Modeling the Peste des Petits Ruminants (PPR) disease transmission dynamics with impacts of vaccination and restocking in small ruminant population in Amhara region, Ethiopia

Peste des Petits Ruminants (PPR) is a highly contagious transboundary viral disease of small ruminants with significant economic implications caused by the Peste des Petits Ruminants virus. This study employs mathematical modeling to investigate the impact of imperfect PPR vaccines and restocked small ruminants on the transmission dynamics of PPR. A deterministic mathematical model is developed by incorporating vaccinated and restocked subpopulations into the classical SEIR model. The influence of infected animals introduced through restocking on vaccination efficacy in preventing PPR spread is examined. The global dynamics of equilibrium points in the model are analyzed using the Lyapunov-LaSalle invariance principle. Parameter values for numerical simulations are estimated based on monthly PPR data from the Amhara regional state in Ethiopia, obtained from the Ministry of Agriculture. The basic reproduction number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mi>v</mml:mi></mml:mrow> </mml:msub> </mml:math> ) is calculated to assess the level of PPR in the small ruminant population, and sensitivity analysis of parameters is performed on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mi>v</mml:mi></mml:mrow> </mml:msub> </mml:math> . The analytical and numerical results reveal that infected restocked small ruminants significantly facilitate the spread of PPR in the population. Moreover, even with high efficacy vaccination, the system exhibits a unique asymptotically stable endemic equilibrium. These findings emphasize that appropriate vaccination alone is insufficient to control and eradicate PPR in the region. Implementing strict movement restrictions and biosecurity measures are necessary. These findings provide valuable insights for national policymakers in achieving the regional and national targets for PPR eradication by 2027.