Journal of Mathematical Modeling
Volume:6 Issue: 1, Summer-Autumn 2018

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 R0. 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.

As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only O(h2) 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 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.

A tuberculosis (TB) model with lost sight and multiple latent classes is considered and studied. We derive the basic reproduction ratio R 0 . There is always a globally asymptotically stable equilibrium state. Depending on the value of R0, this state can be either endemic (R 0 >1), or infection-free (R0≤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.

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.

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.

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.