Disease eradication on large industrial farms.

Many modern farms exhibit all-in-all-out dynamics in which entire cohorts of livestock are removed from a farm before a new cohort is introduced. This industrialization has enabled diseases to spread rapidly within farms. Here we look at one such example, Marek's disease. Marek's disease is an economically important disease of poultry. The disease is transmitted indirectly, enabling the spread of disease between cohorts of chickens who have never come into physical contact. We develop a model which allows us to track the transmission of disease within a barn and between subsequent cohorts of chickens occupying the barn. It is described by a system of impulsive differential equations. We determine the conditions that lead to disease eradication. For a given level of transmission we find that disease eradication is possible if the cohort length is short enough and/or the cohort size is small enough. Marek's disease can also be eradicated from a farm if the cleaning effort between cohorts is large enough. Importantly complete cleaning is not required for eradication and the threshold cleaning effort needed declines as both cohort duration and size decrease.