Review and critical discussion of assumptions and modelling options to study the spread of the bovine viral diarrhoea virus (BVDV) within a cattle herd

Abstract

Relevance of epidemiological models depends on assumptions on the population structure and dynamics, on the biology of the host-parasite interaction, and on mathematical modelling. In this paper we reviewed published models of the bovine viral diarrhoea virus (BVDV) spread within a herd. Modelling options and assumptions on herd dynamics and BVDV transmission were discussed. A cattle herd is a population with a controlled size. Animals are separated into subgroups according to their age or their physiological status inducing heterogeneity of horizontal transmission. Complexity of models results from: (1) horizontal and vertical virus transmission, (2) birth of persistently infected animals, (3) excretion by transiently and persistently infected animals. Areas where there was a lack of knowledge were identified. Assumptions on the force of infection used to model the horizontal virus transmission were presented and discussed. We proposed possible ways of improving models (e.g. force of infection, validation) and essential model features for further BVDV models.

Fig. 1

Comparison of the values of horizontal transmission coefficients considered in six bovine viral diarrhoea virus models: estimation of the epidemic curves obtained in a similar stable population. The cumulative numbers of infected animals were estimated at 1, 3 and 12 months assuming an introduction of one persistently infected animal in a closed group of 100 animals with no excretion by transiently infected animals, no births and no deaths. A precautious approach should be followed when interpreting the figure: the straight lines between data marks are drawn to connect estimates for one transmission coefficient but do not correspond to a linear relationship.

Fig. 2

Probabilities of consequences of an infection by the bovine viral diarrhoea virus during pregnancy used in four selected models for dams and embryo or foetus according to pregnancy stage at infection. An overall probability was estimated by us assuming a uniform distribution of the time of infection during pregnancy for comparison between the different models.