Dynamics of a fractional order mathematical model for COVID-19 epidemic transmission.

To achieve the aim of immediately halting spread of COVID-19 it is essential to know the dynamic behavior of the virus of intensive level of replication. Simply analyzing experimental data to learn about this disease consumes a lot of effort and cost. Mathematical models may be able to assist in this regard. Through integrating the mathematical frameworks with the accessible disease data it will be useful and outlay to comprehend the primary components involved in the spreading of COVID-19. There are so many techniques to formulate the impact of disease on the population mathematically, including deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional derivative modeling is one of the essential techniques for analyzing real-world issues and making accurate assessments of situations. In this paper, a fractional order epidemic model that represents the transmission of COVID-19 using seven compartments of population susceptible, exposed, infective, recovered, the quarantine population, recovered-exposed, and dead population is provided. The fractional order derivative is considered in the Caputo sense. In order to determine the epidemic forecast and persistence, we calculate the reproduction number R 0 . Applying fixed point theory, the existence and uniqueness of the solutions of fractional order derivative have been studied . Moreover, we implement the generalized Adams-Bashforth-Moulton method to get an approximate solution of the fractional-order COVID-19 model. Finally, numerical result and an outstanding graphic simulation are presented.

Stability Analysis of an Extended SEIR COVID-19 Fractional Model with Vaccination Efficiency.

This work is aimed at presenting a new numerical scheme for COVID-19 epidemic model based on Atangana-Baleanu fractional order derivative in Caputo sense (ABC) to investigate the vaccine efficiency. Our construction of the model is based on the classical SEIR, four compartmental models with an additional compartment V of vaccinated people extending it SEIRV model, for the transmission as well as an effort to cure this infectious disease. The point of disease-free equilibrium is calculated, and the stability analysis of the equilibrium point using the reproduction number is performed. The endemic equilibrium's existence and uniqueness are investigated. For the solution of the nonlinear system presented in the model at different fractional orders, a new numerical scheme based on modified Simpson's 1/3 method is developed. Convergence and stability of the numerical scheme are thoroughly analyzed. We attempted to develop an epidemiological model presenting the COVID-19 dynamics in Italy. The proposed model's dynamics are graphically interpreted to observe the effect of vaccination by altering the vaccination rate.

Modeling the impact of the vaccine on the COVID-19 epidemic transmission via fractional derivative.

To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand the dynamical behavior of the proliferation of the virus at an intense level. Studying this disease simply based on experimental analysis is very time consuming and expensive. Mathematical modeling might play a worthy role in this regard. By incorporating the mathematical frameworks with the available disease data it will be beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are many vaccines available globally at present, henceforth, by including the effect of vaccination into the model will also support to understand the visible influence of the vaccine on the spread of COVID-19 virus. There are several ways to mathematically formulate the effect of disease on the population like deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative modeling is one of the fundamental methods to understand real-world problems and evaluate accurate situations. In this article, a fractional order epidemic model S p E p I p E r p R p D p Q p V p on the spread of COVID-19 is presented. S p E p I p E r p R p D p Q p V p consists of eight compartments of population namely susceptible, exposed, infective, recovered, the quarantine population, recovered-exposed, and dead population. The fractional order derivative is considered in the Caputo sense. For the prophecy and tenacity of the epidemic, we compute the reproduction number R 0 . Using fixed point theory, the existence and uniqueness of the solutions of fractional order derivative have been studied. Furthermore, we are using the generalized Adams-Bashforth-Moulton method, to obtain the approximate solution of the fractional-order COVID-19 model. Finally, numerical results and illustrative graphic simulation are given. Our results suggest that to reduce the number of cases of COVID-19 we should reduce the contact rate of the people if the population is not fully vaccinated. However, to tackle the issue of reducing the social distancing and lock down, which have very negative impact on the economy as well as on the mental health of the people, it is much better to increase the vaccine rate and get the whole nation to be fully vaccinated.

Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative.

In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grünwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.

Use of medical abbreviations and acronyms: knowledge among medical students and postgraduates.

