Experimental and Mathematical Model for the Study of the In-vitro Susceptibility of Antimicrobial Agents against Escherichi coli Isolates Obtained from Abattoir Centres in Ikorodu, Lagos, Nigeria

Escherichia coli (E. coli) cause a variety of intestinal and extra-intestinal infections, such as urinary tract infection, diarrhea, meningitis, peritonitis and septicemia. E. coli still remains the leading bacterium that lives in the digestive tract of humans and animals. A total of 66 Escherichia coli isolates obtained from faeces and effluents from abattoir were examined for their susceptibility to 11 antimicrobial agents. Pathogenic E. coli can be released with the animal wastes coming from slaughter houses into the environment, where they can persist and cause infections. In this study we have evaluated the sensitivity to antibiotics by E. coli strains isolated from several types of infected faeces and effluents. Strains of E. coli were identified based on their cultural and biochemical characterisation. The antibiotic sensitivity test was performed using the disc diffusion method according to standards of the Clinical and Laboratory Standard Institute. High resistance levels (≥60) were detected against antimicribial agents like septrin and tetracycline. Moderate resistances (between 40-59%) were detected against chloramphenicol, augmentin, ampicillin, cotrimoxazole and streptomycin. Ciprofloxacin (87.9%), nitrofurantoin (80.3%), gentamicin (77.3%) and amoxycillin (62.1%) were highly sensitive to the E. coli strains. This work presents a four compartmental model, which describes the interactions of infections with Escherichia Coli in the in-vitro study, to gain more insight into the in-vitro analysis of the model formulated. The classical threshold for basic reproduction number,R0 is obtained: if R0<1, the E. coli will clear/die out of the population agar medium that was considered but if R0>1, then the E. coli will grow and persist within the agar medium. We also determine the local and global stability of the E. coli model in the in-vitro, using the comparison theorem. Our result shows that when the threshold parameter is less than unity, the disease – free equilibrium will be asymptotically stable and unstable at thresholds greater than unity. Numerical simulations were carried out using maple software to show the effects of treatment on the E. coli model. The result showed the pronounced effect of treatment which gives more insight about the E. coli model which was in great accord with the investigational analysis of the experimental work.