2018-09-20T21:41:43Z
http://jmm.guilan.ac.ir/?_action=export&rf=summon&issue=511
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
Influence of awareness programs by media in the typhoid fever: a study based on mathematical modeling
Jayanta
Mondal
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
2018
07
01
1
26
http://jmm.guilan.ac.ir/article_2760_5a9bd5d991f6d86eb9eccb99c62065e9.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
An ${cal O}(h^{8})$ optimal B-spline collocation for solving higher order boundary value problems
Shokofeh
Sharifi
Rashidinia
Jalil
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
2018
07
01
27
46
http://jmm.guilan.ac.ir/article_2761_4be105a37e6619351966cdec74a917d0.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
Global properties of a tuberculosis model with lost sight and multi-compartment of latents
Anatole
Temgoua
Yannick
Malong
Joseph
Mbang
Samuel
Bowong
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
2018
07
01
47
76
http://jmm.guilan.ac.ir/article_2775_9fed0f438341d3fda516b0ff91d03318.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
Solution of Troesche's problem by double exponential Sinc collocation method
Mohammad
Nabati
Soudabeh
Nikmanesh
Mehdi
Jalalvand
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
2018
07
01
77
90
http://jmm.guilan.ac.ir/article_2808_8095113b966623525302c21a934b11b5.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
Modified Laplace decomposition method for fractional Volterra-Fredholm integro-differential equations
Ahmed
Hamoud
Kirtiwant
Ghadle
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
2018
07
01
91
104
http://jmm.guilan.ac.ir/article_2826_1a4bd959146587f09e8bad9682cd14d4.pdf
Journal of Mathematical Modeling
JMM
2345-394X
2345-394X
2018
6
1
Biorthogonal wavelet-based full-approximation schemes for the numerical solution of elasto-hydrodynamic lubrication problems
Siddu C.
Shiralashetti
Mounesha H.
Kantli
Aravind B.
Deshi
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
2018
07
01
105
122
http://jmm.guilan.ac.ir/article_2829_25297e5e419946881705133aa8d484ea.pdf