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Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number R og is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever R og < 1 and an asymptotic stable EE whenever R og > 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper presents a study on the numerical solutions of the Burgers' equation with forcing effects. The article proposes three hybrid methods that combine two-point, three-point, and four-point discretization in time with the Galerkin finite element method in space (TDFEM2, TDFEM3, and TDFEM4). These methods use backward finite difference in time and the finite element method in space to solve the Burgers' equation. The resulting system of the nonlinear ordinary differential equations is then solved using MATLAB computer codes at each time step. To check the efficiency and accuracy, a comparison between the three methods is carried out by considering the three Burgers' problems. The accuracy of the methods is expressed in terms of the error norms. The combined methods are advantageous for small viscosity and can produce highly accurate solutions in a shorter time compared to existing numerical schemes in the literature. In contrast to many existing numerical schemes in the literature developed to solve Burgers' equation, the methods can exhibit the correct physical behavior for very small values of viscosity. It has been demonstrated that the TDFEM2, TDFEM3, and TDFEM4 can be competitive numerical methods for addressing Burgers-type parabolic partial differential equations arising in various fields of science and engineering. [ABSTRACT FROM AUTHOR]

This study employs the Lie symmetry technique to explore the symmetry features of the time fractional Kupershmidt equation. Specifically, we use the Lie symmetry technique to derive the symmetry generators for this equation, which incorporates a conformal fractional derivative. We use the symmetry generators to transform the fractional partial differential equation into a fractional ordinary differential equation, thereby simplifying the analysis. The obtained reduced equation is of fourth order nonlinear ordinary differential equation. To find the wave solutions, F/G‐expansion process has been used to obatin different types of solutions of the time‐fractional Kuperschmidt equation. The obtained wave solutions are hyperbolic and trigonometric in nature. We then use Maple software to visually depict these wave solutions for specific parameter values, providing insights into the behaviour of the system under investigation. Peak and kink wave solutions are achieved for the given problem. [ABSTRACT FROM AUTHOR]