The Middle East respiratory syndrome coronavirus (MERS-CoV) is a highly infectious respiratory illness that poses a significant threat to public health. Understanding the transmission dynamics of MERS-CoV is crucial for effective control and prevention strategies. In this study, we develop a precise mathematical model to capture the transmission dynamics of MERS-CoV. We incorporate some novel parameters related to birth and mortality rates, which are essential factors influencing the spread of the virus. We obtain epidemiological data from reliable sources to estimate the model parameters. We compute its basic reproduction number (R0). Stability theory is employed to analyze the local and global properties of the model, providing insights into the system’s equilibrium states and their stability. Sensitivity analysis is conducted to identify the most critical parameter affecting the transmission dynamics. Our findings revealed important insights into the transmission dynamics of MERS-CoV. The stability analysis demonstrated the existence of stable equilibrium points, indicating the long-term behavior of the epidemic. Through the evaluation of optimal control strategies, we identify effective intervention measures to mitigate the spread of MERS-CoV. Our simulations demonstrate the impact of time-dependent control variables, such as supportive care and treatment, in reducing the number of infected individuals and controlling the epidemic. The model can serve as a valuable tool for public health authorities in designing effective control and prevention strategies, ultimately reducing the burden of MERS-CoV on global health.

In this work, we present new oscillation conditions for the oscillation of the higher-order differential equations with the middle term. We obtain some oscillation criteria by a comparison method with first-order equations. The obtained results extend and simplify known conditions in the literature. Furthermore, examining the validity of the proposed criteria is demonstrated via particular examples.

The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg–de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.