On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Small-plasmid-mediated antibiotic resistance is enhanced by increases in plasmid copy number and bacterial fitness

Plasmids play a key role in the horizontal spread of antibiotic resistance determinants among bacterial pathogens. When an antibiotic resistance plasmid arrives in a new bacterial host, it produces a fitness cost, causing a competitive disadvantage for the plasmid-bearing bacterium in the absence of antibiotics. On the other hand, in the presence of antibiotics, the plasmid promotes the survival of the clone. The adaptations experienced by plasmid and bacterium in the presence of antibiotics during the first generations of coexistence will be crucial for the progress of the infection and the maintenance of plasmid-mediated resistance once the treatment is over. Here we developed a model system using the human pathogen Haemophilus influenzae carrying the small plasmid pB1000 conferring resistance to β-lactam antibiotics to investigate host and plasmid adaptations in the course of a simulated ampicillin therapy. Our results proved that plasmid-bearing clones compensated for the fitness disadvantage during the first 100 generations of plasmid-host adaptation. In addition, ampicillin treatment was associated with an increase in pB1000 copy number. The augmentation in both bacterial fitness and plasmid copy number gave rise to H. influenzae populations with higher ampicillin resistance levels. In conclusion, we show here that the modulations in bacterial fitness and plasmid copy number help a plasmid-bearing bacterium to adapt during antibiotic therapy, promoting both the survival of the host and the spread of the plasmid.