University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 Effects of ionic parameters on behavior of a skeletal muscle fiber model 77 88 2343 10.22124/jmm.2017.2343 EN Samaneh Shahi Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Hossein Kheiri Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Journal Article 2017 07 25 All 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.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 Numerical solution of non-planar Burgers equation by Haar wavelet method 89 118 2460 10.22124/jmm.2017.2460 EN Sumana R Shesha Bangalore University Achala L. Nargund Department of Studies in Mathematics, Karnatak University, Dharwad, India Nagendrappa M. Bujurke Department of Studies in Mathematics, Karnatak University, Dharwad, India Journal Article 2017 10 04 In 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.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response 119 136 2482 10.22124/jmm.2017.2482 EN Sambath Muniyagounder Department of Mathematics, Periyar University, Salem-636011, India Ramajayam Sahadevan Ramanujan Institute for Advanced Study in Mathematics, University of Madras, hennai-600005, India Journal Article 2017 11 01 In 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.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 A mathematical model for treatment of bovine brucellosis in cattle population 137 152 2523 10.22124/jmm.2017.2523 EN Julius Tumwiine Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda Godwin Robert Department of Mathematics, Mbarara University of Science and Technology, P.O. Box 1410 Mbarara, Uganda Journal Article 2017 12 01 Brucellosis 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.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 Existence and continuous dependence for fractional neutral functional differential equations 153 170 2535 10.22124/jmm.2017.2535 EN Mohammed Salem Abdo Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India Satish Kushaba Panchal Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004 India Journal Article 2017 12 05 In 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.pdf
University of Guilan Journal of Mathematical Modeling 2345-394X 5 2 2017 12 01 An interior-point algorithm for \$P_{ast}(kappa)\$-linear complementarity problem based on a new trigonometric kernel function 171 197 2537 10.22124/jmm.2017.2537 EN Sajad Fathi-Hafshejani Department of Mathematics, Shiraz University of Technology, Shiraz, Iran Hossein Mansouri Department of Applied Mathematics, Shahrekord University, Shahrekord, Iran Mohammad Reza Peyghami Faculty of Mathematics, K.N. Toosi Univ. of Tech., Tehran, Iran Journal Article 2017 12 08 In 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+2kappa)sqrt{n} log nlogfrac{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