A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

Praise to Allah, Lord of the Worlds. Thank you very much. Blessed. As his face should be majestic and great. His authority, and may peace and blessings be upon our master Muhammad, a perpetual blessing until the Day of Judgment

And upon the God of purity, His righteous companions, and those who follow them in righteousness until the Day of Judgment. But after:-

Anyone who looks into the history of nations, peoples, and the conditions of human beings will see that naturalization as a person’s affiliation to a particular state is something that happened only in recent centuries. In ancient times, a person’s loyalty was to the tribe to which the person belonged, and he was integrated into it and attributed to it, and in

In this study, sulfur was removed from imitation oil using oxidative desulfurization process. Silicoaluminophosphate (SAPO-11) was prepared using the hydrothermal method with a concentration of carbon nanotubes (CNT) of 0% and 7.5% at 190 °C crystallization temperature. The final molar composition of the as-prepared SAPO-11 was Al2O3: 0.93P2O5: 0.414SiO2. 4% MO/SAPO-11 was prepared using impregnation methods. The produced SAPO-11 was described using X-ray diffraction (XRD) and Brunauer-Emmet-Teller (N2 adsorption–desorption isotherms). It was found that the addition of CNT increased the crystallinity of SAPO-11. The results showed that the surface area of SAPO-11 containing 7.5% CNT was 179.54 m2/g, and the pore volume was 0.31

This systematic review aimed to investigate the relation between orthodontic treatment (OT) and the incidence of the gingival black triangle (GBT) after completing treatment with a fixed orthodontic appliance, as well as the associated risk factors and the level of alveolar bone. Electronic and hand searches were conducted in three electronic databases for relevant articles published up to March 2022. Retrieved articles went through a two-step screening procedure, and the risk of bias (RoB) was assessed by the Joanna Briggs Institute checklists. The incidence of GBT after OT was set as the primary outcome, while the secondary outcomes were the risk factors associated with GBT and alveolar bone loss following OT. Out of 421 papers, 5

    The main goal of this paper is to introduce the higher derivatives multivalent harmonic function class, which is defined by the general linear operator. As a result, geometric properties such as coefficient estimation, convex combination, extreme point, distortion theorem and convolution property are obtained. Finally, we show that this class is invariant under the Bernandi-Libera-Livingston integral for harmonic functions.

This work studied the electrical and thermal surface conductivity enhancement of polymethylmethacrylate (PMMA) clouded by double-walled carbon nanotubes (DWCNTs) and multi-walled carbon nanotube (MWCNTs) by using pulsed Nd:YAG laser. Variable input factors are considered as the laser energy (or the relevant power), pulse duration and pulse repetition rate. Results indicated that the DWCNTs increased the PMMA’s surface electrical conductivity from 10-15 S/m to 0.813×103 S/m while the MWCNTs raised it to 0.14×103 S/m. Hence, the DWCNTs achieved an increase of almost 6 times than that for the MWCNTs. Moreover, the former increased the thermal conductivity of the surface by 8 times and the later by 5 times.

In this study, sulfur was removed from imitation oil using oxidative desulfurization process. Silicoaluminophosphate (SAPO-11) was prepared using the hydrothermal method with a concentration of carbon nanotubes (CNT) of 0% and 7.5% at 190 °C crystallization temperature. The final molar composition of the as-prepared SAPO-11 was Al₂O₃: 0.93P²O⁵: 0.414SiO². 4% MO/SAPO-11 was prepared using impregnation methods. The produced SAPO-11 was described using X-ray diffraction (XRD) and Brunauer-Emmet-Teller (N² adsorption–desorption isotherms). It was found that the addition of CNT increased the crystallinity of SAPO-11. The results showed that the surface area of SAPO-11 cont