J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.2760 Research Paper Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling Influence of awareness programs by media in the typhoid fever Mondal Jayanta Department of Mathematics, Diamond Harbour Women&#039;s University, Sarisha-743368, India 01 07 2018 6 1 1 26 19 03 2018 19 03 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2760.html

In this paper, we propose and analyze a mathematical model describing the effect of awareness programs by public media on the prevalence of Typhoid fever. A threshold quantity \$R_{0}\$, similar to the basic reproduction number is derived. We investigate the biologically meaningful equilibrium points and their local stability analysis. The global stability analysis has been performed with respect to the disease free equilibrium (DFE) \$E_{0}\$ by considering suitable Lyapunov function. We derive the stability condition of the DFE point \$E_{0}\$ and the interior steady-state \$E^{*}\$ with respect to the basic reproduction number \$R_{0}\$. We perform the analysis of Hopf-bifurcation with respect to the rate of executing awareness programs which has a substantial role on the dynamics of the model system. We investigate extensive numerical simulations to validate our analytical findings.

Typhoid fever awareness program Hopf-bifurcation basic reproduction number Stability analysis
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.2761 Research Paper An \${cal O}(h^{8})\$ optimal B-spline collocation for solving higher order boundary value problems An \${cal O}(h^{8})\$ optimal B-spline collocation for higher order BVPs Sharifi Shokofeh Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran Jalil Rashidinia School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran 01 07 2018 6 1 27 46 19 03 2018 19 03 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2761.html

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only \${cal O}(h^{2})\$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The \${cal O}(h^{8})\$ convergence analysis, mainly based on the Green's function approach, has been proved. Numerical illustration demonstrate the applicability of the purposed method. Three test problems have been solved and the computed results have been compared with the results obtained by recent existing methods to verify the accurate nature of our method.

Nonlinear boundary value problems eighth degree B-spline collocation method convergence Analysis Green&#039;s function
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.2775 Research Paper Global properties of a tuberculosis model with lost sight and multi-compartment of latents Global properties of a tuberculosis model Temgoua Anatole Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon Malong Yannick Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon Mbang Joseph Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon Bowong Samuel Laboratory of Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon. UMI 209 IRD & UPMC UMMISCO, Bondy, France Project team GRIMCAPE-Cameroon 01 07 2018 6 1 47 76 28 03 2018 28 03 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2775.html

A  tuberculosis (TB) model with  lost sight  and multiple latent classes  is considered and studied. We derive the basic reproduction ratio \$mathcal R_0\$. There is always a globally asymptotically stable equilibrium state. Depending on the value of   \$mathcal{R}_0\$, this state can be either endemic (\$mathcal{R}_0> 1\$), or infection-free (\$mathcal{R}_0leq 1\$). The global asymptotic stability of equilibria is established using Lyapunov functions that combine quadratic, Volterra-type and linear functions. The theory is supported by numerical simulations.

TB mathematical models basic reproduction number Stability
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.2808 Research Paper Solution of Troesche's problem by double exponential Sinc collocation method Solution of Troesche's problem by DE Sinc collocation method Nabati Mohammad Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran Nikmanesh Soudabeh Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran Jalalvand Mehdi Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran 01 07 2018 6 1 77 90 24 04 2018 24 04 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2808.html

In this investigation, the Sinc collocation method based on double exponential transformation is developed to solve the Troesche's problem. Properties of this method are utilized to reduce the system of strongly nonlinear two point boundary value problem to same nonlinear algebraic equations. Combining double exponential transformation through Sinc collocation method causes the remarkable results. To illustrate the high accuracy of the method, the obtained solutions are compared with results of other methods in open literature. The demonstrated results show the simplicity and considerably accuracy of this method in comparison with other methods.

Sinc function collocation method double exponential transformation nonlinear Troesche&#039;s problem
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.2826 Research Paper Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations Fractional Volterra-Fredholm integro-differential equation Hamoud Ahmed A. Department of Mathematics, Taiz University, Taiz, 96704, Yemen and Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431004, India Ghadle Kirtiwant P. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India. 01 07 2018 6 1 91 104 20 05 2018 20 05 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2826.html

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate.  Moreover, the paper proves the convergence and uniqueness of the solution. Finally, this study includes an example to demonstrate the validity and applicability of the proposed techniques.

Laplace transform Adomian decomposition method fractional Volterra-Fredholm integro-differential equation Caputo fractional derivative
J. Math. Model. دانشگاه گیلان Journal of Mathematical Modeling 2345-394X دانشگاه گیلان 17 10.22124/jmm.2018.5019.1059 Research Paper Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems Biorthogonal wavelet-based full-approximation schemes Shiralashetti Siddu C. Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India Kantli Mounesha H. Department of Mathematics, KLE Society&#039;s J. T. College, Gadag-582101, India Deshi Aravind B. Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India 01 07 2018 6 1 105 122 01 01 1970 06 06 2018 Copyright © 2018, دانشگاه گیلان. 2018 https://jmm.guilan.ac.ir/article_2829.html

Biorthogonal wavelet-based full-approximation schemes are introduced in this paper for the numerical solution of elasto-hydrodynamic lubrication line and point contact problems. The proposed methods give higher accuracy in terms of better convergence with low computational time, which have been demonstrated through the illustrative problems.

CDF wavelets filter coefficients Full-approximation scheme Elasto-hydrodynamic lubrication problems