8Antibiotics are the major tool for treating bacterial infections. In the case of acute bacterial infections, 9 which last for several days, a typical recommended treatment is 7-14 days long. Because of the variety 10 of bacterial infections humans are exposed to, for many infections the duration of antibiotic treatment 11 has not been tested in randomized clinical trials. Recently, the necessity of a relatively long antibiotic 12 treatment has been questioned, including with the use of mathematical models suggesting that longer 13 treatment may in fact result in poorer outcomes, for example, in increased antibiotic resistance. Other 14 studies have shown that longer treatment is needed to guarantee bacterial control, lending support to 15 the notion of a definite optimum duration. By using a mathematical model for a generic intracellular 16 bacterial infection, here we show that it is impossible to select for universally optimal treatment duration. 17In particular, short (3 day) or long (7 day) treatments may be both beneficial depending on the time 18 when the treatment is started, on the metric used to define successful treatment, and on the antibiotic 19 efficacy (defined as the antibiotic kill rate). Our results strongly suggest that generic predictions on the 20 optimality of antibiotic treatment duration are unlikely to be practical. Better quantitative understanding 21 of details of actual within-host dynamics of bacterial infections in humans, of pathology generated during 22 the infection, of the bacterial or immune response thresholds at which patients seek treatment, and of how 23 immunity is involved in infection control should be instrumental to meaningfully guide rational therapy.24

Antibiotics are the major tool for treating bacterial infections. Rising antibiotic resistance, however, calls for a better use of antibiotics. While classical recommendations favor long and aggressive treatments, more recent clinical trials advocate for moderate regimens. In this debate, two axes of ‘aggression’ have typically been conflated: treatment intensity (dose) and treatment duration. The third dimension of treatment timing along each individual’s infection course has rarely been addressed. By using a generic mathematical model of bacterial infection controlled by immune response, we examine how the relative effectiveness of antibiotic treatment varies with its timing, duration, and antibiotic kill rate. We show that short or long treatments may both be beneficial depending on treatment onset, the target criterion for success, and on antibiotic efficacy. This results from the dynamic trade-off between immune response build-up and resistance risk in acute, self-limiting infections, and uncertainty relating symptoms to infection variables. We show that in our model early optimal treatments tend to be ‘short and strong’, while late optimal treatments tend to be ‘mild and long’. This suggests a shift in aggression axis depending on timing of treatment. We find that any specific optimal treatment schedule may perform more poorly if evaluated by other criteria, or under different host-specific conditions. Our results suggest that major advances in antibiotic stewardship must come from deeper empirical understanding of bacterial infection processes in individual hosts. To guide rational therapy, mathematical models need to be constrained by data, including a better quantification of personal disease trajectory in humans.

Understanding bacterial infection is challenging because it involves a complex interplay of host, pathogen, and intervention factors. To design successful control measures, mathematical models that quantify such interplay at the level of populations and phenotypes are needed. Here, we study a key aspect of intracellular infection: the interaction dynamics between bacteria and target cells, applicable to pathogens such as Salmonella, E. coli or Listeria monocytogenes. Our mathematical model focuses on the macrophage-bacteria system, implicitly accounting for host immunity, and illustrates three infection scenarios driven by the balance between bacterial growth and death processes. Our analysis reveals critical parameter combinations for the intracellular vs. extracellular fitness advantage of persistent bacteria, and the drivers of overall infection success across acute and persistent regimes. Our results provide quantitative insights on transitions from persistent, to acute, to containment of infection, and suggest biological parameters, such as infected macrophage apoptosis rate and burst size, as suitable intervention targets.