Microbiologic Background and Hypotheses

β-lactam antibiotics, such as penicillin G, bind to PBPs in the bacterial cell wall. In both S. pneumoniae and N. meningitidis, the main mechanism of penicillin G resistance is mediated by the alteration of these penicillin target enzymes. The genetic events leading to reduced affinity for penicillin G are point mutations. These mutations confer slight increases in resistance and acquisition by transformation from other commensal species of the pharynx of intragenic sequences. This process leads to the synthesis of mosaic PBPs and confers higher levels of resistance (14–16).

By convention, the decrease in susceptibility to penicillin G is defined by an MIC >0.1 µg/mL and resistance by an MIC >2 µg/mL (5). In the laboratory, the MIC is determined by successive dilutions and presented on a log₂ scale. However, genetic events may lead to a difference of less than a log₂ unity between two MICs; for example, an increase from 0.04 to 0.06 µg/mL was reported by Hakenbeck et al. (17).

To take this progressive evolution into account, we theorized that each bacterial generation provided an opportunity for an increase in resistance. More precisely, we randomly selected for each new generation an increase in the bacterial MIC, defined as d, according to the seminormal law:

f_Δ(d) =

With this formulation, a high probability exists that either no genetic event occurs or that such an event will only convey a small increase in MIC, although an increase to any resistance level as a result of one genetic event remains possible. In particular, a detectable genetic event, that is, an event conveying an increase in the MIC of more than one log₂ unity, will occur with a frequency of 10^-7, which is consistent with previous in vitro observations (18).

Bacteria colonize human hosts in large quantities. Therefore, even though the occurrence of genetic events remains possible for each bacterium, competition makes it unlikely that a host’s bacterial population will suddenly be replaced by genetically altered strains. However, in the presence of antibiotic treatment, selective killing of the susceptible bacterial population may allow replacement by a less susceptible population. We therefore assumed that genetic events leading to effective bacterial replacement were only possible in treated persons. We represented the entire bacterial population of a colonized host by one MIC.

Model Description

Figure 1

Figure 1. Model structure of the emergence and transmission of penicillin G resistance in Streptococcus pneumoniae and Neisseria meningitidis.

To reproduce the selection and spread of resistant bacteria in the community through interhuman transmission, we divided the human population under study into several groups or “compartments” (Figure 1). Each compartment was composed of persons with the same characteristics regarding colonization and antibiotic treatment. The colonized compartments were split into several subcompartments according to MIC.

Uncolonized persons are colonized after an infectious contact with colonized persons at rate β. In the absence of antibiotic treatment, the persons are then naturally decolonized after a time 1/λ, regardless of MIC. This period, called the duration of carriage, is followed by a refractory period of duration 1/θ, during which these persons cannot be colonized again.

With antibiotic treatment, bacterial colonization is cleared with a probability σ. In persons in whom colonization is not eliminated, bacteria with a mutation towards a higher MIC may replace the original strains.

Finally, progression from the untreated category to the treated category occurs at the start of an antimicrobial treatment, which takes place with a frequency α, and the return to the untreated category occurs when the treatment comes to an end, after an average duration of 1/γ

Parameters

The mean duration of carriage is reportedly 2.2 months for S. pneumoniae and 10 months for N. meningitidis (8,9). Although temporary systemic immunization has occurred after colonization by these bacteria (19), the exact duration of this refractory phase is not clear. We chose a duration of 2 weeks and investigated the range from 4 days to 2 months.

In studies of treatment patterns in France, the average duration of antibiotic treatment was 8 days (20,21) and the frequency of treatment changed with age. Young children may be treated several times a year with penicillin G, while healthy adults are only treated once every 4 to 5 years on average. The colonization frequency also changes with age, corresponding to colonization peaks in children for S. pneumoniae and in young adults for N. meningitidis. In our model, the population was not structured by age, but we wanted to reflect these heterogeneities. We therefore calculated effective treatment frequencies by weighting observed frequencies of treatment with probabilities of colonization according to age, which led us to study the effects of one treatment every 2 years for S. pneumoniae and one treatment every 3 years for N. meningitidis.

We assumed that, with treatment, all bacteria were submitted to the same concentration of antibiotics; therefore, we considered the probability of decolonization after treatment as a function of MIC only. A commonly used model for the effect of an antibiotic on bacteria with a given MIC according to drug concentration is the saturating model (13). By analogy, we expressed the effect of a given antibiotic concentration in terms of the probability of nondecolonization as a function of the MIC m, by

σ(m) = .

