This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order
SIR
type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.
This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.
The research was aimed to unravel the enzymatic potential of sequentially transformed new triazoles by chemically converting 4-methoxybenzoic acid via Fischer's esterification to 4-methoxybenzoate which underwent hydrazinolysis and the corresponding hydrazide (1) was cyclized with phenyl isothiocyanate (2) via 2-(4-methoxybenzoyl)-N-phenylhydrazinecarbothioamide (3); an intermediate to 5-(4-methoxyphenyl)-4-phenyl-4H-1,2,4-triazol-3-thiol (4). The electrophiles; alkyl halides 5(a-g) were further reacted with nucleophilic S-atom to attain a series of S-alkylated 5-(4-methoxyphenyl)-4-phenyl-4H-1,2,4-triazole-3-thiols 6(a-g). Characterization of synthesized compounds was accomplished by contemporary spectral techniques such as FT-IR, 1H-NMR, 13C-NMR and EI-MS. Excellent cholinesterase inhibitory potential was portrayed by 3-(n-heptylthio)-5-(4-methoxyphenyl)-4-phenyl-4H-1,2,4-triazole; 6g against AChE (IC50; 38.35±0.62μM) and BChE (IC50; 147.75±0.67μM) enzymes. Eserine (IC50; 0.04±0.01μM) was used as reference standard. Anti-proliferative activity results ascertained that derivative encompassing long straight chain substituted at S-atom of the moiety was the most potent with 4.96 % cell viability (6g) at 25μM and with 2.41% cell viability at 50μMamong library of synthesized derivatives. In silico analysis also substantiated the bioactivity statistics.