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Abstract
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.
Highlights
There are many epidemic diseases in the swine population such as swine fever disease, foot and mouth disease and Aujesky’s disease
One of the most devastating diseases is porcine reproductive and respiratory syndrome (PRRS), which was first reported in the United States in [ ]
We introduce the traveling wave coordinate ξ = x – ct, where c is the constant speed at which the wave is assumed to be moving
Summary
There are many epidemic diseases in the swine population such as swine fever disease, foot and mouth disease and Aujesky’s disease. In , Pitkin et al [ ] developed a model of a swine production region and demonstrated the airborne spread of PRRS virus over a distance representative of building separation in commercial agriculture They quantified infectious virus in bio-aerosols and evaluated a method of biosecurity designed to reduce this risk. In , Chang and Manoranjan [ ] studied a contaminant transport model with a cubic sorption isotherm and presented the method for finding exact solutions, which is a traveling wave front, by using traveling wave coordinate to obtain a coupled system of ordinary differential equations that can be reduced to a single second-order differential equation. Based on the above works, we modify the reaction-diffusion equations which have been often used to describe the spread of infection to incorporate both time and spatial dimensions as well as the decline of infectiousness with time, arriving at the following model system:.
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