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Coastlines are irregular in nature having (random) fractal geometry and are formed by various natural activities. Fractal dimension is a measure of degree of geometric irregularity present in the coastline. A novel multicore parallel processing algorithm is presented to calculate the fractal dimension of coastline of Australia. The reliability of the coastline length of Australia is addressed by recovering the power law from our computational results. For simulations, the algorithm is implemented on a parallel computer for multi-core processing using the QGIS software, R -programming language and Python codes.

Several human diseases are caused by viruses, including cancer, Type I diabetes, Alzheimer’s disease, and hepatocellular carcinoma. In the past, people have suffered greatly from viral diseases such as polio, mumps, measles, dengue fever, SARS, MERS, AIDS, chikungunya fever, encephalitis, and influenza. Recently, COVID-19 has become a pandemic in most parts of the world. Although vaccines are available to fight the infection, their safety and clinical trial data are still questionable. Social distancing, isolation, the use of sanitizer, and personal productive strategies have been implemented to prevent the spread of the virus. Moreover, the search for a potential therapeutic molecule is ongoing. Based on experiences with outbreaks of SARS and MERS, many research studies reveal the potential of medicinal herbs/plants or chemical compounds extracted from them to counteract the effects of these viral diseases. COVID-19′s current status includes a decrease in infection rates as a result of large-scale vaccination program implementation by several countries. But it is still very close and needs to boost people’s natural immunity in a cost-effective way through phytomedicines because many underdeveloped countries do not have their own vaccination facilities. In this article, phytomedicines as plant parts or plant-derived metabolites that can affect the entry of a virus or its infectiousness inside hosts are described. Finally, it is concluded that the therapeutic potential of medicinal plants must be analyzed and evaluated entirely in the control of COVID-19 in cases of uncontrollable SARS infection.

As per the report of W.H.O. about 7 million people died in India till date due to COVID-19 infection. The transmission of COVID-19 infection can affect the temporal and geographic diversity of environmental pollution, thereby disrupting “planetary health” and livelihood. The consensus is that COVID-19 could have significant long-lasting effects on ecosystem and society. It is possible to reach an agreement to create and maintain an ecologically sound environment and a circular bio-economy to try to solve these issues. For the first time, a fractional mathematical model is formulated where the infection is considered due to unhygienic environment with a synergy between mathematical fractal parameters and biology of the disease transmission. Other mathematical analysis such as the boundedness of solutions, the wellposedness of the proposed model concerning existence results, etc. are investigated. Additionally, evaluation of vaccine-clearance equilibrium point is performed. Sensitivity parameters analysis and model’s stability also steps in. To get numerical results, the “Adams–Bashforth–Moulton” method with slight modification in the kernel is used. The fractional parameters: memory effect and fractional diffusion shows a good performance of the proposed model in depicting the disease dynamics. Consequences of follow-up optimal control functions in Susceptives and Vaccinated individuals, where feasible strategies in terms of the control maps are presented.

The focus of this research work is to obtain the chaotic behaviour and bifurcation in the real dynamics of a newly proposed family of functions fλ,ax=x+1−λxlnax;x>0, depending on two parameters in one dimension, where assume that λ is a continuous positive real parameter and a is a discrete positive real parameter. This proposed family of functions is different from the existing families of functions in previous works which exhibits chaotic behaviour. Further, the dynamical properties of this family are analyzed theoretically and numerically as well as graphically. The real fixed points of functions fλ,ax are theoretically simulated, and the real periodic points are numerically computed. The stability of these fixed points and periodic points is discussed. By varying parameter values, the plots of bifurcation diagrams for the real dynamics of fλ,ax are shown. The existence of chaos in the dynamics of fλ,ax is explored by looking period-doubling in the bifurcation diagram, and chaos is to be quantified by determining positive Lyapunov exponents.

Healthcare reporting methods have seen a common problem with actual incidence of scrub typhus cases in Northeast India that were reported during post rainy season. We propose a Host-Vector model, a first of its kind, with a significant modification in the disease infection transmission rate. Our work aims to investigate a mathematical model by Atangana-Baleanu fractal-fractional operator that has seasonal pattern incorporating 2010–2022 data. The existence-uniqueness property is investigated using the fixed point theory, and also Ulam-Hyers stability is performed. Based on Lagrange’s interpolation polynomial in the numerical scheme, a numerical investigation for various values of the fractional parameters is presented. The numerical simulation and phase plane trajectories demonstrates excellent performance of the suggested model as the number of individuals who recover rises gradually after herd immunity threshold points and turning points. Furthermore, the information gathered here may be useful for enhancing spatiotemporally dynamic scrub typhus disease models.

Water scarcity is one of the major problems in the world and millions of people have no access to freshwater. Untreated wastewater is widely used for agriculture in many countries. This is one of the world-leading serious environmental and public health concerns. Instead of using untreated wastewater, treated wastewater has been found more applicable and ecofriendly option. Moreover, environmental toxicity due to solid waste exposures is also one of the leading health concerns. Therefore, intending to combat the problems associated with the use of untreated wastewater, we propose in this review a multidisciplinary approach to handle wastewater as a potential resource for use in agriculture. We propose a model showing the efficient methods for wastewater treatment and the utilization of solid wastes in fertilizers. The study also points out the associated health concern for farmers, who are working in wastewater-irrigated fields along with the harmful effects of untreated wastewater. The consumption of crop irrigated by wastewater has leading health implications also discussed in this review paper. This review further reveals that our current understanding of the wastewater treatment and use in agriculture with addressing advancements in treatment methods has great future possibilities.

The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin’s Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number R 0 is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of R 0 using the parameters value. In the numerical simulations, we concluded that reducing R 0 below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures.

The current research uses the Grünwald–Letnikov (GL) fractional differential mask to improve satellite and medical images. One of the important image enhancement methods in digital image processing is texture enhancement. A fractional differential-based two-dimensional discrete gradient operator is based on the definition of Grünwald–Letnikov (GL) interpretation of fractional calculus, which is extended from a one-dimensional operator through the analysis of its spectrum to improve the image texture. Which then extracts more subtle texture information, and gets around the lack of a classical gradient operator. Based on the GL fractional differential, an approximate two-dimensional isotropic gradient operator mask was created using the GL fractional derivative, the technique generates 3 × 3 and 5 × 5 pixel-sized masks that preserve the correlation between neighboring pixels. The strength of the mask, which was a variable and non-linear filter, could be changed by varying the intensity factor to enhance the image. Experimental results show that the operator may emphasize the texture and obtain more complex information. Compared to the conventional classical methods, the suggested way has an excellent promotional effect on texture enhancement compared to the previous method on grayscale images.

Steganography is the technique for exchanging concealed secret information in a way to avoid suspicion. The aim of Steganography is to transfer secrete message to another party by hiding the data in a cover object, so that the imposter who monitors the traffic should not distinguish between genuine secret message and the cover object. This paper presents the comparative study and performance analysis of different image Steganography methods using various types of cover media ((like BMP/JPEG/PNG etc.) with the discussion of their file formats. We also discuss the embedding domains along with a discussion on salient technical properties, applications, limitations, and Steganalysis.