International Journal of Biomathematics

An existing growth model of Edelstien is extended and modified for multiple root branching structure or root hairs of any plant. Numerical and analytical solutions for the model are developed and compared. In the derivation it is assumed that multiple root branches are attached to the root surface that acts as a continuous source of new tips. The numerical scheme is derived with anticipation of the fact that comparison with experimental data may necessitate a more complicated model.

In this paper, we discuss the behavior of a predator–prey model with disease in the prey with and without stochastic perturbation, respectively. First, we briefly give the dynamic of the deterministic system, by analyzing stabilities of its four equilibria. Then, we consider the asymptotic behavior of the stochastic system. By Lyapunov analysis methods, we show the stochastic stability and its long time behavior around the equilibrium of the deterministic system. We obtain there are similar properties between the stochastic system and its corresponding deterministic system, when white noise is small. But large white noise can make a unstable deterministic system to be stable.

The relations between the Human Immunodeficiency Virus-1 (HIV-1) and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes (CTLs) in the suppression of viral replication in HIV-1 infected individuals cannot be ignored. In this research paper, we have proposed a mathematical model incorporating half saturation constant through the CTL mediated killing process and also in that sense, it has been infiltrated in the generation process of CTL through infected cells. To make the model more realistic, a time lag is introduced in the generation term of CTL population. Also an optimal control theory paradigm is used in our mathematical model to suppress the viral production. From our entire analysis, we have found threshold condition of half saturation constant and treatment schedule so that we can handle the situation of Acquired Immunodeficiency Syndrome (AIDS) patients in a better way. Our analysis reveals that, if the half saturation constant is around 47 mm^-3 in the saturation process and the drug therapy is to be used around 76 days, then we can get adequate results for better treatment of a HIV-1 patient. Based on numerical results, we observed that in a highly unstable situation, administration of chemotherapy at a high dose can stabilize the system.

Breast cancer is the leading cause of cancer-related death for women in Tunisia and the prognosis of its metastasis remains a major problem for oncologists despite advances in treatment. In this work we use Bayesian networks to develop a decision support system that is based on the modeling of relationships between key signaling proteins and clinical and pathological characteristics of breast tumors and patients. Motivated by the lack of prior information on the parameters of the problem, we use the Implicit inference for the structure and parameter learning. A dataset of 84 Tunisian breast cancer patients was used and new prognosis factors were identified. The system predicts a metastasis risk for different patients by computing a score that is the joint probability of the Bayesian network using parameters estimated on the learning database. Based on the results of the developed system we identified that overexpression of ErbB2, ErbB3, bcl2 as well as of oestrogen and progesterone receptors associated with a low level of ErbB4 was the predominant profile associated with high risk of metastasis.

In this paper, we propose a variable selection procedure for partially linear varying coefficient model under quantile loss function with adaptive Lasso penalty. The functional coefficients are estimated by B-spline approximations. The proposed procedure simultaneously selects significant variables and estimates unknown parameters. The major advantage of the proposed procedures over the existing ones is easy to implement using existing software, and it requires no specification of the error distributions. Under the regularity conditions, we show that the proposed procedure can be as efficient as the Oracle estimator, and derive the optimal convergence rate of the functional coefficients. A simulation study and a real data application are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Analytical solutions are obtained for steady flow of an incompressible second grade fluid in an axisymmetric channel of varying width. Three approximate methods are used depending upon three different geometrical configuration. The results obtained are applied to study the flow of a second grade fluid through a smooth constriction. To understand the flow behavior near stenosis, resistance to the flow, shear stress at the wall and stress at the stenosis throat are calculated. The results obtained are numerically evaluated for different values of dimensionless non-Newtonian parameters λ₁ and λ₂ and maximum height of the stenosis δ_m. It is observed that as we increase the value of these parameters the resistance to the flow, wall shear stress and stress at the stenosis throat increase.

This paper obtains the 1-soliton solution by the ansatz method for the proposed model that governs the propagation of solitons through the neurons. This model is an improved one that describes the solitons in neurosciences more accurately. The ansatz method is applied to obtain the 1-soliton solution to the model. The Lie symmetry analysis is subsequently applied to obtain the conservation laws for the model.

To study the transition dynamics of resistant-type human immunodeficiency virus 1 (HIV-1) in highly active antiretroviral therapy (HAART) and the affect of neutral mutation in the evolution of HIV-1, a mathematical model is proposed when mutation occurs mainly during reproduction. The derived results show that the resistant-type will certainly colonize in patients once mutation occurs. Furthermore, a neutral mutation is closely related to the colonized pattern of resistant-type HIV-1 quasispecies and there are some changes in the pattern of transmission dynamics when mutation occurs mainly during reproduction or in the absence of reproduction, which may lead to significant strategies for predicting or checking HIV-1 drug resistance in HAART.