In this research work, a ratio‐dependent prey–predator system is investigated for bifurcation and stability analysis. The unique existence of the solution, boundedness, and positivity of the temporal model is derived. Stability analysis of positive steady states is analyzed. Stable and unstable regions for both equilibria are drawn in different parametric spaces. The parametric plots for the different initial conditions are drawn. The diffusive prey–predator model is analyzed for the bifurcation and stability regions. It is observed that the stability regions under the effect of diffusion are increased. To gain the numerical solution of the spatially extended prey–predator model, the operator splitting scheme is derived. The scheme preserves the positivity and other important features of the continuous model. Lastly, a test problem is considered to visualize the accuracy of our scheme. To show the physical behavior of the scheme, 3D and 2D plots are drawn, which clearly show the dynamics of the scheme. Theoretical results are supported by simulations.

This study presents analytical and numerical‐analytical decomposition methods for determining complex one‐parameter generalized inverse Moore–Penrose matrices. The analytical approach is based on the third Moore–Penrose condition, offering three solution options. The first option employs complex decompositions of the given matrix and its Moore–Penrose inverse. The second option combines the first and third Moore–Penrose conditions, while the third option integrates the second and third conditions. For the first and third options, if any derived iterative procedure converges, the Moore–Penrose inverse matrix can be constructed using the corresponding matrix blocks. In contrast, the second option provides simplified relations, enabling the direct computation of the Moore–Penrose inverse matrix. Numerical‐analytical methods build on the second analytical solution, utilizing differential Pukhov transformations as the primary mathematical tool. A model example featuring a rectangular complex matrix is analyzed. A numerical‐analytical solution is derived using three matrix discretes, from which corresponding matrix blocks are reconstructed. The Moore–Penrose inverse matrix is then obtained through its complex decomposition.

In this study, we present a mathematical model for the codynamics of taeniasis and neurocysticercosis and rigorously analyze it. To understand the underlying dynamics of the proposed model, basic system properties such as the positivity and boundedness of solutions are investigated through the completing differential process. The basic reproduction number was calculated using the next-generation matrix method, and the analysis showed that when R0<1, the disease in the community eventually dies out, and when R0>1, the diseases persist. Local stability of the equilibria was analyzed using the Jacobian matrix, and Lyapunov function techniques were used to determine the global analysis, which showed that the endemic equilibrium point was globally stable when R0>1. On the other hand, the disease-free equilibrium was determined to be globally stable when R0<1. To identify the most influential parameters of the proposed model, partial correlation coefficient techniques were used. The numerical results depict that the model aligns well with the transmission dynamics, which goes through two populations: humans and pigs, whereby the model system stabilizes after some time, showing the validity of the proposed model. Furthermore, the simulations of the proposed model revealed that the shedding habit of infected humans with taeniasis and the bad cooking habit or eating of raw or undercooked pork products have a higher impact on the spread of neurocysticercosis and taeniasis in the community. Hence, this study proposes that in order to control taeniasis and neurocysticercosis, effective disease control measures should primarily prioritize hygienic behaviour and proper cooking of pork meat to the required temperature.

The Sumudu transform is presented in this paper in a modified form which is aimed at improving its performance and employing it along with a modified iteration method in order to determine the solution to a system of nonlinear partial differential equations. This includes a theoretical analysis of the associated modified Sumudu transform. It also includes an explanation of the mathematical method for utilizing the transform in conjunction with the modified iteration technique. The iteration method is employed to determine the nonlinear terms of the equations. The research is valuable in the sense that it allows approximate and exact solution configurations to be determined by combining the modified Sumudu transform with a modified iteration method. As another benefit, the modified Sumudu transform can be developed and enhanced to be applicable to a wide range of equations, making it an effective solution tool. By combining techniques, a final advantage is that the solutions can be derived quickly and easily as a result of the combined approach. Finally, an old transformation which has been modified from the Sumudu transform is combined with the modified iteration method to examine its capability of yielding convergent solutions by incorporating the modified iteration method into it.

This paper is aimed at constructing and analyzing a fitted approach for singularly perturbed time delay parabolic problems with two small parameters. The proposed computational scheme comprises the implicit Euler and especially finite difference method for the time and space variable discretization, respectively, on uniform step size. The stability and convergence analysis of the method is provided and is first-order parameter uniform convergent. Further, the numerical results depict that the present method is more convergent than some methods available in the literature.

In recent years, the developments of new families of probability distributions have received greater attention as a result of desirable properties they exhibit in the modelling of data sets. The Harmonic Mixture Weibull-G family of distributions was developed in this study. The statistical properties were comprehensively presented and five special distributions developed from the family. The hazard functions of the special distributions were shown to exhibit various forms of monotone and nonmonotone shapes. The applications of the developed family to real data sets in medical studies revealed that the special distribution (Harmonic mixture Weibul Weibull distribution) provided a better fit to the data sets than other competitive models. A location-scale regression model was developed from the family and its application demonstrated using survival time data of hypertensive patients.

Dengue fever is a viral mosquito-borne disease, a significant global health concern, with more than one third of the world population at risk of acquiring the disease. Caused by 4 antigenically distinct but related virus serotypes, named DENV-1, DENV-2, DENV-3, and DENV-4, infection by one serotype confers lifelong immunity to that serotype and a short period of temporary cross immunity to other related serotypes. Severe dengue is epidemiologically associated with a secondary infection caused by a heterologous serotype via the so-called antibody-dependent enhancement (ADE), an immunological process enhancing a new infection. Within-host dengue modeling is restricted to a small number of studies so far. With many open questions, the understanding of immunopathogenesis of severe disease during recurrent infections is important to evaluate the impact of newly licensed vaccines. In this paper, we revisit the modeling framework proposed by Sebayang et al. and perform a detailed sensitivity analysis of the well-known biological parameters and its possible combinations to understand the existing data sets. Using numerical simulations, we investigate features of viral replication, antibody production, and infection clearance over time for three possible scenarios: primary infection, secondary infection caused by homologous serotype, and secondary infection caused by heterologous serotype. Besides, describing well the infection dynamics as reported in the immunology literature, our results provide information on parameter combinations to best describe the differences on the immunological dynamics of secondary infections with homologous and heterologous viruses. The results presented here will be used as baseline to investigate a more complex within-host dengue model.

In this paper, a computational procedure for solving singularly perturbed nonlinear delay differentiation equations (SPNDDEs) is proposed. Initially, the SPNDDE is reduced into a series of singularly perturbed linear delay differential equations (SPLDDEs) using the quasilinearization technique. A trigonometric spline approach is suggested to solve the sequence of SPLDDEs. Convergence of the method is addressed. The efficiency and applicability of the proposed method are demonstrated by the numerical examples.