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.

Occurrence of Mycobacterium avium subspecies paratuberculosis across host species and European countries with evidence for transmission between wildlife and domestic ruminants

BACKGROUND Mycobacterium avium subspecies paratuberculosis (Map) causes an infectious chronic enteritis (paratuberculosis or Johne's disease) principally of ruminants. The epidemiology of Map is poorly understood, particularly with respect to the role of wildlife reservoirs and the controversial issue of zoonotic potential (Crohn's disease). Genotypic discrimination of Map isolates is pivotal to descriptive epidemiology and resolving these issues. This study was undertaken to determine the genetic diversity of Map, enhance our understanding of the host range and distribution and assess the potential for interspecies transmission. RESULTS 164 Map isolates from seven European countries representing 19 different host species were genotyped by standardized IS900--restriction fragment length polymorphism (IS900-RFLP), pulsed-field gel electrophoresis (PFGE), amplified fragment length polymorphisms (AFLP) and mycobacterial interspersed repeat unit-variable number tandem repeat (MIRU-VNTR) analyses. Six PstI and 17 BstEII IS900-RFLP, 31 multiplex [SnaBI-SpeI] PFGE profiles and 23 MIRU-VNTR profiles were detected. AFLP gave insufficient discrimination of isolates for meaningful genetic analysis. Point estimates for Simpson's index of diversity calculated for the individual typing techniques were in the range of 0.636 to 0.664 but a combination of all three methods increased the discriminating power to 0.879, sufficient for investigating transmission dynamics. Two predominant strain types were detected across Europe with all three typing techniques. Evidence for interspecies transmission between wildlife and domestic ruminants on the same property was demonstrated in four cases, between wildlife species on the same property in two cases and between different species of domestic livestock on one property. CONCLUSION The results of this study showed that it is necessary to use multiple genotyping techniques targeting different sources of genetic variation to obtain the level of discrimination necessary to investigate transmission dynamics and trace the source of Map infections. Furthermore, the combination of genotyping techniques may depend on the geographical location of the population to be tested. Identical genotypes were obtained from Map isolated from different host species co-habiting on the same property strongly suggesting that interspecies transmission occurs. Interspecies transmission of Map between wildlife species and domestic livestock on the same property provides further evidence to support a role for wildlife reservoirs of infection.