Resilience of a beef cow-calf farming system to variations in demographic parameters.

Beef cow-calf farming systems are assumed to be resilient to biological disturbances that induce variations in herd demography; however, this hypothesis has not been fully investigated to date. Modeling is an interesting approach to study farming system resilience and to evaluate the impact of biological disturbances, taking into account interactions between system components, including biological variability and management practices. Our objective was to evaluate the resilience of beef cow-calf farming systems to variations in fertility and mortality using a modeling approach. We studied the direct effect of variations in demographic parameters on production objectives without explicitly representing the causes of the variations. We developed a stochastic model to represent the population dynamics of a beef cow-calf herd with breeding by natural service and biological processes occurring at the animal level. The model was validated by comparing observed and simulated distributions of the calving-to-calving interval, which were found to be consistent. Resistance was evaluated by the proportion of simulations where the objective in terms of number of weaned calves is reached even when there is a disturbance that persists for 10 yr. Reversibility was evaluated by the time needed to return to the predisturbance production level. Beef cow-calf farming systems did not appear to be resistant to variations in mortality and infertility rates except when increases in the infertility rates were low (0.02 for cows and 0.03 for heifers). Critical situations, consequently, may emerge with regard to farm production if management practices are not adapted. Reversibility was observed for disturbances that persist for up to 5 yr. However, the system needed 2 to 3 yr to recover its predisturbance production level and up to 4 yr after an increase in cow infertility of 0.12.

Illustration of some limits of the Markov assumption for transition between groups in models of spread of an infectious pathogen in a structured herd.

In epidemic models concerning a structured population, sojourn times in a group are usually described by an exponential distribution. For livestock populations, realistic distributions may be preferred for group changes (e.g. depending on sojourn time). We illustrated the effect on pathogen spread of the use of an exponential distribution, instead of the true distribution of the transition time, between groups for a population separated into two groups (youngstock, adults) when this true distribution is a triangular one. Concerning the epidemic process, two assumptions were defined: one type of excreting animal (SIR model), and two types of excreting animals (transiently or persistently infected animals). The study was conducted with two indirect-transmission levels between groups. Among the adults, the epidemic size and the last infection time were significantly different. For persistence, epidemic sizes (in the entire population and in youngstock) and first infection time, results varied according to models (excretion assumption, indirect-transmission level).

Influence of the transmission function on a simulated pathogen spread within a population.

The mathematical function for the horizontal transmission of a pathogen is a driving force of epidemiological models. This paper aims at studying the influence of different transmission functions on a simulated pathogen spread. These functions were chosen in the literature and their biological relevance is discussed. A theoretical SIR (Susceptible-Infectious-Recovered) model was used to study the effect of the function used on simulated results. With a constant total population size, different equilibrium values for the number of infectious (NI) were reached, depending on the transmission function used. With an increasing population size, the transmission functions could be assimilated to either density-dependent (DD), where an equilibrium was obtained, or frequency-dependent (FD), with an exponential increase in NI. An analytical study corroborated the simulated results. As a conclusion, the choice between the different transmission functions, particularly between DD and FD, must be carefully considered for a varying population size.

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

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.

Simulation study to assess the efficiency of a test-and-cull scheme to control the spread of the bovine viral-diarrhoea virus in a dairy herd.

To control the spread of bovine viral-diarrhoea virus (BVDV), test-and-cull schemes have been used in Scandinavian countries, with success, when combined with strict control of new animal introductions into herds. In situations where BVDV reintroduction is likely to occur, it is necessary to assess precisely the expected efficiency of test-and-cull schemes. The objective of this study was to compare, by simulation, the persistence and consequences of BVDV infection in a fully susceptible dairy herd with either a test-and-cull scheme or no control action. We used a stochastic individual-based model representing the herd structure as groups of animals, herd dynamics, the contact structure within the herd and virus transmission. After an initial introduction of the virus into a fully susceptible herd, the frequency of purchases of animals that introduced the virus was simulated as high, intermediate or null. Virus persistence and epidemic size (total number of animals infected) were simulated over 10 years. The test-and-cull reduced the epidemic size and the number of days the virus was present except in herds with complete prevention of contact between groups of animals. Where no virus was reintroduced, virus persistence did not exceed 6 years with a test-and-cull scheme, whereas the virus was still present 10 years after the virus introduction in some replications with no control action (<2%). Where frequent purchases were made that led to virus introduction (6 within 10 years), with an intermediate virus transmission between groups, the probability of virus persistence 10 years after the first virus introduction fell from 31% to 8% with the test-and-cull scheme (compared to the do-nothing strategy). Within the newly infected herd, the test-and-cull scheme had no effect, on inspection, on the number of PI births, embryonic deaths or abortions over 10 years. Given this, the economic efficiency of the test-and-cull scheme should be further investigated.

Stochastic dynamics of immunity in small populations: a general framework.

Assessment of immunological status is a powerful tool in the surveillance and control of infectious pathogens in livestock and human populations. The distribution of immunity levels in the population provides information on time and age dependent transmission. A stochastic model is developed for a livestock population which relates the dynamics of the distribution of immunity levels at the population level to those of pathogen transmission. A general model with K immunity level categories is first proposed, taking into account the increase of the immunity level due to an infection or a re-exposure, the decrease of the immunity level with time since infection or exposure, and the effect of immunity level on the susceptibility and the infectivity of individuals. Numerical results are presented in the particular cases with K=2 and K=3 immunity level categories. We demonstrate that for a given distribution of the immunity levels at the population level, the model can be used to identify quantities such as most likely periods of time since introduction of infection. We discuss this approach in relation to analysis of serological data.

Epidemiological modeling in a branching population. Particular case of a general SIS model with two age classes.

This paper covers the elaboration of a general class of multitype branching processes for modeling in a branching population, the evolution of a disease with horizontal and vertical transmissions. When the size of the population may tend to infinity, normalization must be carried out. As the initial size tends to infinity, the normalized model converges a.s. to a dynamical system the solution of which is the probability law of the state of health for an individual ancestors line. The focal point of this study concerns the transient and asymptotical behaviors of a SIS model with two age classes in a branching population. We will compare the asymptotical probability of extinction on the scale of a finite population and on the scale of an individual in an infinite population: when the rates of transmission are small compared to the rate of renewing the population of susceptibles, the two models lead to a.s. extinction, giving consistent results, which no longer applies to the opposite situation of important transmissions. In that case the size of the population plays a crucial role in the spreading of the disease.