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.

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.