Solutions to SIR/SEIR epidemic models with exponential series: Numerical and non numerical approaches.

This study revisits the mathematical SIR/SEIR epidemic models, aiming to introduce novel exponential-type series solutions. Beyond standard non-dimensionalization, we implement a successful rescaling technique that reduces the parameter count in classical epidemiology. Consequently, solutions for the SIR model are determined solely by the basic reproduction number and initial infected fractions.

Hyperthermia therapy of cancerous tumor sitting in breast via analytical fractional model.

The heat transfer in bi-layer spherical composite region representing a cancerous tumor embedded in a homogenous muscle tissue (Andra et al., 1999; Yu and Jiang, 2019) is modeled by means of fractional energy equations with additional interface boundary constrictions. This hyperthermia problem was explored before in literature with proper hyperthermia experimental parameters and numerical simulations were later on devised by substituting the integer order energy model with the fractional order one.

Full Solutions to Flow and Heat Transfer from Slip-Induced Microtube Shapes.

The main concern of this paper is to introduce some new tubular shapes whose cross-sections result from the imposition of Navier's velocity slip at the surface. A new family of pipes induced by the slip mechanism is thus discovered. The family is shown to modify the traditional pipes with elliptical cross-sections in the absence of slip, and they partly resemble collapsible tubes.

Indoor transmission of airborne viral aerosol with a simplistic reaction-diffusion model.

A simplistic reaction-diffusion model is undertaken in the present work to mathematically explore the spatio-temporal development of concentration of indoor aerosols containing infectious COVID-19 respiratory virus nuclei. Extracting exact solutions of concentration field under the influence of several physical parameters is preferred rather than adopting a more realistic complex model requiring time-consuming numerical simulations. Even though the proposed model is not sophisticated, the analytical solutions can provide quick prediction of the probability of contracting the virus in a ventilated closed room.

An extended epidemic model with vaccination: Weak-immune SIRVI.

A new modification of the SIR epidemic model incorporating vaccination is proposed in the present paper. The recent trend of vaccinating against COVID-19 pandemic reveals a strong control of infectious disease. On the other hand, it is observed in some countries that, the vaccine application offers less control over the spread of virus, since some portion of vaccinated people is not totally protected/immuned and viable to infection again after a while due to weak/loss immunity offered by the vaccine.

Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?

An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible-infectious-recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021).

Explicit formulae for the peak time of an epidemic from the SIR model.

Reducing the peak time of an epidemic disease in order for slowing down the eventual dynamics and getting prepared for the unavoidable epidemic wave is utmost significant to fight against the risks of a contagious epidemic disease. To serve to this purpose, the well-documented infection model of SIR is examined in the current research to propose an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak. Initially, the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments.

Magnetohydrodynamic Moving Liquid Plug Within a Microchannel: Analytical Solutions.

The wide applications of plug flows in microscale in science and engineering help them attract a great deal recent interest. An analytical study is undertaken here to study the impacts of a transversely applied external uniform magnetic field affecting the motion of liquid in the plug in terms of hydrodynamic mixing properties. The well-known symmetric vortex structure occurring in a long plug with moderate aspect ratio is observed to be preserved, while the recirculation phenomenon is highly affected by the action of the magnetic field.

Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis.

Background And Objective: The hydrodynamic stability of nanofluids of one phase is investigated in this paper based on linear stability theory. The overall thrust here is that the linear stability features of nanofluids can be estimated from their corresponding working fluid, at least in special circumstances.

Methods: The approach uses the adjusting parameter to make assertions about stability.

Fully developed slip flow in a concentric annuli via single and dual phase nanofluids models.

In the present work it is aimed to obtain closed-form exact solutions for the fully developed momentum, thermal and concentration layers through a concentric annulus filled with various nanoparticle mixtures of water-based nanofluids in the presence of wall slip nanofluid velocity. The thermal boundary conditions of either both walls at fixed temperatures or of the inner wall at prescribed temperature and of the outer wall at specified heat flux are considered. Initially, the classical single phase model is adopted leading to simple formulas for the nanofluid flow and heat transfer.

A New Theoretical Approach of Wall Transpiration in the Cavity Flow of the Ferrofluids.

An idea of permeable (suction/injection) chamber is proposed in the current work to control the secondary vortices appearing in the well-known lid-driven cavity flow by means of the water based ferrofluids. The Rosensweig model is conveniently adopted for the mathematical analysis of the physical problem. The governing equation of model is first transformed into the vorticity transport equation.