Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh–Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model’s solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams–Bashforth–Moulton method, whereas for the Atangana–Baleanu–Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.

We propose a new mathematical model to investigate the recent outbreak of the coronavirus disease (COVID-19). The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents an epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. The global asymptotic stability conditions for the disease free equilibrium are obtained. The real COVID-19 incidence data entries from 01 July, 2020 to 14 August, 2020 in the country of Pakistan are used for parameter estimation thereby getting fitted values for the biological parameters. Sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. To view more features of the state variables in the proposed model, we perform numerical simulations by using different values of some essential parameters. Moreover, profiles of the reproduction number through contour plots have been biologically explained.

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Polymer composites are fabricated by incorporating fillers into a polymer matrix. The intent for addition of fillers is to improve the physical, mechanical, chemical and rheological properties of the composite. This study reports on a unique polymer composite using hydrochar, synthesised by microwave-assisted hydrothermal carbonization of rice husk, as filler in polylactide matrix. The polylactide/hydrochar composites were fabricated by incorporating hydrochar in polylactide at 5%, 10%, 15% and 20 wt% by melt processing in a Haake rheomix at 170 °C. Both the neat polylactide and polylactide/hydrochar composite were characterized for mechanical, structural, thermal and rheological properties. The tensile modulus of polylactide/hydrochar composites was improved from 2.63 GPa (neat polylactide) to 3.16 GPa, 3.33 GPa, 3.54 GPa, and 4.24 GPa after blending with hydrochar at 5%, 10%, 15%, and 20%, respectively. Further, the incorporation of hydrochar had little effect on storage modulus (G′) and loss modulus (G″). The findings of this study reported that addition of hydrochar improves some characteristics of polylactide composites suggesting the potential of hydrochar as filler for polymer/hydrochar composites.

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The process parameters of microwave-induced hydrothermal carbonization (MIHTC) play an important role on the hydrothermal chars (hydrochar) yield. The effect of reaction temperature, reaction time, particle size and biomass to water ratio was optimized for hydrochar yield by modeling using the central composite design (CCD). Further, the rice straw and hydrochar at optimum conditions have been characterized for energy, chemical, structural and thermal properties. The optimum condition for hydrochar synthesis was found to be at a 180 °C reaction temperature, a 20 min reaction time, a 1:15 weight per volume (w/v) biomass to water ratio and a 3 mm particle size, yielding 57.9% of hydrochar. The higher heating value (HHV), carbon content and fixed carbon values increased from 12.3 MJ/kg, 37.19% and 14.37% for rice straw to 17.6 MJ/kg, 48.8% and 35.4% for hydrochar. The porosity, crystallinity and thermal stability of the hydrochar were improved remarkably compared to rice straw after MIHTC. Two characteristic peaks from XRD were observed at 2θ of 15° and 26°, whereas DTG peaks were observed at 50–150 °C and 300–350 °C for both the materials. Based on the results, it can be suggested that the hydrochar could be potentially used for adsorption, carbon sequestration, energy and agriculture applications.

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