We chose a constant infectious contact rate β in the absence of treatment. We adjusted the value of β so that the predicted proportion of carriers matched the observed values of 45% in the case of S. pneumoniae (10) and of 10% in the case of N. meningitidis (9). This gave β=0.23 weeks^-1 person^-1 for S. pneumoniae and β=0.026 weeks^-1 person^-1 for N. meningitidis. However, we assumed that a treated person had a better chance of being colonized after a contact than an untreated person if the bacteria involved had a high MIC and that colonization was less probable with susceptible bacteria. We also adopted the following sigmoidal function of the MIC m for the contact rate in the presence of treatment

β’(m) = .

The values of the model’s parameters are specified in Table 1. Model simulations are described in the Appendix.

S. pneumoniae Historical Data in France

To validate the predictions of the model for changes in resistance, we used data on S. pneumoniae reported to the French National Reference Center (NRC) for pneumococci (22). In short, 40–50 centers throughout France collected and sent S. pneumoniae strains to the NRC. Each year approximately 2,000 strains were typed and evaluated for susceptibility to various antibiotics. We used data from 1987 to 1997 and looked at changes in the distribution of penicillin G MICs over time.

Predictions for S. pneumoniae

Emergence

Figure 2

Figure 2. (a) Time to emergence of the first Streptococcus pneumoniae with a given MIC (full line) and time required for 20% of the bacterial population to reach this MIC (dotted line), starting...

By applying the model to a population in which all the pneumococci were initially susceptible to penicillin G (MIC < 0.06 µg/mL), we determined the time of emergence of the first strains with decreased susceptibility (MIC = 0.125, 0.25, 0.5, and 1 µg/mL), as well as the first resistant strains (MIC = 2 µg/mL) and highly resistant strains (MIC = 4 µg/mL). The model also provided information on the variability of these emergence times (Figure 2a). In particular, the model predicted the emergence of high resistance levels (MIC >2 µg/mL) after approximately 20 years of antibiotic use.

At low resistance levels, the mean time to emergence depended strongly on MIC. At higher levels (MIC >1 µg/mL), however, it reached a plateau, as the lag between the emergence of two successive levels decreased. The variability of these estimated times to emergence was marked, ranging from 10 to 30 years when starting from the same situation for the emergence of a strain with MIC 2 µg/mL.

We sought to clarify the relationship between the time required for a strain with a given MIC to be selected and the time in which the strain spreads to a large portion of the population. We determined the time at which 20% of the colonized population would be carrying strains with MIC levels ranging from >0.125 to 4 µg/mL (Figure 2a). This time appeared to depend very little on the MIC, even at low resistance levels, in contrast to the time to emergence, which began with a large increase with MIC. However, both times displayed comparable variability (data not shown).

Transmission

We applied the model to a population in which resistance had already emerged, so that most pneumococcal strains were still susceptible to penicillin G, but some strains had high MICs. This pattern corresponds to the situation in France around 1987 (22). Figure 2b illustrates the model’s predictions for the evolution with distribution time of pneumococcal strains according to their MIC. In particular, after a few years, this distribution acquired a bimodal shape, with a peak for susceptible bacteria and another for resistant bacteria.

Figure 2c shows the evolution of pneumococcal resistance to penicillin G during 1987 to 1997, as observed by the French National Reference Center for Pneumococci (4). In 1997, the distribution of resistance levels, which was initially unimodal, exhibited a bimodal shape, with a peak for susceptible bacteria and another for resistant bacteria. These levels are consistent with the model’s predictions (Figure 2b).

Predictions for N. meningitidis

Figure 3

Figure 3. Simulated changes with time in the distribution of resistance levels in the meningococcal population, starting from a situation close to that of France in 2001, under (a) constant antibiotic treatment conditions...

With approximately 30% of strains with reduced susceptibility to penicillin G, we used the same model to predict changes in the distribution of meningococcal MIC levels. Meningococcal resistance seemed to increase in the same way as pneumococcal resistance and also exhibited a bimodal distribution of MIC levels (Figure 3a). However, change was slower in this case because of reduced frequency of treatment in the population concerned and reduced transmissibility.

We studied a situation in which intervention would reduce the frequency of treatment by half (Figure 3b). Even under this reduced antibiotic pressure, high levels of resistance eventually appeared but with a delay of approximately 15 years.