Chikungunya virus (CHIKV) is a mosquito-transmitted alphavirus that is emerging as a global threat because of the highly debilitating nature of the associated disease and unprecedented magnitude of its spread. Chikungunya originated in Africa and has since spread across the entire globe causing large numbers of epidemics that have infected millions of people in Asia, the Indian subcontinent, Europe, the Americas, and Pacific Islands. Phylogenetic analysis has identified four different genotypes of CHIKV: Asian, West African, East/Central/South African (ECSA), and Indian Ocean Lineage (IOL). In the absence of well-designed epidemiological studies, the aim of this review article was to summarize the global epidemiology of CHIKV and to provide baseline data for future research on the treatment, prevention, and control of this life-threatening disease.

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO₂) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO₂) nanotubes.