University of GuilanJournal of Mathematical Modeling2345-394X5220171201Effects of ionic parameters on behavior of a skeletal muscle fiber model7788234310.22124/jmm.2017.2343ENSamanehShahiFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranHosseinKheiriFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20170725All living cells have a membrane which separates inside the cell from it's outside. There is a potential difference between inside and outside of the cell. This potential difference will change during an action potential. It is quite common to peruse action potentials of skeletal muscle fibers with the Hodgkin-Huxley model. Since Hodgkin and Huxley summarized some controlling currents like inward rectifier current or chloride current as a leak current when we try to study the sensitivity of model to some parameters we lose some details. In this paper we use a model which contains sodium, potassium, chloride, Na-K pump, and inward rectifier currents. Firstly, we find critical point of the system, and discuss on how action potential changes for different initial values of variables. Then we study sensitivity of the critical point and maximum of potential to different parameters.https://jmm.guilan.ac.ir/article_2343_1731f1b7f451e3db89d4f150c13bdc9d.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X5220171201Numerical solution of non-planar Burgers equation by Haar wavelet method89118246010.22124/jmm.2017.2460ENSumana RSheshaBangalore UniversityAchala L.NargundDepartment of Studies in Mathematics, Karnatak University, Dharwad, IndiaNagendrappa M.BujurkeDepartment of Studies in Mathematics, Karnatak University, Dharwad, IndiaJournal Article20171004In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a finite number of variables. The solution obtained by Haar wavelet collocation method is compared with that obtained by finite difference method and are found to be in good agreement. Shock waves are found to be formed due to nonlinearity and dissipation. We have analyzed the effects of non-planar and nonlinear geometry on shock existence. We observe that non-planar shock structures are different from planar ones. It is of interest to find that Haar wavelets enable to predict the shock structure accurately.https://jmm.guilan.ac.ir/article_2460_de6a3c4204cdd70ae58a47355b658fa6.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X5220171201Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response119136248210.22124/jmm.2017.2482ENSambathMuniyagounderDepartment of Mathematics, Periyar University, Salem-636011, IndiaRamajayamSahadevanRamanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-600005, IndiaJournal Article20171101In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spatially homogeneous. In order to verify our theoretical results, some numerical simulations are also presented.https://jmm.guilan.ac.ir/article_2482_0f775ecfc0197e23541d4f5fbcaa278c.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X5220171201A mathematical model for treatment of bovine brucellosis in cattle population137152252310.22124/jmm.2017.2523ENJuliusTumwiineDepartment of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, UgandaGodwinRobertDepartment of Mathematics, Mbarara University of Science and Technology,
P.O. Box 1410 Mbarara, UgandaJournal Article20171201Brucellosis is an infectious bacterial zoonosis of public health and economic significance. In this paper, a mathematical model describing the propagation of bovine brucellosis within cattle population is formulated. Model analysis is carried out to obtain and establish the stability of the equilibrium points. A threshold parameter referred to as the basic reproduction number $\mathcal{R}_{0}$ is calculated and the conditions under which bovine brucellosis can be cleared in the cattle population are established. It is found out that when $\mathcal{R}_{0}<1,$ the disease can be eliminated in the cattle population or persists when $\mathcal{R}_{0}>1$. Using Lyapunov function and Poincair\'{e}-Bendixson theory, we prove that the disease-free and endemic equilibrium, respectively are globally asymptotic stable. Numerical simulation reveals that control measures should aim at reducing the magnitude of the parameters for contact rate of infectious cattle with the susceptible and recovered cattle, and increasing treatment rate of infected cattle.https://jmm.guilan.ac.ir/article_2523_c01bbe2d4b27e2285b641b5ef7880983.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X5220171201Existence and continuous dependence for fractional neutral functional differential equations153170253510.22124/jmm.2017.2535ENMohammed SalemAbdoDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, IndiaSatish KushabaPanchalDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 IndiaJournal Article20171205In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.https://jmm.guilan.ac.ir/article_2535_56ca6929d8a86326b7a2970116eeeb03.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X5220171201An interior-point algorithm for $P_{\ast}(\kappa)$-linear complementarity problem based on a new trigonometric kernel function171197253710.22124/jmm.2017.2537ENSajadFathi-HafshejaniDepartment of Mathematics, Shiraz University of Technology, Shiraz, Iran0000-0002-9907-0695HosseinMansouriDepartment of Applied Mathematics, Shahrekord University, Shahrekord, IranMohammad RezaPeyghamiFaculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, IranJournal Article20171208In this paper, an interior-point algorithm for $P_{\ast}(\kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2\kappa)\sqrt{n} \log n\log\frac{n}{\epsilon})$ iteration bound for large-update methods, which coincides with the best known complexity bound. Moreover, numerical results confirm that our new proposed kernel function is doing well in practice in comparison with some existing kernel functions in the literature.https://jmm.guilan.ac.ir/article_2537_cf3ea063a8ab351a654ae8a859b24f8d.pdf