Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Measurement of total phenolic content and antioxidant activity of aerial parts of medicinal plant Coronopus didymus

Objective: To evaluate the total phenolic content and compare the antioxidant activity of various solvent extracts and fractions from the aerial parts of Coronopus didymus through various assays. Methods: Total phenolic content was determined using the Folin-Ciocalteu assay and the in vitro antioxidant activity of a number of different extracts was investigated in a dose-dependent manner with three different methods: the 2,2-diphenyl-1-picrylhydrazyl(DPPH), 2,2'-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt(ABTS) and ferric reducing antioxidant power(FRAP) assays. A flavone was isolated from the most active ethanolic extract with high antioxidant activity using size exclusion chromatography. IC_(50) values were calculated for the DPPH and ABTS methods. The FRAP activity was assessed in terms of μM Fe(II) equivalent. Results: The phenolic content was found to be highest in the ethanol extract(CDA Et; 47.8 mM GAE) and the lowest in the dichloromethane extract(CDA DCM; 3.13 mM GAE). The ethanol extract showed high radical scavenging activity towards DPPH and ABTS radicals with IC_(50) values of(7.80 × 10~2) and(4.32 × 10~2) μg/m L, respectively. The most active ethanol extract had a FRAP value of 1 921.7 μM Fe(Ⅱ) equivalent. The isolated flavone F10C(5,7,4'-trihydroxy-3'-methoxy flavone) was far more effective for scavenging free radicals in the DPPH and ABTS assays with IC_(50) of 43.8 and 0.08 μg/m L, than the standard trolox, with IC_(50) values of 97.5 and 21.1 μg/m L, respectively. In addition, the flavone F10C and the standard ascorbic acid had FRAP values of 1 621.7 and 16 038.0 μM Fe(Ⅱ) equivalents, respectively. Conclusions: The total phenolic content of extracts in decreasing order is ethanol extract(CDA Et)> acetone extract(CDA ACE)> phenolic extract(CDA MW)> n-hexane extract(CDA nHX)> chloroform extract(CDA CHL)> dichloromethane extract(CDA DCM). The ordering of extracts in terms of antioxidant activity from highest to lowest is CDA Et> CDA MW> CDA DCM> CDA CHL> CDA ACE> CDA nHX in DPPH, ABTS and FRAP assays. A significant relationship is found between antioxidant potential and total phenolic content, suggesting that phenolic compounds are the major contributors to the antioxidant activity of Coronopus didymus.

Dynamical Transmission of Coronavirus Model with Analysis and Simulation

COVID-19 acts as a serious challenge to the whole world.Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease.We analyze the diseases free and endemic equilibrium point including stability of the model.The certain threshold value of the basic reproduction number R0 is found to observe whether population is in disease free state or endemic state.Moreover,the epidemic peak has been obtained and we expect a considerable number of cases.Finally,some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.

An updated review on pharmacological activities and phytochemical constituents of evening primrose(genus Oenothera)

Genus Oenothera includes medicinal plants that are distributed throughout the world and are known since ancient times. Popular indications of different species of this genus include treatment of inflammations, diabetes, microbial infections, ulcers, tumors, kidney and liver problems. The plants of this genus are a botanical source for various pharmaceutically active components like sterols, alkaloids, phenolic acids, flavonoids, triterpenoids, saponins, biflavonols and tocopherols. This review article is a compilation of chemical composition and biological activities of the various species of the genus Oenothera.

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

Today,coronavirus appears as a serious challenge to the whole world.Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis.New data on COVID-19 are available daily,yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited,and uncertainty remains around nearly all its parameters’values.This research provides the scientic and public health communities better resources,knowledge,and tools to improve their ability to control the infectious diseases.Using the publicly available data on the ongoing pandemic,the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections.Formulation of the testing hypotheses for different countries with a 95%level of condence,and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries.The results will be helpful in decision making as well as in further mathematical analysis and control strategy.Statistical tools are used to investigate this pandemic,which will be useful for further research.The testing of the hypothesis is done for the differences in various effects including standard errors.Changes in states’variables are observed over time.The rapid outbreak of coronavirus can be stopped by reducing its transmission.Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.