A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.

The Chen circuit system, a three-dimensional autonomous system with intriguing dynamics, has gained considerable attention due to its potential applications in diverse scientific fields. In this article, a Chen circuit-like system is defined and a comprehensive dynamics has been studied. The system exhibits chaotic dynamics, limit cycles, and bifurcations, making it a captivating subject of study. By employing numerical simulations and analytical techniques, we explore the system's stability and identify critical parameter values leading to qualitative changes. Notably, we delve Hopf bifurcations, which give rise to stability changes and the emergence of limit cycles. Furthermore, we analyze the fractal dimension of the system's attractor, providing insights into its complexity and self-similarity. Through a systematic examination of the Chen circuit-like system, we deepen our understanding of its intricate dynamics and offer valuable insights into the underlying mechanisms. The findings contribute to the field of dynamical systems and hold potential implications in areas such as chaos-based secure communications, signal processing, and nonlinear control. This work serves as a valuable reference for researchers and practitioners interested in the dynamics and bifurcation analysis of nonlinear systems.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

The world is now undergoing through a global emergency due to COVID-19 which needs immediate remedies in order to strengthen the healthcare facility to save the nations. Looking towards to the remedies, research on different aspects including the genomic and proteomic level characterizations of the SARS-CoV2 are necessarily important. In this present study, the spatial representation/composition of twenty amino acids across the primary protein sequences of SARS-CoV2 have been looked into through different parameters viz. Shannon entropy, Hurst exponent in order to fetch the autocorrelation and amount of information over the spatial representations. Also frequency distribution of each of the amino acids over the protein sequences have been chalked out.

In the NCBI database, as on June 6, 2020, total number of available complete genome sequences of SARS-CoV2 across the world is 3617. The envelope protein of SARS-CoV2 possesses several non-synonymous mutations over the transmembrane domain and (C)-terminus in 0.414\% of these 3617 genomes. The C-terminus motif DLLV has been changed to DFLV and YLLV in the proteins QJR88103 (Australia: Victoria) and QKI36831 (China: Guangzhou) respectively, which might affect the binding of this motif with the host protein PALS1.

In 2020, the pandemic caused by the Coronaviruses (CoV) that are a large family of viruses that cause illness ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS-CoV) and Severe Acute Respiratory Syndrome (SARS-CoV2). The Coronavirus disease (COVID-19) is a new strain that was discovered in 2019 and has not been previously identified in humans. It is the high time to investigate the quantitative and/or qualitative genomic informations of the virus SARS-CoV2 in order to strengthen the healthcare facility to fight against this viral disease. In this article, a through quantitative understanding of the purine and pyrimidine spatial distribution/organization of all 89 complete sequences of SARS-CoV (available as on date in the NCBI virus database, is made using different parameters such as fractal dimension, Hurst exponent, Shannon entropy and GC content of the nucleotide sequences of the genome of SARS-CoV2. Also a cluster among all the the SARS-CoV sequences of nucleotide have been made based on their phylogeny made through their closeness (Hamming distance) based on respective purine-pyrimidine distribution.

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

Coronaviruses are a large family of RNA viruses which cause respiratory infections ranging from the common cold to more severe diseases such as Middle East Respiratory Syndrome (MERS), Severe Acute Respiratory Syndrome (SARS) and COVID-19. This article highlights some key findings based on a thorough scanning of genes of 475 SARS-CoV2 genomes, including the co-presence of ORF7a and ORF8 over the 256 SARS-CoV2 genomes and the absence of the gene ORF7b over the 219 SARS-CoV2 genomes collected from various countries including India. The presence of the gene ORF7b is found in the SARS-CoV2 genomes containing the L-type strain which is reported to having much higher virulence as compared to the S-type strain.

