RESUMO
The study explores the dynamics of a COVID-19 epidemic in multiple susceptible populations, including the various stages of vaccination administration. In the model, there are eight human compartments: completely susceptible; susceptible with dose-1 vaccination; susceptible with dose-2 vaccination; susceptible with booster dose vaccination; exposed; infected with and without symptoms, and recovered compartments. The biological feasibility of the model is analysed. The threshold value, R 0 , is derived using the next-generation matrix. The stability analysis of the equilibrium points was performed locally and globally using the threshold parameter of the model. The conditions determining disease persistence is obtained. The model is subjected to sensitivity analysis, and the most sensitive parameters are identified. Also, MATLAB is used to verify the mathematical outcomes of the system's dynamic behaviour and suggests that necessary steps should be taken to keep the spread of the omicron variant infectious disease under control. The findings of this study could aid health officials in their efforts to combat the spread of COVID-19.
RESUMO
In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID-19 in India. The proposed SI u I k R model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: I u (unknown infected class) and I k (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID-19 infection. Furthermore, a non-monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease-free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long-run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.
RESUMO
Hyaluronate lyases are a class of endoglycosaminidase enzymes with a high level of complexity and heterogeneity. The main function of the Streptococcus pyogenes bacteriophage protein hyaluronate lyase, HylP2, is to degrade hyaluronan into unsaturated disaccharide units. HylP2 was cloned, over-expressed and purified to homogeneity. The recombinant HylP2 exists as a homotrimer with a molecular mass of approximately 110 kDa under physiological conditions. The HylP2 was crystallized and the crystals were soaked in two separate reservoir solutions containing ascorbic acid and lactose, respectively. The crystal structures of native HylP2 and its two complexes with ascorbic acid and lactose have been determined. HylP2 folds into four distinct domains with a central core consisting of 16 antiparallel beta-strands forming an irregular triangular tube designated as triple-stranded beta-helix. The structures of complexes show that three molecules each of ascorbic acid and lactose bind to protein at the sugar binding groove in the triple-stranded beta-helix domain. Both ascorbic acid and lactose molecules occupy almost identical subsites in the long saccharide binding groove. Both ligands are involved in several hydrogen bonded interactions at each subsite. The binding characteristics and stereochemical properties indicate that Tyr264 may be involved in the catalytic activity of HylP2. The mutation of Tyr264 to Phe264 supports this observation.