International Journal of Biomathematics

Peristaltic transport of a Newtonian incompressible fluid in the presence of applied magnetic field in an inclined channel with slip is investigated. A perturbation method of solution is obtained in terms of wall slope parameter and analytical expressions are derived for average velocity and stream function using Saffman slip condition. The effects of various relevant parameters on average velocity and stream line pattern have been studied. It is found that average velocity increases with slip and decreases with permeability and magnetic parameter.

A competitive Lotka–Volterra reaction-diffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive constant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies competition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters (delays) in the system cross some critical values. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifurcation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.

In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of disease-free equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the disease-free equilibrium is globally asymptotically stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

In this paper the concept of a nonlinear verticum-type observation system is introduced. These systems are composed from several "subsystems" connected sequentially in a particular way: a part of the state variables of each "subsystem" also appears in the next "subsystem" as an "exogenous variable" which can also be interpreted as a control generated by an "exosystem". Therefore, these "subsystems" are not observation systems, but formally can be considered as control-observation systems. The problem of observability of such systems can be reduced to rank conditions on the "subsystems". Indeed, under the condition of Lyapunov stability of an equilibrium of the "large", verticum-type system, it is shown that the Kalman rank condition on the linearization of the "subsystems" implies the observability of the original, nonlinear verticum-type system.

For an illustration of the above linearization result, a stage-structured fishery model with reserve area is considered. Observability for this system is obtained by applying the above linearization and decomposition approach. Furthermore, it is also shown that, applying an appropriate observer design method to each subsystem, from the observation of the biomass densities of the adult (harvested) stage, in both areas, the biomass densities of the pre-recruit stage can be efficiently estimated.

The purpose of this paper is to study the effect of cross diffusion in a competition model with stage structure, under homogeneous Neumann boundary condition. It will be shown that cross diffusion cannot only destabilize a uniform positive equilibrium, it can also help diffusion to induce instability of the uniform positive equilibrium. Moreover, stationary patterns can arise from the effect of cross diffusion.

Survival of patients with childhood hematological malignancies has increased markedly in the past decades. To examine the fine-scale details of how this progress has occurred, we carried out Kaplan–Meier cause-specific survival analysis using the Surveillance Epidemiology and End Results (SEER) dataset for patients with childhood hematological malignancies — Hodgkin's Lymphoma, Non-Hodgkin's Lymphoma, Lymphoblastic Leukemia and Myeloid Leukemia — diagnosed in five eras: 1983–1987; 1988–1992; 1993–1997; 1998–2002 and 2003–2007. We generated Kaplan–Meier estimates of survival for each of the first 24 years after diagnosis. These figures agree with previously reported five- and ten-year values and attest to the remarkable increase in survival that has occurred over the past three decades of medical progress. The trend towards progressively increasing survival shows no sign of slowing, suggesting that we may expect further increases in survival in the years ahead. Most of the increase in survival for childhood hematological malignancies has occurred by reducing the risk of death in the first two years after diagnosis. This may be largely explained by the fact that this is the time period when patients are at highest risk of death.

The analysis of the consequences of land use (in particular forest use) may be considered as a partial step towards an integrated modeling of a land system. In the paper a forest territory is considered, where a gap-cut is made, and after a given time period the eventual change in the spatial distribution of undergrowth plants and tree seedlings is to be detected. Floristic data are collected along a line transect. A method for the detection of the change in the plant distributions along the transect is proposed to see whether this occurs at the geometric frontier of the human intervention.

Since in the considered case the distribution of the change-point estimate is not known, as a substitute of its confidence interval, the so-called change-interval is calculated, using an adaptation of the bootstrap method. As an illustration, for a concrete plant species, the maximum likelihood estimation of the change-point and the calculation of the above mentioned change-interval is presented. Finally, the validation of the proposed method against some typical ecological situations is also presented, which provides a justification of the used algorithms.

This work investigates frequency distributions of strings within a text. The mathematical derivation accounts for variable alphabet size, character probabilities, and string/text lengths, under both the Bernoullian and the Markovian model for string generation. The analysis is limited to the set of non-clumpable strings, that cannot overlap with themselves. Two formulae (exact and approximated) are derived, calculating the frequency distribution of a string of length m found inside a text of length n (with m < n). The approximated formula has a constant complexity (in contrast to an exponential complexity of the exact) and makes it applicable to very long texts. The proposed formulae were applied to analyze string frequencies in a portion of the human genome, and to recalculate frequencies of known repeated motif within genes, associated to genetic diseases. A comparison with state-of-the-art methods was provided. The formulae presented here can be of use in the statistical evaluation of specific motif frequencies within very long texts (e.g. genes or genomes) and help in characterizing motifs in pathologic conditions.

In this paper, we investigate global dynamics for a distributed time delayed HCV infection model. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. By employing the method of Lyapunov functional, we prove that the uninfected equilibrium is global asymptotically stable if the basic reproduction number is less than one, it is unstable and the infected equilibrium is global asymptotically stable if the basic reproduction number is larger than one. The simulations results are in good accordance with our analytic results.

In this paper, we consider a stage-structured predator–prey model with modified Leslie–Gower and Holling-type II schemes. Using an iterative technique, we investigate the global stability of the positive equilibrium of the system. Finally, some examples are presented to verify our main result.

In this paper, we investigate global dynamics for an in-host HIV-1 infection model with the long-lived infected cells and four intracellular delays. Our model admits two possible equilibria, an uninfected equilibrium and infected equilibrium depending on the basic reproduction number. We derive that the global dynamics are completely determined by the values of the basic reproduction number: if the basic reproduction number is less than one, the uninfected equilibrium is globally asymptotically stable, and the virus is cleared; if the basic reproduction number is larger than one, then the infection persists, and the infected equilibrium is globally asymptotically stable.

In this paper, a class of homoclinic bifurcations in semi-continuous dynamic systems are investigated. On the basis of rotated vector fields theory, existence of order-1 periodic solution and the rotated vector fields of the semi-continuous dynamic system are discussed. Furthermore, homoclinic cycles and homoclinic bifurcations are described. Finally, an example is provided to show the validity of our theoretical results.

In this paper, a strongly coupled diffusive predator–prey system with a modified Leslie–Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns.