We present a three-step family of iterative methods to solve systems of nonlinear equations. This family is a generalization of the well-known fourth-order King’s family to the multidimensional case. The convergence analysis of the methods is provided under mild conditions. The analytical discussion of the work is upheld by performing numerical experiments on some application oriented problems. Finally, numerical results demonstrate the validity and reliability of the suggested methods.

Background. MERS-CoV (Middle East Respiratory Syndrome Coronavirus) is a severe respiratory illness that poses a significant threat to the Arabic community and has the potential for global spread. In this paper, we present deterministic and stochastic models to study the dynamics of MERS infection within hosts. Objective. For the purpose of describing the dynamics of MERS transmission throughout host populations, a deterministic model is created. To gauge the likelihood of an epidemic spreading, the reproduction number is calculated. Furthermore, Lyapunov function theory is used to assess the stability of the deterministic model. In order to account for the intrinsic heterogeneity in the disease dynamics, a stochastic model is also developed. In order to verify the analytic conclusions and learn more about the behavior of the system, numerical simulations are carried out. Methods. Investigating the reproduction rate yields vital details about MERS’s capacity to start an outbreak. The stability analysis based on Lyapunov function theory sheds light on the deterministic model’s long-term behavior. The analytical results are supported by numerical simulations, which also provide a thorough insight into the dynamics of the disease. Conclusion. The deterministic and stochastic models for MERS infection inside hosts are thoroughly examined in this paper. Our knowledge of the dynamics of the disease and its potential for epidemic transmission is improved by the examination of the reproduction number and stability analysis. The combination of analytical and numerical approaches contributes to a more comprehensive assessment of MERS-CoV and aids in informing public health interventions and control strategies.

A viral respiratory disease, MERS spread by a novel coronavirus, was first detected in Saudi Arabia in 2012. It is a big threat for the Arab community and is a horrible prediction that the disease may rapidly propagate to other parts of the world. In this research endeavor, a mathematical model of MERS-Corona virus (MERS-CoV) is presented. Initially, we formulate a model, governing the dynamics of MERS-CoV disease and then determine basic reproductive number [ ]. Local stability analysis results are formulated at the equilibrium points. It has been found that one of the eigenvalues is zero, therefore bifurcation exists. Afterward, in formulating proper Lyapunov functional [J. P. LaSalle, The Stability of Dynamical Systems, Vol. 25 (Society for Industrial and Applied Mathematics, 1976)], we successfully established results about global stability of the proposed model at both equilibrium points. Sensitivity analysis of the parameters as well as of threshold value for the underlying model has been exhibited. The numerical illustration of theoretical findings is explained via examples.