Hepatitis E virus (HEV) can cause enterically-transmitted hepatitis in humans. The zoonotic nature of Hepatitis E infections has been established in industrialized areas and domestic pigs are considered as the main reservoir. The dynamics of transmission in pig herds therefore needs to be understood to reduce the prevalence of viremic pigs at slaughter and prevent contaminated pig products from entering the food chain. An experimental trial was carried out to study the main characteristics of HEV transmission between orally inoculated pigs and naïve animals. A mathematical model was used to investigate three transmission routes, namely direct contact between pigs and two environmental components to represent within-and between-group oro-fecal transmission. A large inter-individual variability was observed in response to infection with an average latent period lasting 6.9 days (5.8; 7.9) in inoculated animals and an average infectious period of 9.7 days (8.2; 11.2). Our results show that direct transmission alone, with a partial reproduction number of 1.41 (0.21; 3.02), can be considered as a factor of persistence of infection within a population. However, the quantity of virus present in the environment was found to play an essential role in the transmission process strongly influencing the probability of infection with a within pen transmission rate estimated to 2 ⋅ 10− 6 g ge − 1 d − 1(1 ⋅ 10− 7; 7 ⋅ 10− 6). Between-pen environmental transmission occurred to a lesser extent (transmission rate: 7 ⋅ 10− 8 g ge − 1 d − 1(5 ⋅ 10− 9; 3 ⋅ 10− 7) but could further generate a within-group process. The combination of these transmission routes could explain the persistence and high prevalence of HEV in pig populations.

The discontinuous Galerkin method is highly flexible for handling complex meshes. One of the challenges of the method lies in the calculation of the coefficients of the elementary matrices. Indeed, these coefficients involve integrals of polynomials over the cells, and as soon as these cells have a complex shape, the integration becomes difficult. In this paper, we focus on how to perform such integration by reducing volume integrals over a cell to line integrals along the edges of the cell. In some cases, the integration can be done exactly, and in others, the line integration can be performed using quadrature formulas. We will provide a recipe, for example, in the case where the cell is an arbitrary polyhedron with flat faces, to compute the integral of a polynomial exactly. However, the method we propose also allows for the calculation of the integral of a function over a polyhedron with curved surfaces.