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As of March 2022, there have been 3,116,564 infections and 32,827 coronavirus-related deaths reported in the country since the pandemic began on 1st March 2022. This drastic increase in numbers has been alarming everyone. Malaysia has successfully handled the first and second waves of the COVID-19 cases. However, the recent wave of omicron variants in Malaysia sees a massive increase in COVID-19 infections. Therefore, forecasting plays a vital role in determining preparedness for the current pandemic. This study aims to understand the behaviour of the current infection trend and provide valuable information to the authority to prevent future spikes of active cases. In this paper, the SIR model (Susceptible - Infected Recovered) was used to estimate the active cases in Malaysia. This forecast is essential to prepare for the current wave outbreak. Besides that, the number of susceptible can be reduced via vaccinations to reduce future outbreaks. Therefore, with proper planning and execution, the inoculation rates in Malaysia proved to be successful, and the impact of mass vaccination would be seen in future. [ABSTRACT FROM AUTHOR]

In this note, a general form of Fredholm-Volterra integro-differential equation order one is considered. The truncated Legendre series is used as bases function to approximate unknown function and Gauss-Legendre quadrature formula is applied for kernel integrals. Reduced algebraic equations are solved by using collocation method with roots of Legendre polynomials as collocation points. Three numerical examples with the comparisons are provided to show the validity and accuracy of the suggested method. Numerical results reveal that proposed method is dominated with repeated trapezoidal rule and differential transform method. [ABSTRACT FROM AUTHOR]

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed. [ABSTRACT FROM AUTHOR]

This paper presents a boundary integral equation method with the adjoint generalized Neumann kernel for conformal mapping of unbounded multiply connected regions. The canonical region is the entire complex plane bounded by an infinite straight slit on the line Im ω = 0 and finite logarithmic spiral slits. Some linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on a multiply connected region. These integral equations are uniquely solvable. The kernel involved in these integral equations is the adjoint generalized Neumann kernel. [ABSTRACT FROM AUTHOR]

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods. [ABSTRACT FROM AUTHOR]

This paper presents a boundary integral equation method for conformal mapping of an unbounded multiply connected region onto a radial slits region. Two linear boundary integral equations are constructed from a boundary relationship satisfied by an analytic function on an unbounded multiply connected region. These integral equations are uniquely solvable. The kernels involved in these integral equations are the adjoint generalized Neumann kernels. Two numerical examples are presented to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]