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.

Risk of African swine fever introduction into the European Union through transport-associated routes: returning trucks and waste from international ships and planes

BACKGROUND The uncontrolled presence of African swine fever (ASF) in Russian Federation (RF) poses a serious risk to the whole European Union (EU) pig industry. Although trade of pigs and their products is banned since the official notification in June 2007, the potential introduction of ASF virus (ASFV) may occur by other routes, which are very frequent in ASF, and more difficult to control, such as contaminated waste or infected vehicles. This study was intended to estimate the risk of ASFV introduction into the EU through three types of transport routes: returning trucks, waste from international ships and waste from international planes, which will be referred here as transport-associated routes (TAR). Since no detailed and official information was available for these routes, a semi-quantitative model based on the weighted combination of risk factors was developed to estimate the risk of ASFV introduction by TAR. Relative weights for combination of different risk factors as well as validation of the model results were obtained by an expert opinion elicitation. RESULTS Model results indicate that the relative risk for ASFV introduction through TAR in most of the EU countries (16) is low, although some countries, specifically Poland and Lithuania, concentrate high levels of risk, the returning trucks route being the analyzed TAR that currently poses the highest risk for ASFV introduction into the EU. The spatial distribution of the risk of ASFV introduction varies importantly between the analyzed introduction routes. Results also highlight the need to increase the awareness and precautions for ASF prevention, particularly ensuring truck disinfection, to minimize the potential risk of entrance into the EU. CONCLUSIONS This study presents the first assessment of ASF introduction into the EU through TAR. The innovative model developed here could be used in data scarce situations for estimating the relative risk associated to each EU country. This simple methodology provides a rapid and easy to interpret results on risk that may be used for a target and cost-effective allocation of resources to prevent disease introduction.