A data-driven individual-based model of infectious disease in livestock operation: A validation study for paratuberculosis

Abstract

Chronic livestock diseases cause large financial loss and affect animal health and welfare. Controlling these diseases mostly requires precise information on both individual animal and population dynamics to inform the farmer's decisions, but even successful control programmes do by no means assure elimination. Mathematical models provide opportunities to test different control and elimination options rather than implementing them in real herds, but these models require robust parameter estimation and validation. Fitting these models to data is a difficult task due to heterogeneities in livestock processes. In this paper, we develop an infectious disease modeling framework for a livestock disease (paratuberculosis) that is caused by Mycobacterium avium subsp. paratuberculosis (MAP). Infection with MAP leads to reduced milk production, pregnancy rates, and slaughter value and increased culling rates in cattle and causes significant economic losses to the dairy industry. These economic effects are particularly important motivations in the control and elimination of MAP. In this framework, an individual-based model (IBM) of a dairy herd was built and MAP infection dynamics was integrated. Once the model produced realistic dynamics of MAP infection, we implemented an evaluation method by fitting it to data from three dairy herds from the Northeast region of the US. The model fitting exercises used least-squares and parameter space searching methods to obtain the best-fitted values of selected parameters. The best set of parameters were used to model the effect of interventions. The results show that the presented model can complement real herd statistics where the intervention strategies suggest a reduction in MAP prevalence without elimination. Overall, this research not only provides a complete model for MAP infection dynamics in a dairy herd but also offers a method for estimating parameters by fitting IBM models.

Fig 1. A flow diagram of animal movements among infection categories for the adult, calves, and heifers within the herd.

Each horizontal gray box classifies the animals according to their initial age group. The green and red boxes define the susceptible and infected states, respectively, for each animal in the three age categories. The probabilities of exit at each time point from susceptible to latent, latent to low shedding and low shedding to high shedding animals are s₁, h₁, and y₁, respectively. Vertical transmission probabilities from latent, low shedding and high shedding animals are V_h, V_y1, and V_y2, respectively. Horizontal transmission probabilities to calves from low shedding and high shedding animals are H_y1 and H_y2, respectively. The probability an animal gets infected by the environment is β_environment. Calf-to-calf and heifer-to-heifer transmission probabilities are C_inf and Y_inf, respectively. Stochastic death/sale probabilities for adult, calves, and heifers are μ_a, μ_c, and μ_h, respectively. μ is the replacement animals coming from heifer compartment upon completion of two years.

Fig 2. The comparison of observed and model predicted milk yield distribution for 1% simulation using best-fit parameters for the milk yield.

In the box plot, the bottom and top end of the bars are minimum and maximum values respectively, the top of the box is the 75th percentile, the bottom of the box is the 25th percentile, and the horizontal line within the box is median; outliers are presented as a solid black circle and the density of the milk yield is presented by the width of the violin.

Fig 3. The fitting results of three in silico herds A (top), B (middle), and C (bottom) compared to the observed apparent prevalence for 7 years by biannual sampling.

The shaded region shows the 95% confidence interval of the best 1% simulation runs.

Fig 4. The apparent prevalence during the pre- and post-intervention period during the simulation of three in silico herds with two control strategies.

Control I: culling red animals immediately and control II: culling only red animal with a delay of 305 days in milk. The two control measures are simulated in separating runs of the three in silico herds.