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.

Prevalence of Escherichia coli Virulence Genes in Patients with Diarrhea and a Subpopulation of Healthy Volunteers in Madrid, Spain

Etiological diagnosis of diarrheal diseases may be complicated by their multi-factorial nature. In addition, Escherichia coli strains present in the gut can occasionally harbor VGs without causing disease, which complicates the assessment of their clinical significance in particular. The aim of this study was to detect and quantify nine VGs (stx1, stx2, eae, aggR, ehxA, invA, est and elt) typically present in five E. coli enteric pathotypes (EHEC, ETEC, EPEC, EAEC and EIEC) in fecal samples collected from 49 patients with acute diarrhea and 32 healthy controls from Madrid, Spain. In addition, the presence of four serotype-related genes (wzxO104 and fliCH4, rbfO157 and fliCH7) was also determined. Presence of target genes was assessed using a quantitative real-time PCR assay previously developed, and the association of presence and burden of VGs with clinical disease and/or other risk factors was explored. Prevalence of ehxA (typically associated with STEC and EPEC), invA (EIEC) and the rbfO157+fliCH7 (STEC and/or STEC/EAEC) combination were significantly (p<0.02) higher in the diarrheic group, while the wzxO104+fliCH4 combination was significantly (p=0.014) more prevalent in the control group. On the other hand, eae was detected in more than 90% of the individuals in both patient and control populations, and it was not associated with bfpA, suggesting the absence of typical EPEC. No significant differences in the quantitative values were detected for any VG among study groups, but the difference in the load of aggR (EAEC) and invA in the patients with respect to the controls was close to the significance, suggesting a potential role of these VGs in the clinical signs observed when they are present at high levels.