Mathematical modeling of corona virus (COVID-19) and stability analysis.

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us.

Bacteriocin Production by Lactobacilli and Their Role as Antibacterial Tool against Common Pathogens.

Lactobacilli are commonly found in raw and fermented foods. These bacteria are of common interest because of their capability of bacteriocin production. Bacteriocins are compounds that may be used as natural preservatives in place of chemical additives. In the present study five different samples of poultry, meat and pickle were used to isolate lactic acid bacteria (LAB) by using the MRS culture medium. Antibacterial activity was checked against Pseudomonas aeruginosa, E. coli and Staphylococcus aureus. Five strains from the poultry meat and six strains from pickle had shown antibacterial activity out of eight strains against pathogenic bacteria. Three strains of poultry meat i.e. M3, M7, M11, had shown antibacterial activity against all three indicator strains. While one strain M1 was active against Pseudomonas aeruginosa and E. coli but it was found not to be active against Staphylococcus aureus. E. coli and Staphylococcus aureus were not susceptible to M2. In the case of pickle strains H1, H2, NAT1, NAT2, were found to be active against Pseudomonas aeruginosa and E. coli but Staphylococcus aureus was not susceptible to bacteriocins of these strains. NAT3 and SHZa strains showed antibacterial activity against all the three used pathogens. The highest activity (6 mm) had shown by the lNAT3 strain of pickle against Pseudomonas aeruginosa. The least antimicrobial activity had shown by SHZa strain. M3 had an inhibition zone of 5 mm against Pseudomonas aeruginosa. M11 had an inhibition zone of 5 mm against E. coli. Bacteriocins of all isolates were sensitive towards enzyme pepsin showing their proteinaceous nature. Detection of the bacteriocin gene by PCR the strains M2, M7 were amplified for Curvacin and plantaricin genes. From current study, it is concluded that different species of Lactobacilli can be used as antibacterial tool against common bacterial pathogens.