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Abstract
Porcine reproductive and respiratory syndrome virus (PRRSV) causes reproductive failure in sows and respiratory disease in piglets and growing pigs. The disease rapidly spreads in swine populations, making it a serious problem causing great financial losses to the swine industry. However, past mathematical models used to describe the spread of the disease have not yielded sufficient understanding of its spatial transmission. This work has been designed to investigate a mathematical model for the spread of PRRSV considering both time and spatial dimensions as well as the observed decline in infectiousness as time progresses. Moreover, our model incorporates into the dynamics the assumption that some members of the infected population may recover from the disease and become immune. Analytical solutions are derived by using the modified extended hyperbolic tangent method with the introduction of traveling wave coordinate. We also carry out a stability and phase analysis in order to obtain a clearer understanding of how PRRSV spreads spatially through time.
Highlights
Porcine reproductive and respiratory syndrome (PRRS) was first reported in the United States in 1987
Our model incorporates into the dynamics the assumption some members of the infected population may recover from the disease and become immune
The novel insights into the dynamics of PRRS provided by the above analysis may be implied from the above theorem, which states that the equilibrium points of the model system are both unstable, which means that it will not be possible for us to control the infection to remain at a steady level, even though some of the infected swine can recover or are put in isolation
Summary
Porcine reproductive and respiratory syndrome (PRRS) was first reported in the United States in 1987. In 2020, Madapong et al [14] investigated cell-mediated immunity (CMI), IL-10, and the protective efficacy of modified-live porcine reproductive and respiratory syndrome virus (PRRSV) vaccines (MLV) against co-challenge with PRRSV-1 and PRRSV-2 (HP-PRRSV). They divided pigs into seven groups, six of which were intramuscularly vaccinated with MLV, including Porcilis (PRRSV-1 MLV, MSD Animal Health, Boxmeer, The Netherlands), Amervac (PRRSV-1 MLV, Laboratorios Hipra, Girona, Spain), Fostera (PRRSV-2 MLV, Zoetis Inc., Troy Hills, U.S.), Ingelvac PRRS MLV and Ingelvac PRRS ATP (PRRSV-2, Boehringer Ingelheim, Rhein, Germany), Prime Pac PRRS (PRRSV-2 MLV, MSD Animal Health, Boxmeer, The Netherlands) and one of which was unvaccinated.
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