The European Physical Journal Plus

Vector-host infectious diseases remain a challenging issue and cause millions of deaths each year globally. In such outbreaks, many countries especially developing or underdevelopment faces a situation where the number of infected individuals is getting larger and the medical facilities are limited. In this paper, we construct an epidemic model to explore the transmission dynamics of vector-borne diseases with nonlinear saturated incidence rate and saturated treatment function. This type of incidence rate, as well as the saturated treatment function, is also known as the Holling type II form and describes the effect of delayed treatment. Initially, we formulate a mathematical model and then present the basic analysis of the model including the positivity and boundedness of the solution. The threshold quantity $${\mathcal {R}}_{0}$$ is presented and the stability analysis of the system is carried out for the model equilibria. The global stability results are shown using the Lyapunov function of Goh–Voltera type. The existence of backward bifurcation is discussed using the central manifold theory. Further, the global sensitivity analysis of the model is carried out using the Latin Hypercube sampling and the partial rank correlation coefficient techniques. Moreover, an optimal control problem is formulated and the necessary optimality conditions are investigated in order to eradicate the disease in a community. Four strategies are presented by choosing different set of controls combination for the disease minimization. Finally, the numerical simulations of each strategy are depicted to demonstrate the importance of suggesting control interventions on the disease dynamics and eradication.

Two physically important potentials (Manning–Rosen and Pöschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov–Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene–Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, $$\lambda $$ and $$\nu $$ . The original approximations are recovered for certain special values of these two parameters. This offers a simple effective scheme for these and other relevant potentials in quantum mechanics.

We discuss the dynamics of stellar filaments with cylindrical symmetry in the context of f(G) gravity. For this purpose, we consider the modified gravity coupled with a dissipative anisotropic fluid and construct scalar functions through orthogonal splitting of the Riemann tensor. We formulate the set of equations governing the evolution and structure of stellar filaments in terms of these scalars. Finally, we discuss all static solutions for cylindrical filaments with anisotropy as well as isotropy and conclude that stellar filaments are necessarily inhomogeneous in this gravity.

This paper explores conformal Killing vectors in teleparallel theory for the plane-symmetric static spacetime. Ten non-linear coupled teleparallel conformal Killing equations are solved to get the general form of teleparallel conformal Killing vectors and the conformal factor along with the integrability conditions. Three different possibilities are considered where the spacetime may exhibit a teleparallel conformal Killing vector. In two cases the integrability conditions are solved completely and teleparallel conformal Killing vectors are obtained along with the conformal factor for the special choice of metric functions. Another possibility reveals that no teleparallel proper conformal Killing vector exists and the spacetime admits only a teleparallel homothetic vector.