INTRODUCTION: Inappropriate use of abbreviations and acronyms in healthcare has become an international patient safety issue. The aim of this study was to assess the knowledge of medical abbreviations and acronyms among residents of the department of medicine at a tertiary-care hospital. METHODS: Internal medicine residents (IMRs), subspecialty residents (SRs) and students were asked to complete a self-administered questionnaire which comprised standard abbreviations used in medicine and its various subspecialties. Scores obtained by the residents were classified into three categories: >70% correct answers; 50-69% correct answers; <50% correct answers. RESULTS: A total of 77 IMRs, SRs and medical students participated. Overall, good responses were achieved by 53 (68.8%), 16 (20.8%) attained satisfactory responses, and eight (10.4%) had unsatisfactory scores. The majority of SRs achieved good responses (19/22 (86%)), followed by IMRs (30/40 (75%)) and students (4/15 (26.7%)). Evaluation of their knowledge taken from the list of 'do not use' abbreviations showed that 89.6% reported using 'Q.D.' instead of 'once a day', and 93% used 'IU' instead of the entire phrase 'international unit'. The top five 'not to use' abbreviations were ZnSO4, µg, MgSO4, IU and SC, with the frequency 100%, 96%, 94.8%, 93% and 90%, respectively. CONCLUSIONS: This study showed that there is a knowledge gap among trainees in medicine regarding the meaning and usage of common medical abbreviations. We therefore recommend proper education of trainees in medicine to ensure they understand the meaning of abbreviations and are aware of the list of 'do not use' abbreviations.

Clinical predictors of mortality in hospitalized patients with infective endocarditis at a tertiary care center in Pakistan.

OBJECTIVE: To evaluate the clinical characteristics and predictors of in-hospital mortality in patients with infective endocarditis at a tertiary care centre in Pakistan. METHODS: The cross-sectional study was conducted at the Aga Khan University Hospital, Karachi, from January 1, 2002, to December 31, 2006, and comprised 84 consecutive patients hospitalised with infective endocarditis,. All patients underwent verification of the diagnosis according to the Modified Duke criterion. Data was collected through a questionnaire and analysed using Student's t test, Chi square and Fisher's exact test. Univariate and multivariate logistic regression analysis was performed to assess predictors of mortality. RESULTS: Of the total, 53(63%) patients were male and 31(37%) female. The mean age of the patients was 42+17 years. Overall, 34(41%) patients had rheumatic valve disease as a predisposing condition. The most commonly affected valve was mitral in 43(51%) patients, and the most commonly isolated organism was methicillin-resistant staphylococcus aureus in 12(14.3%). Overall in-hospital mortality was 27(32.1%), while 18(21%) patients, developed congestive cardiac failure, 15(18%) developed arrhythmias, 16(19%) developed peripheral embolism and renal failure was present in 38(54%). Besides, 17(20%) patients underwent surgical intervention. The final multivariate model that can be used to predict mortality in this study consisted of the presence of neurological complications (p <0.001) Odds Ratio 7.26, Confidence Interval (2.27-23.18), congestive cardiac heart failure (p <0.023) Odds Ratio 5.39, Confidence Interval (1.26-23.04), and arrhythmias (p <0.034) Odds Ratio 4.21, Confidence Interval (1.11-15.88). CONCLUSION: Significant predictors of mortality in hospitalised patients with infective endocarditis in our study were the presence of neurological complications, congestive cardiac heart failure, and the presence of arrhythmias.

Outcomes in ST elevation Myocardial Infarction; a comparison of a tertiary care center in Pakistan with European centers.

