In the present analysis, we aim to construct a new subclass of analytic bi-univalent functions defined on symmetric domain by means of the Pascal distribution series and Gegenbauer polynomials. Thereafter, we provide estimates of Taylor–Maclaurin coefficients $\left|a_2\right|$ and $\left|a_3\right|$ for functions in the aforementioned class, and next, we solve the Fekete–Szegö functional problem. Moreover, some interesting findings for new subclasses of analytic bi-univalent functions will emerge by reducing the parameters in our main results.

In this paper, we have investigated the global dynamics of a discrete-time middle east respiratory syndrome (MERS-Cov) model. The proposed discrete model was analyzed and the threshold conditions for the global attractivity of the disease-free equilibrium (DFE) and the endemic equilibrium are established. We proved that the DFE is globally asymptotically stable when ${\mathcal{R}}_0\le 1$. Whenever ${\tilde{\mathcal{R}}}_0>1$, the proposed model has a unique endemic equilibrium that is globally asymptotically stable. The theoretical results are illustrated by a numerical simulation.

In this paper we will study the relationship between the baseline pdf and the corresponding MO pdf, we will show the effectiveness on the percentile points, also we will give a closed form for the MLE estimator of the new parameter and will study some examples.