University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling
1
26
EN
Jayanta
Mondal
Department of Mathematics, Diamond Harbour Women's University, Sarisha-743368, India
jayantajumath@gmail.com
10.22124/jmm.2018.2760
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
https://jmm.guilan.ac.ir/article_2760.html
https://jmm.guilan.ac.ir/article_2760_5a9bd5d991f6d86eb9eccb99c62065e9.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
27
46
EN
Shokofeh
Sharifi
Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
sh.sharifi_m61@yahoo.com
Rashidinia
Jalil
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
rashidinia@iust.ac.ir
10.22124/jmm.2018.2761
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's function
https://jmm.guilan.ac.ir/article_2761.html
https://jmm.guilan.ac.ir/article_2761_4be105a37e6619351966cdec74a917d0.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
Global properties of a tuberculosis model with lost sight and multi-compartment of latents
47
76
EN
Anatole
Temgoua
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
temgouaanatole@yahoo.fr
Yannick
Malong
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
ycmalong@yahoo.fr
Joseph
Mbang
Department of Mathematics, Faculty of Science,
University of Yaounde I, PO Box 812 Yaounde, Cameroon
mbangjoseph74@gmail.com
Samuel
Bowong
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
sbowong@univ-douala.com
10.22124/jmm.2018.2775
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
https://jmm.guilan.ac.ir/article_2775.html
https://jmm.guilan.ac.ir/article_2775_9fed0f438341d3fda516b0ff91d03318.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
Solution of Troesche's problem by double exponential Sinc collocation method
77
90
EN
Mohammad
Nabati
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
nabati@put.ac.ir
Soudabeh
Nikmanesh
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
soudabeh.nikmanesh@put.ac.ir
Mehdi
Jalalvand
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
m.jalalvand@scu.ac.ir
10.22124/jmm.2018.2808
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's problem
https://jmm.guilan.ac.ir/article_2808.html
https://jmm.guilan.ac.ir/article_2808_8095113b966623525302c21a934b11b5.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations
91
104
EN
Ahmed
A.
Hamoud
0000-0003-3205-5498
Department of Mathematics, Taiz University, Taiz, 96704, Yemen
and
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431004, India
drahmedselwi985@gmail.com
Kirtiwant
P.
Ghadle
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India.
drkp.ghadle@gmail.com
10.22124/jmm.2018.2826
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
https://jmm.guilan.ac.ir/article_2826.html
https://jmm.guilan.ac.ir/article_2826_1a4bd959146587f09e8bad9682cd14d4.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
6
1
2018
07
01
Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems
105
122
EN
Siddu C.
Shiralashetti
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
shiralashettisc@gmail.com
Mounesha H.
Kantli
Department of Mathematics, KLE Society's J. T. College, Gadag-582101, India
mkantli@gmail.com
Aravind B.
Deshi
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
aravind42d@gmail.com
10.22124/jmm.2018.5019.1059
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
https://jmm.guilan.ac.ir/article_2829.html
https://jmm.guilan.ac.ir/article_2829_25297e5e419946881705133aa8d484ea.pdf