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

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.

Modeling the spread of porcine reproductive and respiratory syndrome virus (PRRSV) in a swine population: transmission dynamics, immunity information, and optimal control strategies

“…Mathematical modeling has been used as an important tool to help understand the dynamics of infectious diseases among farm animals. However, mathematical models for describing the spread of PRRSV are not numerous [9][10][11][12][13]. Evans et al [9] developed a stochastic model of a farrow-finish heard and found that the persistence of PRRSV increases according to increased herd size, increased contact between different age groups, and increased reintroduction of infectious swines.…”

“…Their results highlighted the importance of maintaining internal biosecurity practices as control strategies may not prevent the infection from spreading among the swine population. Suksamran et al [13] used a two-step parameter-driven Bayesian approach to model the spatio-temporal dynamics of PRRS and demonstrated the importance of pig trade in PRRS transmission in the US. To the best of our knowledge, none of preceding studies have addressed the effects of optimal vaccination strategies and immunity information.…”

Pig herd management and infection transmission dynamics: a challenge for modellers

“…Previous models represented the impact of management practices on the transmission dynamics, to assess how husbandry practices could be modified to better handle health issues at the herd level (Cador et al, 2016;Suksamran et al, 2017) Clinical aspects and their potential consequences, in terms of management and infection dynamics, were nevertheless rarely considered. PRRS virus is recognized as a major economic burden for swine producers, inducing huge loss due to growth retardation, abortions or reproduction failures, birth of stillborn fetuses or weak-condition piglets (Charpin et al, 2012;Le Coz, 2007;Renken et al, 2021).…”

Pig herd management and infection transmission dynamics: a challenge for modellers

“…This was recently illustrated with a model representing the transmission of a swine influenza A virus in a pig herds with different spatial configurationsSicard et al (2022). Previous models represented the impact of management practices on the transmission dynamics, to assess how husbandry practices could be modified to better handle health issues at the herd levelCador et al (2016);Suksamran et al (2017) Clinical aspects and their potential consequences, in terms of management and infection dynamics, were nevertheless rarely considered. PRRS virus is recognized as a major economic burden for swine producers, inducing huge loss due to growth retardation, abortions or reproduction failures, birth of stillborn fetuses or weak-condition piglets LeCoz (2007);Renken et al (2021);Charpin et al (2012).…”