Hosts are not always successful at controlling and eliminating a pathogen. Insects can sustain persistent bacterial infections, but the conditions under which clearance occurs are not well understood. Here we asked what role pathogen virulence and infection dose play in bacterial persistence and clearance in both live and dead flies. We also sought to understand the basis of variation in virulence, by asking if it is due to differences in exploitation, i.e., how well bacteria can replicate inside the host, or due to differences in the amount of damage per parasite inflicted on the host, i.e., per parasite pathogenicity (PPP), and how exploitation and PPP relate to clearance probability. We injected Drosophila melanogaster with one of four bacterial species, which we hypothesised should cover a spectrum of virulence: Enterobacter cloacae, Providencia burhodogranariea, Lactococcus lactis and Pseudomonas entomophila. The injection doses spanned four orders of magnitude, and survival was followed to estimate virulence. Bacterial load was quantified in live flies during the acute (1-4 days) and chronic (7-35 days) phases of infection, and we assayed infection status of flies that had died up to ten weeks post infection. We show that sustained persistent infection and clearance are both possible outcomes for bacterial species across a range of virulence. Bacteria of all species could persist inside the host for at least 75 days, and injection dose partly predicts within species variation in clearance. Our decomposition of virulence showed that species differences in bacterial virulence could be explained by a combination of variation in both exploitation and PPP, and that higher exploitation leads to lower bacterial clearance. These results indicate that bacterial infections in insects persist for considerably longer than previously thought, and that decomposing virulence into exploitation and PPP will help us to understand more about the factors affecting infection clearance.

1Efficacy assessment of antimicrobials is essential, both to determine the best 2 clinical use of the antimicrobial and as input for predictive mathematical mod-3 eling. The pharmacodynamic (PD) function is a tool to describe antimicrobial 4 efficacy and can be seen as an extension of the commonly used MIC. While the 5 PD function describes the efficacy of a given dose of antimicrobials, it is based 6 on one bacterial inoculum size only. Therefore, the PD function does not inform 7 us about the change in efficacy due to changes in the inoculum size, also known 8 as the inoculum effect. Here, we used mathematical modeling to quantify the 9 inoculum effect in terms of PD parameters. In particular, we used the multi-hit 10 model that describes the mechanism of action of antimicrobials: When a cer-11 tain number of antimicrobial molecules have hit a bacterial cell, it dies. This 12 framework allowed us to examine the effect of reversible binding and enzymatic 13 degradation of antimicrobials on the pharmacodynamics. A change in bacte-14 rial inoculum size resulted in a change of the PD parameter A 50 , M IC P D , and 15 therefore κ due to reversible binding. We determined an extended PD function 16 that captured the inoculum effect as change in the PD parameters. When we 17 allowed for degradation of antimicrobials by bacterial enzymes, the inoculum 18 effect was intensified. The extended PD function could mimic long term pop-19 ulation dynamics based on the multi-hit model with reversible binding only, 20 1 but deviated from long-term predictions based on a multi-hit model including 21 degradation. We then used the multi-hit framework to estimate outcomes of 22 competition experiments with a sensitive and resistant strain and compared it 23 to predictions of the PD function. When we do not take the inoculum effect into 24 account, our simulations underestimated the ability of the sensitive population 25 to survive for a given PK regime and the competitiveness of the sensitive strain 26 against the resistant strain. Our work emphasizes that the PD function -and 27 in general any efficacy measure -should, at least, include information about 28 the inoculum size and, ideally, account for the inoculum effect. 29 Introduction 30 Efficacy of antimicrobials against bacteria is quantified using time-kill curves 31 and is subsequently captured in so-called pharmacodynamic (PD) functions, 32 also known as E max and Zhi models (1 -3 ). A time-kill curve captures how 33 a bacterial population changes over time in presence of a given concentration 34 of an antimicrobial (fig. 1a). During exponential growth, time-kill curves are 35 approximately linear on a logarithmic scale. Thus, the slopes of these log-linear 36 time-kill curves describe the change of the bacterial population over time and 37 are a direct measure of the bacterial net growth rate. The PD function returns 38 the net growth rate for any given antimicrobial concentration. The parameters 39 of the PD function are estimated based on several time-kill curves with the...

Pathogens that are resistant against drug treatment are widely observed. In contrast, pathogens that escape the immune response elicited upon vaccination are rare. Previous studies showed that the prophylactic character of vaccines, the multiplicity of epitopes to which the immune system responds within a host, and their diversity between hosts delay the evolution and emergence of escape mutants in a vaccinated population. By extending previous mathematical models, we find that, depending on the cost of the escape mutations, there even exist critical levels of immune response diversity that completely prevent vaccine escape. Furthermore, to quantify the potential for vaccine escape below these critical levels, we propose a concept of escape depth which measures the fraction of escape mutants that can spread in a vaccinated population. Determining this escape depth for a vaccine could help to predict its sustainability in the face of pathogen evolution.