Role of antibiotic therapy in bacterial disease: A mathematical study

Abstract

Pathogenic bacteria in human system mature through the bio-synthesis of protective layer known as cell wall. This bacterial cell wall growth occurs in the presence of enzyme released by it. After maturation by the cell wall formation, pathogenic bacteria become harmful for human body as they are responsible for different diseases. Antibiotics or drugs are employed for curing bacterial diseases through the inhibition of this maturation process and it occurs by the binding progression of antibiotics with the released enzyme. But nowadays, drugs or antibiotics like [Formula: see text]-lactum family (Amoxcillin) which are generally used for inhibition of bio-synthesis of cell wall become ineffective due to evolution of antibiotic resistance by the bacteria. Antibiotic resistance occurs when an antibiotic has lost its ability to effectively control or kill bacterial growth. As a result, the bacteria becomes “resistant” and continue to multiply for the generation of robust pathogenic bacteria in spite of drug administration. This is due to the release of another type of enzyme by the resistant bacteria which binds with the active antibiotic or drug making it ineffective. Hence, another type of drug (Clauvanic acid) is combined to resist the activity of drug hydrolyzing enzyme so that the initial drug can act effectively. Hence a combination of drug therapy is applied to cure the bacterial diseases successfully. We developed a mathematical model based on the bacterial enzyme and bacterial cell wall proliferation mechanism and showed how we can reduce the bacterial infection in the resistant cases with application of combination drugs (Amoxcillin and Clauvanic acid) to restore normal health. Based on the enzymatic activity and individual drug dynamics we studied the overall system under the single drug and combinational drug administration through our formulated model analysis. We also demonstrated the different dosing time interval and dosing concentration to evaluate the optimized drug administration for arresting the cell wall formation completely. Sensitivity of the different kinetic rate constant also has been performed with subject to drug hydrolyzing enzyme. Our analytical and numerical studies also confirm the efficiency of the combinational drug treatment compared to single drug treatment being more effective in drug resistant cases providing recovery from bacterial disease.