Analyzing the Mathematical Impact of Vaccination in Mitigating Rift Valley Fever Spread among Livestock

Abstract

The persistence mechanisms of Rift Valley fever (RVF), a zoonotic arboviral hemorrhagic fever, are not fully understood and need thorough quantification at both local and broader geographical scales. Rift Valley Fever (RVF) is a viral zoonosis primarily transmitted by mosquitoes, predominantly affecting livestock with the potential to impact humans. The virus has the capacity for rapid spread, posing a potential epidemic threat to both human and the livestock. The transmission dynamics of Rift Valley Fever (RVF) involving mosquitoes and livestock are investigated and analyzed through a compartmental model, with vaccination considered as a control measure. The basic reproduction number ( ) is calculated using the next-generation matrix, indicating that the disease-free equilibrium state is locally asymptotically stable when ( ). This suggests that Rift Valley Fever could be controlled in a livestock population where the reproduction number is below 1, but it becomes endemic when ( ). Sensitivity analysis identifies key parameters for consideration by livestock policy makers and veterinary workers. Numerical simulations offer insightful results to delve deeper into the disease dynamics, considering the efficacy of vaccination and other control measures introduced in the model.