Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A game-theoretic approach to diagnostic test adoption and disease control in livestock
Rodney Beard

Last modified: 2014-03-31


We develop a stochastic game model for the adoption of a newly available diagnostic test for sheep scab (psoroptes ovis), a serious disease of sheep that is endemic in the UK and increasing in incidence. Farmers face the decision to adopt a testing and treatment technology or to choose the status quo. Adopting the test incurs a cost to the farmer, but by allowing prompt treatment of the animals, it reduces the farmer’s production losses. The model is a bio-economic model incorporating both economic payoffs and disease population dynamics. Disease may spread between farms so a neighbour’s decisions and infection status impact the risk of infection and a farmer’s payoffs. Test adoption therefore involves a strategic decision. The model builds on existing literature in mathematical epidemiology by Abakuks and others, employing stochastic dynamic programming to study disease control, but extends these approaches to a game theoretic setting.  The model is calibrated against Scottish farm data and for known parameters of the disease available from the scientific literature on sheep scab.  The model is solved using the non-linear programming approach of Filar and Vrieze, which extends the Mangasarian and Stone algorithm for N-player non-cooperative games to stochastic games. Our results provide insight into the conditions, in particular the cost of the test, under which farmers would adopt a diagnostic test and into the conditions under which the disease might be controlled.


stochastic games; bio-economic modeling; economic epidemiology; parasitic diseases