International Journal of Biomathematics

We propose and analyze mathematical models to study the dynamics of smoking behavior under the influence of educational programs and also individual's determination to quit smoking. We establish the positivity and boundedness of the solutions in a biologically feasible region. A threshold value responsible for persistence of smoking is obtained and stability analysis on models is performed. We find that determination alone is not enough to eradicate smoking but it can reduce the prevalence of smoker population. Whereas the increase in education can possibly eradicate it. We performed numerical simulation for representative set of parameters to verify and discuss results obtained analytically.

In this paper, finite element approach using two-dimensional unsteady state problem has been developed to study radial and angular calcium diffusion problem in neurons. Calcium is responsible messenger for transmitting information in communication process between neurons. The most important Ca²⁺ binding proteins for the dynamics of Ca²⁺ is itself buffer and other physiological parameters are located in Ca²⁺ stores. In this study, the model incorporates the physiological parameters like diffusion coefficient, receptors, exogenous buffers etc. Appropriate boundary conditions have been framed in view of the physiological conditions. Computer simulations in MATLAB 7.11 are employed to investigate mathematical models of reaction–diffusion equation, the details of the implementation can heavily affect the numerical solutions and, thus, the outcome simulated on Core(TM) i3 CPU M 330 @ 2.13 GHz processing speed and 3 GB memory.

In the last decades Exp-function method has been used for solving fractional differential equations. In this paper, we obtain exact solutions of fractional generalized reaction Duffing model and nonlinear fractional diffusion–reaction equation. The fractional derivatives are described in the modified Riemann–Liouville sense. The fractional complex transform has been suggested to convert fractional-order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation.

Graphical representation of DNA sequences is a key component in studying biological problems. In order to gain new insights in DNA sequences, this paper combined the digitized methods of single-base, base pairs and coding in triplet bases with the times of base appearing, and then a novel 4D graphical representation method of DNA sequences was put forward. It was a one-to-one correspondence of the arbitrary DNA sequence and 4D graphical representation, that avoided causing non-unique 4D graphical representation and overlapping lines. The method could reflect the biological information features of DNA sequence more comprehensively and effectively without any losses. Based on the 4D graphical representation, we used the geometric center of 4D graphical representation as eigenvalue of DNA sequences analyses, which kept the original features of the data, and then established the Euclidean distances and included angles between vectors' terminal point for similarity analyses of the first extron of the beta-globulin gene among 11 species. Finally, we established the graph of systematic hierarchical cluster analysis of 11 species to observe more easily the relationship between species. A positive outcome was reached, and the results were in accord with biological taxonomy, which also supported the rationality and effectiveness of the novel 4D graphical representation.

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible (SIS) type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate. In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard (self-diffusion) system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.

In this paper, we investigate a new model with a generalized feedback mechanism in weighted networks. Compare to previous models, we consider the initiative response of people and the important impact of nodes with different edges on transmission rate as epidemics prevail. Furthermore, by constructing Lyapunov function, we prove that the disease-free equilibrium E⁰ is globally asymptotically stable as the epidemic threshold R* < 1. When R* > 1, we obtain the permanence of epidemic and the local stability of endemic equilibrium E*. Finally, one can find a good agreement between numerical simulations and our analytical results.

We consider a model of the exploitative competition of two micro-organisms for two complementary nutrients in a chemostat and take into account the interspecific interaction. The growth functions occurring in the model are of general type and the interaction functions are monotonic and positive. By the mean of the Thieme–Zhao theorem, we establish conditions for uniform persistence of the model.

In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincaré's Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that: (1) the pest population can be controlled below some threshold; (2) compared to single measure, it is more efficient to take two measures for reducing the level of the pests.

In this paper, a mathematical model for steady blood flow through blood vessels with uniform cross-section in stenoses arteries has been proposed. Blood is assumed to be non-Newtonian, incompressible and homogeneous fluid. Blood in human artery is represented as Bingham plastic fluid. Expressions for flow rate, wall shear stress, and resistance to flow against stenoses size have been obtained. Obtained results indicate that stenoses size decreases the flow rate and increases the wall shear stress as well as resistance to flow.

A community composition island biogeography model was developed to explain and predict two community patterns (beta diversity and endemism) with the consideration of speciation, extinction and dispersal processes. Results showed that rate of speciation is positively and linearly associated with beta diversity and endemism, that is, increasing species rates typically could increase the percentage of both endemism and beta diversity. The influences of immigration and extinction rates on beta diversity and endemism are nonlinear, but with numerical simulation, I could observe that increasing extinction rates would lead to decreasing percentage of endemism and beta diversity. The role of immigration rate is very similar to that of speciation rate, having a positive relationship with beta diversity and endemism. Finally, I found that beta diversity is closely related to the percentage of endemism. The slope of this positive relationship is determined jointly by different combinations of speciation, extinction and immigration rates.

In this paper, we consider a discrete Lotka–Volterra competitive system with the effect of toxic substances and feedback controls. By using the method of discrete Lyapunov function and by developing a new analysis technique, we obtain the sufficient conditions which guarantee that one of the two species will be driven to extinction while the other will be permanent. We improve the corresponding results of Li and Chen [Extinction in two-dimensional discrete Lotka–Volterra competitive system with the effect of toxic substances, Dynam. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 15 (2008) 165–178]. Also, an example together with their numerical simulations shows the feasibility of our main results. It is shown that toxic substances and feedback control variables play an important role in the dynamics of the system.

In this paper, we consider a diffusive Holling–Tanner predator–prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, existence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifurcating periodic solutions of the system in the absence of diffusion. Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied. Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.

This paper deals with the theoretical investigation of a fundamental problem of magnetohydrodynamic (MHD) flow of blood in a capillary in the presence of thermal radiation and chemical reaction. The unsteadiness in the flow and temperature fields is caused by the time-dependence of the stretching velocity and the surface temperature. The fluid is considered to be non-Newtonian, whose flow is governed by the equation of a third-order fluid. The problem is first reduced to solving a system of coupled nonlinear differential equations involving several parameters. Considering blood as an electrically conducting fluid and using the present analysis, an attempt is made to compute some parameters of the blood flow by developing a suitable numerical method and by devising an appropriate finite difference scheme. The computational results are presented in graphical form, and thereby some theoretical predictions are made with respect to the hemodynamical flow of the blood in a hyperthermal state under the action of a magnetic field. Computational results for the variation in velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are presented in graphical/tabular form. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding blood flow and heat transfer in capillaries.