OPTIMAL DOSING STRATEGIES AGAINST SUSCEPTIBLE AND RESISTANT BACTERIA

Abstract

Mathematical models can be very useful in determining efficient and successful antibiotic dosing techniques against bacterial infections. There are several challenging issues involved, the presence of drug resistant bacteria being one. Recent rise in antibiotic resistant strains of bacteria is a grave public health hazard, hence there is a need to develop dosing protocols taking into account the presence of these resistant strains. In this study, we consider a model for antibiotic treatment of a bacterial infection where the bacteria are divided into two sub-populations: susceptible and resistant. The mechanism of acquisition of resistance by the susceptible bacteria considered is via the process of conjugation. We find the steady-state solutions under an antibiotic protocol of discrete periodic doses and analyze their stability. We also prove an extension of a result that pertains to the persistence of bacteria. In addition, we perform the bifurcation analysis under this dosing protocol and show that bi-stability exists for the bacterial population. Furthermore, efficient treatment strategies are devised that ensure bacterial elimination while minimizing the quantity of antibiotic used. Such treatments are necessary to decrease the chances of further development of resistance in bacteria and to minimize the overall treatment cost. We consider the cases of varying antibiotic costs, different initial bacterial densities and bacterial attachment to solid surfaces, and obtain the optimal strategies for all the cases. The results show that the optimal treatments ensure disinfection for a wide range of scenarios.