Critical Behavior in a Cellular Automata Animal Disease Transmission Model

Abstract

Using a cellular automata model, we simulate the British Government Policy (BGP) in the 2001 foot and mouth epidemic in Great Britain. When clinical symptoms of the disease appeared on a farm, there is mandatory slaughter (culling) of all livestock on an infected premise (IP). Those farms that neighbor an IP (contiguous premise, CP), are also culled, aka nearest neighbor interaction. Farms where the disease may be prevalent from animal, human, vehicle or airborne transmission (dangerous contact, DC), are additionally culled, aka next-to-nearest neighbor iteractions and lightning factor. The resulting mathematical model possesses a phase transition, whereupon if the physical disease transmission kernel exceeds a critical value, catastrophic loss of animals ensues. The non-local disease transport probability can be as low as .01% per day and the disease can still be in the high mortality phase. We show that the fundamental equation for sustainable disease transport is the criticality equation for neutron fission cascade. Finally, we calculate that the percentage of culled animals that are actually healthy is ~ 30%.