International Journal of Biomathematics

Magnetohydrodynamic peristaltic flow of Jeffery fluid in an asymmetric channel is addressed. The channel walls satisfy the convective conditions. Asymmetry here is considered due to wave trains of different amplitudes and phases. Solutions for the velocity, temperature and pressure gradient are obtained using long wavelength approximation. Plots reflecting the impact of various parameters of interest are shown and examined.

Small rodents in general and the multimammate rat Apodemus agrarius in particular, damage crops and cause major economic losses in China. Therefore, accurate predictions of the population size of A. agrarius and an efficient control strategy are urgently needed. We developed a population dynamics model by applying a Leslie matrix method, and a capture model based on optimal harvesting theory for A. agrarius. Our models were parametrized using demographic estimates from a capture–mark–recapture (CMR) study conducted on the Qinshui Forest Farm in Northwestern China. The population dynamics model incorporated 12 equally balanced age groups and included immigration and emigration parameters. The model was evaluated by assessing the predictions for four years based on the known starting population in 2004 from the 2004–2007 CMR data. The capture model incorporated two functional age categories (juvenile and adult) and used density-dependent and density-independent factors. The models were used to assess the effect of rodent control measures between 2004 and 2023 on population dynamics and the resulting numbers of rats. Three control measures affecting survival rates were considered. We found that the predicted population dynamics of A. agrarius between 2004 and 2007 compared favorably with the observed population dynamics. The models predicted that the population sizes of A. agrarius in the period between 2004 and 2023 under the control measure applied in August 2004 were very similar to the optimal population sizes, and no significant difference was found between the two population sizes. We recommend using the population dynamics and capture models based on CMR-estimated demographic schedules for rodent, provided these data are available. The models that we have developed have the potential to play an important role in predicting the effects of rodent management and in evaluating different control strategies.

In this paper, by introducing a proper transformation, the (G′/G)-expansion method is further extended into the nonlinear reaction–diffusion equations in mathematical biology whose balancing numbers may be negative integer. As a result, hyperbolic function solutions and trigonometric function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions and the periodic wave solutions are also derived from the traveling wave solutions. Moreover, it is observed that the suggested techniques is compatible of such problems.

In this paper, a stochastic predator–prey (PP) model with mutual interference is considered. Some sufficient conditions for the existence of globally positive solution, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and almost surely extinction of the the model are established. Moreover, the threshold between weak persistence in the mean and almost surely extinction of the prey is obtained. Some examples are given to show the feasibility of the results by numerical simulation. It is significant that such a model is firstly proposed with stochastic perturbation.

The diffusive Leslie–Gower predator–prey model incorporating a prey refuge is reconsidered here. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained, and our results supplement earlier ones.

In this paper, we consider a modified Leslie–Gower predator–prey model with Holling-type II schemes and mutual interference. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov function, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Our results not only supplement but also improve some existing ones.

By using some analytical techniques, modified inequalities and Mawhin's continuous theorem of coincidence degree theory, some simple sufficient conditions for the existence of at least one positive almost periodic solution of a generalized Mackey–Glass model of respiratory dynamics are obtained. Further, the global attractivity of positive almost periodic solution of the above model is also studied. To the best of the author's knowledge, so far, the result of this paper is completely new. Finally, three examples are given to illustrate the main results in this paper.

We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method (SIRM). Unlike in the previous work [M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci.5 (1992) 221–247] where the habitat is assumed to be the one-dimensional whole space ℝ, we consider this system in a bounded one-dimensional domain (interval). Our goal is to derive sufficient conditions for success of the SIRM. We show the existence of the fertile-free steady state and prove its stability. Using the releasing rate as the parameter, and by a saddle-node bifurcation analysis, we obtain conditions for existence of two co-persistence steady states, one stable and the other unstable. Biological implications of our mathematical results are that: (i) when the fertile population is at low level, the SIRM, even with small releasing rate, can successfully eradicate the fertile insects; (ii) when the fertile population is at a higher level, the SIRM can succeed as long as the strength of the sterile releasing is large enough, while the method may also fail if the releasing is not sufficient.

In this paper a finite element model is developed to study cytosolic calcium concentration distribution in astrocytes for a two-dimensional steady-state case in presence of excess buffer. The mathematical model of calcium diffusion in astrocytes leads to a boundary value problem involving elliptical partial differential equation. The model consists of reaction–diffusion phenomena, association and dissociation rates and buffer. A point source of calcium is incorporated in the model. Appropriate boundary conditions have been framed. Finite element method is employed to solve the problem. A MATLAB program has been developed for the entire problem and simulated to compute the numerical results. The numerical results have been used to plot calcium concentration profiles in astrocytes. The effect of EGTA, BAPTA and σ_Ca influx on calcium concentration distribution in astrocytes is studied with the help of numerical results.

In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination is investigated. In vaccination strategy, we perform impulsive vaccination of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effectiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput. Simulat.79 (2009) 3038–3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.

In this paper, we present a diffusive predator–prey system with Beddington–DeAngelis functional response, where the prey species can disperse between the two patches, and there is competition between the two predators. Sufficient conditions for the permanence and extinction of system are established based on the upper and lower solution methods and comparison theory of differential equation. Furthermore, the global asymptotic stability of positive solutions is obtained by constructing a suitable Lyapunov function. By using the continuation theorem in coincidence degree theory, we show the periodicity of positive solutions. Finally, we illustrate global asymptotic stability of the model by a simulation figure.

In this paper, a reaction–diffusion model describing temporal development of tumor tissue, normal tissue and excess H⁺ ion concentration is considered. Based on a combination of perturbation methods, the Fredholm theory and Banach fixed point theorem, we theoretically justify the existence of the traveling wave solution for this model.