and give the critical value of Hopf bifurcation by taking a system parameter as the bifurcation parameter. By comparing the equilibrium states between a paddy ecosystem with herbivore and one without herbivore, we find that the content of inorganic fertilizer can be improved by putting herbivore into a paddy field. An example is given to illustrate the feasibility of the results. Numerical simulation shows that Hopf bifurcation phenomena exist in the system.