Optimal Campaign in the Smoking Dynamics

We present the optimal campaigns in the smoking dynamics. Assuming that the giving up smoking model is described by the simplified PLSQ (potential-light-smoker-quit smoker) model, we consider two possible control variables in the form of education and treatment campaigns oriented to decrease the attitude towards smoking. In order to do this we minimize the number of light (occasional) and persistent smokers and maximize the number of quit smokers in a community. We first show the existence of an optimal control for the control problem and then derive the optimality system by using the Pontryagin maximum principle. Finally numerical results of real epidemic are presented to show the applicability and efficiency of this approach

Unsteady Magnetohydrodynamic Flow of Jeffrey Fluid through a Porous Oscillating Rectangular Duct

This chapter presents some new exact solutions corresponding to unsteady magnetohydrodynamic (MHD) flow of Jeffrey fluid in a long porous rectangular duct oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform (DFFST) and discrete Laplace transform (LT). The series solution of velocity field, associated shear stress and volume flow rate in terms of Fox H-functions, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameter

Transmission dynamic and backward bifurcation of Middle Eastern respiratory syndrome coronavirus

Middle East respiratory syndrome coronavirus (MERS-CoV) remains an emerging disease threat with regular human cases on the Arabian Peninsula driven by recurring camels to human transmission events. In this paper, we present a new deterministic model for the transmission dynamics of (MERS-CoV). In order to do this, we develop a model formulation and analyze the stability of the proposed model. The stability conditions are obtained in term of R0, we find those conditions for which the model become stable. We discuss basic reproductive number R0 along with sensitivity analysis to show the impact of every epidemic parameter. We show that the proposed model exhibits the phenomena of backward bifurcation. Finally, we show the numerical simulation of our proposed model for supporting our analytical work. The aim of this work is to show via mathematical model the transmission of MERS-CoV between humans and camels, which are suspected to be the primary source of infection

The nature, sources and the socio-economic effects of terrorism in Balochistan

Terrorism has badly affected Pakistan and Balochistan is one of its worst – hit provinces. There is no research that accounts for the nature, sources and effects of terrorism on Balochistan; this study, thus, tried to explore the same. A sample size of 250 respondents was chosen to cast their opinion about the problem using a questionnaire through a stratified sample of Quetta city. The results indicated that the nature of terrorism in Balochistan is, at first, Political and is caused by the prevailing social injustice and lack of economic activity, cross-border activities and religious and ethnic extremism. Terrorism has negatively affected business optimism, foreign investment and economic life in Balochistan. As far as the social life is concerned, a sense of fear prevails in the province that has reduced social activities in the province. One of the worst – hit areas by terrorism is education and religious practices. In order to correct the current situation prevailing in Balochistan the government has to play an intelligent, planned and effective role in Balochistan.Socio-economic effects, Terrorism, Balochistan

Unsteady Magnetohydrodynamic Flow of Second Grade Fluid due to Uniform Accelerating Plate

New exact solutions for unsteady magnetohydrodynamic (MHD) flows of a generalized second-grade fluid due to uniform accelerating plate are derived. The generalized second-grade fluid saturates the porous space. Fractional derivative is used in the governing equation. The analytical expressions for velocity and shear stress fields are obtained by using Laplace transform technique for the fractional calculus. The obtained solutions are expressed in series form in terms of Fox H-functions. Similar solutions for ordinary second-grade fluid passing through a porous space are also recovered. Moreover, several figures are sketched for the pertinent parameters to analyze the characteristics of velocity field and shear stress

Solution of an SEIR Epidemic Model in Fractional Order

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model (with out of bilinear incidence rates) in fractional order. First the non-negative solution of the SEIR model in fractional order is discussed. Then calculate an approximate solution of the proposed model. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results

Efficacy of Nasal Continuous Positive Airway Pressure versus Heated Humidified High-Flow Nasal Cannula as a Primary Mode of Respiratory Support in Preterm Infants with RDS

Objective: To determine the efficacy of nasal continuous positive airway pressure (NCPAP) versus heated humidified high-flow nasal cannula (HHHFNC) as a primary mode of respiratory support in preterm infants with respiratory distress. Methodology: This randomized controlled trial study was conducted at in-patient department of neonatology (Nursery & NICU) of Pakistan Insitute of Medical Sciences (PIMS) from July 2020 to Dec 2020. A total of 280 neonates randomly divided (140 in each study group) of both genders, with gestational age between 28-34 weeks and having mild-to-moderate respiratory distress within 1st 6 hours of birth requiring non-invasive ventilation were enrolled. Neonates in NCPAP Group (n=140) were given NCPAP whereas neonates in HHHFNC Group (n=140) were given HHHFNC. The efficacy of both groups were compared on the basis of treatment failure within 1st 3 days, total duration (hours) of non-invasive ventilator (NIV) required and total duration (hours) of supplementary oxygen required. Results: Overall, mean gestational age was noted to be 30.0+6.4 weeks. There were 144 (51.4%) neonates with birth weight between 1 to 1.4 kg, 90 (32.1%) between 1.5 to 1.9 kg and 46 (16.4%0 between 2.0 to 2.4 kg. Treatment failure was noted in 67 (47.6%) neonates in NCAP group while HHHFNC group reported 73 (52.4%) neonates with treatment failure (p=0.4733). No significant difference was observed in mean total duration of NIV support required (p=0.2598) or mean total duration of supplementary oxygen (p=0.1946) in between study groups. Conclusion: HHHFNC had similar efficacy when compared to NCPAP among neonates with RDS. In comparison to NCPAP, HHHFNC could be a simple, well-tolerated and effective alternative in terms of respiratory support. No major difference in terms of complication was observed between both treatment approaches

Prevention of Influenza Pandemic by Multiple Control Strategies

We present the prevention of influenza pandemic by using multiple control functions. First, we adjust the control functions in the pandemic model, then we show the existence of the optimal control problem, and, by using both analytical and numerical techniques, we investigate cost-effective control effects for the prevention of transmission of disease. To do this, we use four control functions, the first one for increasing the effect of vaccination, the second one for the strategies to isolate infected individuals, and the last two for the antiviral treatment to control clinically infectious and hospitalization cases, respectively. We completely characterized the optimal control and compute the numerical solution of the optimality system by using an iterative method

Entropy generation from convective–radiative moving exponential porous fins with variable thermal conductivity and internal heat generations

The performance and thermal properties of convective-radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by 30% approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation.The authors are grateful to the government of Spain for its support through grant RTI2018-094336-B-100 (MCIU/AEI/FEDER, UE) and to the Government of Basque for its support through Grant IT1207-19

On left alternative loops

Left alternative loops are loops satisfying (xy)=(xx)y. We construct an infinite family of non-associative non-commutative left alternative loops whose smallest member is of orde