@article { author = {Mondal, Jayanta}, title = {Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {1-26}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.2760}, abstract = {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.}, keywords = {Typhoid fever,awareness program,Hopf-bifurcation,basic reproduction number,Stability analysis}, url = {https://jmm.guilan.ac.ir/article_2760.html}, eprint = {https://jmm.guilan.ac.ir/article_2760_5a9bd5d991f6d86eb9eccb99c62065e9.pdf} } @article { author = {Sharifi, Shokofeh and Jalil, Rashidinia}, title = {An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {27-46}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.2761}, abstract = {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.}, keywords = {Nonlinear boundary value problems,eighth degree B-spline,collocation method,convergence Analysis,Green's function}, url = {https://jmm.guilan.ac.ir/article_2761.html}, eprint = {https://jmm.guilan.ac.ir/article_2761_4be105a37e6619351966cdec74a917d0.pdf} } @article { author = {Temgoua, Anatole and Malong, Yannick and Mbang, Joseph and Bowong, Samuel}, title = {Global properties of a tuberculosis model with lost sight and multi-compartment of latents}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {47-76}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.2775}, abstract = {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 ($\mathcal{R}_0\leq 1$). 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.}, keywords = {TB,mathematical models,basic reproduction number,Stability}, url = {https://jmm.guilan.ac.ir/article_2775.html}, eprint = {https://jmm.guilan.ac.ir/article_2775_9fed0f438341d3fda516b0ff91d03318.pdf} } @article { author = {Nabati, Mohammad and Nikmanesh, Soudabeh and Jalalvand, Mehdi}, title = {Solution of Troesche's problem by double exponential Sinc collocation method}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {77-90}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.2808}, abstract = {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.}, keywords = {Sinc function,collocation method,double exponential transformation,nonlinear Troesche's problem}, url = {https://jmm.guilan.ac.ir/article_2808.html}, eprint = {https://jmm.guilan.ac.ir/article_2808_8095113b966623525302c21a934b11b5.pdf} } @article { author = {Hamoud, Ahmed and Ghadle, Kirtiwant}, title = {Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {91-104}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.2826}, abstract = {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.}, keywords = {Laplace transform,Adomian decomposition method,fractional Volterra-Fredholm integro-differential equation,Caputo fractional derivative}, url = {https://jmm.guilan.ac.ir/article_2826.html}, eprint = {https://jmm.guilan.ac.ir/article_2826_1a4bd959146587f09e8bad9682cd14d4.pdf} } @article { author = {Shiralashetti, Siddu C. and Kantli, Mounesha H. and Deshi, Aravind B.}, title = {Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems}, journal = {Journal of Mathematical Modeling}, volume = {6}, number = {1}, pages = {105-122}, year = {2018}, publisher = {University of Guilan}, issn = {2345-394X}, eissn = {2382-9869}, doi = {10.22124/jmm.2018.5019.1059}, abstract = {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.}, keywords = {CDF wavelets filter coefficients,Full-approximation scheme,Elasto-hydrodynamic lubrication problems}, url = {https://jmm.guilan.ac.ir/article_2829.html}, eprint = {https://jmm.guilan.ac.ir/article_2829_25297e5e419946881705133aa8d484ea.pdf} }