2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

A new study of unreported cases of 2019-nCOV epidemic outbreaks

The major purpose of the presented study is to analyze and find the solution for the model of nonlinear fractional differential equations (FDEs) describing the deadly and most parlous virus so-called coronavirus (COVID-19). The mathematical model depending of fourteen nonlinear FDEs is presented and the corresponding numerical results are studied by applying the fractional Adams Bashforth (AB) method. Moreover, a recently introduced fractional nonlocal operator known as Atangana-Baleanu (AB) is applied in order to realize more effectively. For the current results, the fixed point theorems of Krasnoselskii and Banach are hired to present the existence, uniqueness as well as stability of the model. For numerical simulations, the behavior of the approximate solution is presented in terms of graphs through various fractional orders. Finally, a brief discussion on conclusion about the simulation is given to describe how the transmission dynamics of infection take place in society.

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On a Comprehensive Model of the Novel Coronavirus (COVID-19) Under Mittag-Leffler Derivative.

We applied a generalized SEIR epidemiological model to the recent SARS-CoV-2 outbreak in the world, with a focus on Italy and its Lombardy, Piedmont, and Veneto regions. We focused on the application of a stochastic approach in fitting the model parameters using a Particle Swarm Optimization (PSO) solver, to improve the reliability of predictions in the medium term (30 days). We analyzed the official data and the predicted evolution of the epidemic in the Italian regions, and we compared the results with the data and predictions of Spain and South Korea. We linked the model equations to the changes in people’s mobility, with reference to Google’s COVID-19 Community Mobility Reports. We discussed the effectiveness of policies taken by different regions and countries and how they have an impact on past and future infection scenarios.

SEIR Modeling of the Italian Epidemic of SARS-CoV-2 Using Computational Swarm Intelligence.

The research work in this paper attempts to describe the outbreak of Coronavirus Disease 2019 (COVID-19) with the help of a mathematical model using both the Ordinary Differential Equation (ODE) and Fractional Differential Equation. The spread of the disease has been on the increase across the globe for some time with no end in sight. The research used the data of COVID-19 cases in Nigeria for the numerical simulation which has been fitted to the model. We brought in the consideration of both asymptomatic and symptomatic infected individuals with the fact that an exposed individual is either sent to quarantine first or move to one of the infected classes with the possibility that susceptible individual can also move to quarantined class directly. It was found that the proposed model has two equilibrium points; the disease-free equilibrium point ( DFE ) and the endemic equilibrium point ( E 1 ) . Stability analysis of the equilibrium points shows ( E 0 ) is locally asymptotically stable whenever the basic reproduction number, R 0 1 and ( E 1 ) is globally asymptotically stable whenever R 0 > 1 . Sensitivity analysis of the parameters in the R 0 was conducted and the profile of each state variable was also depicted using the fitted values of the parameters showing the spread of the disease. The most sensitive parameters in the R 0 are the contact rate between susceptible individuals and the rate of transfer of individuals from exposed class to symptomatically infected class. Moreover, the basic reproduction number for the data is calculated as R 0 ≈ 1.7031 . Existence and uniqueness of solution established via the technique of fixed point theorem. Also, using the least square curve fitting method together with the fminsearch function in the MATLAB optimization toolbox, we obtain the best values for some of the unknown biological parameters involved in the proposed model. Furthermore, we solved the fractional model numerically using the Atangana-Toufik numerical scheme and presenting different forms of graphical results that can be useful in minimizing the infection.

A Mathematical Model of Coronavirus Disease (COVID-19) Containing Asymptomatic and Symptomatic Classes.

We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria Using stability theory of differential equations, the qualitative behavior of model is studied The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations The impacts of various biological parameters on transmission dynamics of COVID-19 is examined These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease In the end, the obtained results are demonstrated graphically to justify our theoretical findings

https://www.techscience.com/cmc/v66n2/40631/pdf

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats–Hosts–Reservoir–People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government. The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach’s fixed point theory have been used for verification of the existence and stability criteria of the model. Further, we conduct stability analysis for both disease-free and endemic equilibrium states. On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model. Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done. The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated. Finally, we illustrate the obtained results graphically.

/pdf/a-mathematical-model-of-covid-19-using-fractional-derivative-261o1g75cz.pdf

A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control

Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020 Taking this into account, in the present work, we have analysed a Bats–Hosts–Reservoir–People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted The Picard successive approximation technique and Banach’s fixed point theory have been used for verification of the existence and stability criteria of the model Further, we conduct stability analysis for both disease-free and endemic equilibrium states On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated Finally, we illustrate the obtained results graphically

/pdf/a-mathematical-model-of-covid-19-using-fractional-derivative-2qyw2tbctn.pdf

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Novel linezolid-based oxazolidinones as potent anticandidiasis and antitubercular agents.

Microwave-assisted green synthesis of 1,5 benzodiazepines using Cu(II)-clay nanocatalyst

A simple and efficient BF3-OEt2 promoted C3-alkylation of indole has been developed to obtain3-indolylsuccinimidesfrom commercially available indoles and maleimides, with excellent yields under mild reaction conditions. Furthermore, anti-proliferative activity of these conjugates was evaluated against HT-29 (Colorectal), Hepg2 (Liver) and A549 (Lung) human cancer cell lines. One of the compounds, 3w, having N,N-Dimethylatedindolylsuccinimide is a potent congener amongst the series with IC50 value 0.02 µM and 0.8 µM against HT-29 and Hepg2 cell lines, respectively, and compound 3i was most active amongst the series with IC50 value 1.5 µM against A549 cells. Molecular docking study and mechanism of reaction have briefly beendiscussed. This method is better than previous reports in view of yield and substrate scope including electron deficient indoles.

Iqbal N. Shaikh

Papers

A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Novel linezolid-based oxazolidinones as potent anticandidiasis and antitubercular agents.

Microwave-assisted green synthesis of 1,5 benzodiazepines using Cu(II)-clay nanocatalyst

BF3-OEt2 Catalyzed C3-Alkylation of Indole: Synthesis of Indolylsuccinimidesand Their Cytotoxicity Studies.