A fractional-order mathematical model for COVID-19 outbreak with the effect of symptomatic and asymptomatic transmissions.

The purpose of this paper is to investigate the transmission dynamics of a fractional-order mathematical model of COVID-19 including susceptible ( S ), exposed ( E ), asymptomatic infected ( I 1 ), symptomatic infected ( I 2 ), and recovered ( R ) classes named SEI 1 I 2 R model, using the Caputo fractional derivative. Here, SEI 1 I 2 R model describes the effect of asymptomatic and symptomatic transmissions on coronavirus disease outbreak. The existence and uniqueness of the solution are studied with the help of Schaefer- and Banach-type fixed point theorems. Sensitivity analysis of the model in terms of the variance of each parameter is examined, and the basic reproduction number ( R 0 ) to discuss the local stability at two equilibrium points is proposed. Using the Routh-Hurwitz criterion of stability, it is found that the disease-free equilibrium will be stable for R 0 < 1 whereas the endemic equilibrium becomes stable for R 0 > 1 and unstable otherwise. Moreover, the numerical simulations for various values of fractional-order are carried out with the help of the fractional Euler method. The numerical results show that asymptomatic transmission has a lower impact on the disease outbreak rather than symptomatic transmission. Finally, the simulated graph of total infected population by proposed model here is compared with the real data of second-wave infected population of COVID-19 outbreak in India.

Pulsatile Bi-Directional Aerosol Flow Affects Aerosol Delivery to the Intranasal Olfactory Region: A Patient-Specific Computational Study.

The nasal olfactory region is a potential route for non-invasive delivery of drugs directly from the nasal epithelium to the brain, bypassing the often impermeable blood-brain barrier. However, efficient aerosol delivery to the olfactory region is challenging due to its location in the nose. Here we explore aerosol delivery with bi-directional pulsatile flow conditions for targeted drug delivery to the olfactory region using a computational fluid dynamics (CFD) model on the patient-specific nasal geometry. Aerosols with aerodynamic diameter of 1 µm, which is large enough for delivery of large enough drug doses and yet potentially small enough for non-inertial aerosol deposition due to, e.g., particle diffusion and flow oscillations, is inhaled for 1.98 s through one nostril and exhaled through the other one. The bi-directional aerosol delivery with steady flow rate of 4 L/min results in deposition efficiencies (DEs) of 50.9 and 0.48% in the nasal cavity and olfactory region, respectively. Pulsatile flow with average flow rate of 4 L/min (frequency: 45 Hz) reduces these values to 34.4 and 0.12%, respectively, and it mitigates the non-uniformity of right-left deposition in both the cavity (from 1.77- to 1.33-fold) and the olfactory region (from 624- to 53.2-fold). The average drug dose deposited in the nasal cavity and the olfactory epithelium region is very similar in the right nasal cavity independent of pulsation conditions (inhalation side). In contrast, the local aerosol dose in the olfactory region of the left side is at least 100-fold lower than that in the nasal cavity independent of pulsation condition. Hence, while pulsatile flow reduces the right-left (inhalation-exhalation) imbalance, it is not able to overcome it. However, the inhalation side (even with pulsation) allows for relatively high olfactory epithelium drug doses per area reaching the same level as in the total nasal cavity. Due to the relatively low drug deposition in olfactory region on the exhalation side, this allows either very efficient targeting of the inhalation side, or uniform drug delivery by performing bidirectional flow first from the one and then from the other side of the nose.

Thermophysical Properties of Hybrid Nanofluids and the Proposed Models: An Updated Comprehensive Study.

Thermal performance of energy conversion systems is one of the most important goals to improve the system's efficiency. Such thermal performance is strongly dependent on the thermophysical features of the applied fluids used in energy conversion systems. Thermal conductivity, specific heat in addition to dynamic viscosity are the properties that dramatically affect heat transfer characteristics. These features of hybrid nanofluids, as promising heat transfer fluids, are influenced by different constituents, including volume fraction, size of solid parts and temperature. In this article, the mentioned features of the nanofluids with hybrid nanostructures and the proposed models for these properties are reviewed. It is concluded that the increase in the volume fraction of solids causes improvement in thermal conductivity and dynamic viscosity, while the trend of variations in the specific heat depends on the base fluid. In addition, the increase in temperature increases the thermal conductivity while it decreases the dynamic viscosity. Moreover, as stated by the reviewed works, different approaches have applicability for modeling these properties with high accuracy, while intelligent algorithms, including artificial neural networks, are able to reach a higher precision compared with the correlations. In addition to the used method, some other factors, such as the model architecture, influence the reliability and exactness of the proposed models.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.