Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling
Jayanta
Mondal
Department of Mathematics, Diamond Harbour Women's University, Sarisha-743368, India
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
1
26
http://jmm.guilan.ac.ir/article_2760_5a9bd5d991f6d86eb9eccb99c62065e9.pdf
dx.doi.org/10.22124/jmm.2018.2760
An ${\cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
Shokofeh
Sharifi
Department of Mathematics and statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran
author
Rashidinia
Jalil
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
27
46
http://jmm.guilan.ac.ir/article_2761_4be105a37e6619351966cdec74a917d0.pdf
dx.doi.org/10.22124/jmm.2018.2761
Global properties of a tuberculosis model with lost sight and multi-compartment of latents
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
author
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
author
Joseph
Mbang
Department of Mathematics, Faculty of Science,
University of Yaounde I, PO Box 812 Yaounde, Cameroon
author
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
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
47
76
http://jmm.guilan.ac.ir/article_2775_9fed0f438341d3fda516b0ff91d03318.pdf
dx.doi.org/10.22124/jmm.2018.2775
Solution of Troesche's problem by double exponential Sinc collocation method
Mohammad
Nabati
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
author
Soudabeh
Nikmanesh
Department of Basic Sciences, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadabn, Iran
author
Mehdi
Jalalvand
Department of Mathematics, Faculty of Mathematical Sciences and Computer,
Shahid Chamran University of Ahvaz, Ahvaz, Iran
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
77
90
http://jmm.guilan.ac.ir/article_2808_8095113b966623525302c21a934b11b5.pdf
dx.doi.org/10.22124/jmm.2018.2808
Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations
Ahmed
Hamoud
Department of Mathematics, Taiz University, Taiz, 96704, Yemen
and
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad, 431004, India
author
Kirtiwant
Ghadle
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, 431004, India.
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
91
104
http://jmm.guilan.ac.ir/article_2826_1a4bd959146587f09e8bad9682cd14d4.pdf
dx.doi.org/10.22124/jmm.2018.2826
Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems
Siddu C.
Shiralashetti
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
author
Mounesha H.
Kantli
Department of Mathematics, KLE Society's J. T. College, Gadag-582101, India
author
Aravind B.
Deshi
Department of Mathematics, Karnatak University Dharwad-580003, India & Department of Mathematics, KLECET Chikodi-591201, India
author
text
article
2018
eng
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.
Journal of Mathematical Modeling
University of Guilan
2345-394X
6
v.
1
no.
2018
105
122
http://jmm.guilan.ac.ir/article_2829_25297e5e419946881705133aa8d484ea.pdf
dx.doi.org/10.22124/jmm.2018.5019.1059