OBJECTIVES: To evaluate the clinical characteristics and in hospital outcome data of patients presenting to the Aga Khan University Hospital with ST elevation Myocardial Infarction (STEMI) and its comparison with data from patients enrolled in the European Heart registry for the same duration. METHODS: Data on 296 patients with STEMI was prospectively collected from 1st January 2010, till 31st December 2010 from the cardiology section at the Aga Khan University Hospital. European data was collected on 7485 patients retrieved from the Eurobservational Research programme Acute Coronary Syndrome Registry 2010 for the same duration. RESULTS: A total of 296 patients were enrolled from AKUH and 7485 from European centers for the year 2010. Majority of patients in both groups were male. Pakistani patients were more likely to be younger and diabetic (p<0.05) with higher frequency of prior myocardial infarction and angina (p<0.05). They were less likely to be smokers and previously diagnosed as dyslipidemic. Most patients presented to hospital with chest pain, median time between symptom onset and hospital arrival was 3.8 (2.0-8.5) hours. One third of European patients received a thrombolytic agent compared with less than 5% of AKU/Pakistani patients. Almost 90% of AKU/Pakistani patients underwent primary percutaneous intervention. Approximately 5.8% of our patients were not candidates for any reperfusion therapy vs. 4.8% of European patients. On coronary angiogram, the majority of patients had single or two vessel Coronary Artery Disease. We had a higher frequency of high risk lesions, 97.86 vs. 84.14 %( p=0.002).Our patients had more drug eluting stents 42.5% vs. 25.9 % (p=0.01) implanted, due to more diabetics and smaller vessel size. We also had a similar proportion of patients undergoing coronary artery bypass graft. Frequency of complications was similar for both cohorts. Median hospital stay in our patients was shorter, survival at hospital discharge being similar between both groups (P=0.42) CONCLUSIONS: The patients presenting to Aga Khan University Hospital with STEMI were younger and more likely to be diabetic. They had a higher frequency of prior Myocardial Infarction and angina. They underwent revascularization with primary percutaneous intervention more often and usually for more complex lesions requiring greater use of drug eluting stents. Survival at discharge was similar compared to European Centers.

Political riots in Pakistan and stress-induced cardiomyopathy: a case report.

A previously healthy middle-aged lady with no prior risk factors for coronary artery disease presented with chest discomfort and ECG changes suggestive of anterolateral ST elevation myocardial infarction. She had had a stressful event prior to the onset of symptoms in that she had been caught up in a riot and had been exposed to intense mental and physical stress. She was found to have severe global left ventricular dysfunction but coronary artery disease was not discovered on coronary angiography. She was treated with antiplatelets, statins, diuretics and aldosterone antagonists. Her left ventricular function was revealed to have improved to normal as shown on echocardiography done on her follow-up 2 months after initial presentation.

Hallucinogen-like actions of 2,5-dimethoxy-4-(n)-propylthiophenethylamine (2C-T-7) in mice and rats.

RATIONALE: Few studies have examined the effects of 2,5-dimethoxy-4-(n)-propylthiophenethylamine (2C-T-7) in vivo. OBJECTIVES: 2C-T-7 was tested in a drug-elicited head twitch assay in mice and in several drug discrimination assays in rats; 2C-T-7 was compared to the phenylisopropylamine hallucinogen R(-)-1-(2,5-dimethoxy-4-methylphenyl)-2aminopropane (DOM) in both assays, with or without pretreatment with the selective 5-HT2A antagonist (+)-(2,3-dimethoxyphenyl)-1-[2-(4-fluorophenylethyl)]-4-piperidine-methanol (M100907). Finally, the affinity of 2C-T-7 for three distinct 5-HT receptors was determined in rat brain. METHODS: Drug-elicited head twitches were quantified for 10 min following administration of various doses of either 2C-T-7 or R(-)-DOM, with and without pretreatments of 0.01 mg/kg M100907. In rats trained to discriminate lysergic acid diethylamide (LSD), 2C-T-7 and R(-)-DOM were tested for generalization. In further studies, rats were trained to discriminate 2C-T-7 from saline, then challenged with 0.05 mg/kg M100907. In competition binding studies, the affinity of 2C-T-7 was assessed at 5-HT2A receptors, 5-HT1A receptors, and 5-HT2C receptors. RESULTS: 2C-T-7 and R(-)-DOM induced similar head twitch responses in the mouse that were antagonized by M100907. In the rat, 2C-T-7 produced an intermediate degree of generalization (75%) to the LSD cue and served as a discriminative stimulus; these interoceptive effects were attenuated by M100907. Finally, 2C-T-7 had nanomolar affinity for 5-HT2A and 5-HT2C receptors and lower affinity for 5-HT1A receptors. CONCLUSIONS: 2C-T-7 is effective in two rodent models of 5-HT2 agonist activity and has affinity at receptors relevant to hallucinogen effects. The effectiveness with which M100907 antagonizes the behavioral actions of 2C-T-7 strongly suggests that the 5-HT2A receptor is an important site of action for this compound.