Current Issue : July - September Volume : 2014 Issue Number : 3 Articles : 6 Articles
We construct and study a differential infectivity model with chronological and infection age. The application\nis done on hepatitis B in Cameroon. We prove the global stability of the disease free equilibrium when the basic\nreproduction ratio R0 is less than one and the existence and uniqueness of an endemic equilibrium when R0>1 ....
Let R be an associative ring with unity 1. In this paper, existence of the group inverse of two classes of 2Ã?â??2 block matrices is investigated. We obtain the sufficient and necessary conditions. And further, the representations of the group inverse of two classes are given. (1) M=(AX+YBBA0), where A? exists, XA=AX and X is invertible; (ii) M=(ACBD), where CA=C,AB=B and (D?CB)? exists. The results extend the early works of Cao and Li (Appl Math Comput 217:10271ââ?¬â??10277, 2011) and Liu and Yang (Appl Math Comput 218:8978ââ?¬â??8986, 2012). Some examples are given to illustrate our results....
Following the paper of Shimizu et al. (Phys Lett A 375:1566, 2011), we consider\nthe Bonhoeffer-van der Pol oscillator with non-autonomous periodic perturbation. We show\nthat the presence of mixed mode oscillations reported in that paper can be explained using\nthe geometric singular perturbation theory. The considered model can be re-written as a fourdimensional\n(locally three-dimensional) autonomous system, which under certain conditions\nhas a folded saddle-node singularity and additionally can be treated as a three time scale one....
In this work, the numerical study of a deterministic mathematical model of an SEIVR (Susceptible-Exposed-\nInfected-Vaccinated-Recovered) epidemic model among infants was carried out. This model incorporates a\ntemporary immune recovery class which involves subsequent dose vaccination for the infants. Hypothetical values\nwere chosen for the parameters to test the validity of the mathematical model. The parameter with the greatest\nimpact on the model was computed using the eigenvalue elasticity and sensitivity analyses and it was found that\nthe parameter of the rate at which the vaccine wanes in the infants (?) has the greatest impact on the mathematical model....
We derive a general expression for the pth power (p ? N) of any complex persymmetric antitridiagonal Hankel (constant\nantidiagonals)matrices.Numerical examples are presented,which showthat our results generalize the results in the related literature\n(Rimas 2008,Wu 2010, and Rimas 2009)....
We consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann, and\nSommerfeld-like boundary conditions based on a compact sixth order approximation scheme and lower order preconditioned\nKrylov subspace methodology. The resulting systems of finite-difference equations are solved by different preconditioned Krylov\nsubspace-based methods. In the analysis of the lower order preconditioning developed here, we introduce the term ââ?¬Å?kth order preconditioned\nmatrixââ?¬Â in addition to the commonly used ââ?¬Å?an optimal preconditioner.ââ?¬Â The necessity of the new criterion is justified\nby the fact that the condition number of the preconditioned matrix in some of our test problems improves with the decrease of\nthe grid step size. In a simple 1D case, we are able to prove this analytically. This new parameter could serve as a guide in the\nconstruction of new preconditioners. The lower order direct preconditioner used in our algorithms is based on a combination\nof the separation of variables technique and fast Fourier transform (FFT) type methods. The resulting numerical methods allow\nefficient implementation on parallel computers. Numerical results confirm the high efficiency of the proposed iterative approach....
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