eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
1
26
10.22124/jmm.2018.2760
2760
مقاله پژوهشی
Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling
Jayanta Mondal
jayantajumath@gmail.com
1
Department of Mathematics, Diamond Harbour Women's University, Sarisha-743368, India
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.
http://jmm.guilan.ac.ir/article_2760_5a9bd5d991f6d86eb9eccb99c62065e9.pdf
Typhoid fever
awareness program
Hopf-bifurcation
basic reproduction number
stability analysis
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
27
46
10.22124/jmm.2018.2761
2761
مقاله پژوهشی
An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
Shokofeh Sharifi
sh.sharifi_m61@yahoo.com
1
Rashidinia Jalil
rashidinia@iust.ac.ir
2
Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
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.
http://jmm.guilan.ac.ir/article_2761_4be105a37e6619351966cdec74a917d0.pdf
Nonlinear boundary value problems
eighth degree B-spline
collocation method
convergence analysis
Green's function
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
47
76
10.22124/jmm.2018.2775
2775
مقاله پژوهشی
Global properties of a tuberculosis model with lost sight and multi-compartment of latents
Anatole Temgoua
temgouaanatole@yahoo.fr
1
Yannick Malong
ycmalong@yahoo.fr
2
Joseph Mbang
mbangjoseph74@gmail.com
3
Samuel Bowong
sbowong@univ-douala.com
4
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
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
Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon
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
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.
http://jmm.guilan.ac.ir/article_2775_9fed0f438341d3fda516b0ff91d03318.pdf
TB
mathematical models
basic reproduction number
stability
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
77
90
10.22124/jmm.2018.2808
2808
مقاله پژوهشی
Solution of Troesche's problem by double exponential Sinc collocation method
Mohammad Nabati
nabati@put.ac.ir
1
Soudabeh Nikmanesh
soudabeh.nikmanesh@put.ac.ir
2
Mehdi Jalalvand
m.jalalvand@scu.ac.ir
3
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
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.
http://jmm.guilan.ac.ir/article_2808_8095113b966623525302c21a934b11b5.pdf
Sinc function
collocation method
double exponential transformation
nonlinear Troesche's problem
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
91
104
10.22124/jmm.2018.2826
2826
مقاله پژوهشی
Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations
Ahmed Hamoud
drahmedselwi985@gmail.com
1
Kirtiwant Ghadle
drkp.ghadle@gmail.com
2
Department of Mathematics, Taiz University, Taiz, 96704, Yemen and Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431004, India
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India.
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.
http://jmm.guilan.ac.ir/article_2826_1a4bd959146587f09e8bad9682cd14d4.pdf
Laplace transform
Adomian decomposition method
fractional Volterra-Fredholm integro-differential equation
Caputo fractional derivative
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2018-07-01
6
1
105
122
10.22124/jmm.2018.5019.1059
2829
مقاله پژوهشی
Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems
Siddu C. Shiralashetti
shiralashettisc@gmail.com
1
Mounesha H. Kantli
mkantli@gmail.com
2
Aravind B. Deshi
aravind42d@gmail.com
3
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
Department of Mathematics, KLE Society's J. T. College, Gadag-582101, India
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
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.
http://jmm.guilan.ac.ir/article_2829_25297e5e419946881705133aa8d484ea.pdf
CDF wavelets filter coefficients
Full-approximation scheme
Elasto-hydrodynamic lubrication problems