Modeling antibiotic treatment in hospitals: A systematic approach shows benefits of combination therapy over cycling, mixing, and mono-drug therapies

Multiple treatment strategies are available for empiric antibiotic therapy in hospitals, but neither clinical studies nor theoretical investigations have yielded a clear picture when which strategy is optimal and why. Extending earlier work of others and us, we present a mathematical model capturing treatment strategies using two drugs, i.e the multi-drug therapies referred to as cycling, mixing, and combination therapy, as well as monotherapy with either drug. We randomly sample a large parameter space to determine the conditions determining success or failure of these strategies. We find that combination therapy tends to outperform the other treatment strategies. By using linear discriminant analysis and particle swarm optimization, we find that the most important parameters determining success or failure of combination therapy relative to the other treatment strategies are the de novo rate of emergence of double resistance in patients infected with sensitive bacteria and the fitness costs associated with double resistance. The rate at which double resistance is imported into the hospital via patients admitted from the outside community has little influence, as all treatment strategies are affected equally. The parameter sets for which combination therapy fails tend to fall into areas with low biological plausibility as they are characterised by very high rates of de novo emergence of resistance to both drugs compared to a single drug, and the cost of double resistance is considerably smaller than the sum of the costs of single resistance.Author summary: For life-threatening infections, antibiotics need to be administered as soon as possible. Because it takes time to acquire data about the disease causing bacteria, the immediate treatment is often empiric. In particular, there are three treatment strategies discussed in the field of empiric treatment: cycling, mixing, and combination therapy. Despite a number of clinical and theoretical studies, it still remains unclear which treatment strategy best prevents the emergence of resistance and why. To address this controversy, we present a mathematical model capturing both mono- and multi-drug therapies. We sample and analyze a large parameter space to assess the effect of parameters on treatment success, and determine which treatment strategy is the best under which circumstances. Using methods such as linear discriminant analysis and particle swarm optimisation, we find that combination therapy outperforms the other strategies by a large margin for most of the biologically relevant parameter space. We also show that the rate of de novo emergence of double resistance and the costs of resistance mutations are the most important parameters determining whether combination therapy succeeds over the others.