The scientific, private and industrial sectors use a wide variety of technological platforms available to achieve protection against SARS-CoV-2, including vaccines. However, the virus evolves continually into new highly virulent variants, which might overcome the protection provided by vaccines and may re-expose the population to infections. Mass vaccinations should be continued in combination with more or less obligation mandatory non-pharmaceutical interventions. Therefore, the key questions to be answered are: (i) How to identify the primary and secondary infections of SARS-CoV-2? (ii) Why are neutralizing antibodies not long-lasting in both the cases of natural infections and post-vaccinations? (iii) Which are the factors responsible for this decay in neutralizing antibodies? (iv) What strategy could be adapted to develop long-term herd immunity? (v) Is the Spike the only vaccine candidate or a vaccine cocktail is better?

The devastating impact of the ongoing coronavirus disease 2019 (COVID-19) on public health, caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has made fighting of the COVID-19 pandemic is a top priority in medical research and pharmaceutical development. Surveillance of SARS-CoV-2 mutations is essential for the comprehension of SARS-CoV-2 variant diversity and their impact on virulence and pathogenicity. The SARS-CoV-2 open reading frame 10 (ORF10) protein interacts with multiple human proteins CUL2, ELOB, ELOC, MAP7D1, PPT1, RBX1, THTPA, TIMM8B, and ZYG11B expressed in the lung tissues. Mutations and co-mutations in the emerging SARS-CoV-2 ORF10 variants are expected to impact the severity of the virus and its associated consequences. In this article, We highlight 128 single mutations and 35 co-mutations in the unique SARS-CoV-2 ORF10 variants in this article. The possible predicted effects of these mutations and co-mutations on the secondary structure of ORF10 variants and host protein interactomes are presented. The findings highlight the possible effects of mutations and co-mutations on the emerging 140 ORF10 unique variants from secondary structure and intrinsic protein disorder perspectives.

Therapeutic options for the highly pathogenic human Severe Acute Respiratory Syndrome-Coronavirus 2 (SARS-CoV-2) causing the current pandemic Coronavirus disease (COVID-19) are urgently needed. COVID-19 is associated with viral pneumonia and acute respiratory distress syndrome causing significant morbidity and mortality. The proposed treatments for COVID-19, such as hydroxychloroquine, remdesivir and lopinavir/ritonavir, have shown little or no effect in the clinic. Additionally, bacterial and fungal pathogens contribute to the SARS-CoV-2 mediated pneumonia disease complex. The antibiotic resistance in pneumonia treatment is increasing at an alarming rate. Therefore, carbon-based nanomaterials (CBNs), such as fullerene, carbon dots, graphene, and their derivatives constitute a promising alternative due to their wide-spectrum antimicrobial activity, biocompatibility, biodegradability and capacity to induce tissue regeneration. Furthermore, the antimicrobial mode of action is mainly physical (e.g. membrane distortion), which is characterized by a low risk of antimicrobial resistance. In this review, we evaluated the literature on the antiviral activity and broad-spectrum antimicrobial properties of CBNs. CBNs had antiviral activity against 12 enveloped positive-sense single-stranded RNA viruses similar to SARS-CoV-2. CBNs with low or no toxicity to the humans are promising therapeutics against COVID-19 pneumonia complex with other viruses, bacteria and fungi, including those that are multidrug-resistant.

Several hypotheses have been presented on the origin of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) from its identification as the agent causing the current coronavirus disease 19 (COVID-19) pandemic. So far, no hypothesis has managed to identify the origin, and the issue has resurfaced. Here we have unfolded a pattern of distribution of several mutations in the SARS-CoV-2 proteins across different continents comprising 24 geo-locations. The results showed an evenly uneven distribution of unique protein variants, distinct mutations, unique frequency of common conserved residues, and mutational residues across the 24 geo-locations. Furthermore, ample mutations were identified in the evolutionarily conserved invariant regions in the SARS-CoV-2 proteins across almost all geo-locations we have considered. This pattern of mutations potentially breaches the law of evolutionary conserved functional units of the beta-coronavirus genus. These mutations may lead to several novel SARS-CoV-2 variants with a high degree of transmissibility and virulence. A thorough investigation on the origin and characteristics of SARS-CoV-2 needs to be conducted in the interest of science and to be prepared to meet the challenges of potential future pandemics.