A model for porcine reproductive and respiratory syndrome with time-dependent infection rate: traveling wave solution

Porcine reproductive and respiratory syndrome (PRRS) gives rise to reproductive disorders in sows and problem with respiratory system in piglets and young pigs. This disease creates serious economic losses to major pork producing countries. The disease, which is characterized by high morbidity and significant mortality, combined with its potential for rapid spread, can devastate the pig industries of the affected countries. However, not much is known about the spatial transmission of PRRSV (porcine reproductive and respiratory syndrome virus) in growing pigs. In previous models, the infection rate has been assumed to be constant with time. Experimental studies on specific cases of this viral infection suggest that this assumption might not hold. A structured model for the spread of PRRSV has therefore been constructed, incorporating time and spatial dimensions as well as the decline of infection rate with time. Using the traveling wave coordinate and the modified extended hyperbolic tangent method, we derive analytical solutions to the model system. Stability and phase plane analyses are also carried out in order to gain insights into the spatial spread of PRRS as time progresses.