Abstract
Bovine viral diarrhea (BVD) is a disease in cattle with complex transmission dynamics that causes substantial economic losses and affects animal welfare. The infection can be transient or persistent. The mostly asymptomatic persistently infected hosts are the main source for transmission of the virus. This characteristic makes it difficult to control the spreading of BVD. We develop a deterministic compartmental model for the spreading dynamics of BVD within a herd and derive the basic reproduction number. This epidemiological quantity indicates that identification and removal of persistently infected animals is a successful control strategy if the transmission rate of transiently infected animals is small. Removing persistently infected animals from the herd at birth results in recurrent outbreaks with decreasing peak prevalence. We propose a stochastic version of the compartmental model that includes stochasticity in the transmission parameters. This stochasticity leads to sustained oscillations in cases where the deterministic model predicts oscillations with decreasing amplitude. The results provide useful information for the design of control strategies.
Highlights
Bovine viral diarrhea (BVD) is a viral disease that affects cattle and has a significant negative economic impact on the global livestock industry.[1]
We investigate the stochastic effects of our BVD model and the impact they have on the spreading behavior of BVD
We have developed a well posed epidemiological compartmental model that simulates the spreading dynamics within a herd with constant size
Summary
Bovine viral diarrhea (BVD) is a viral disease that affects cattle and has a significant negative economic impact on the global livestock industry.[1]. 2 of Ref. 34 holds: If A is a non-singular M-matrix and f ≥ 0, the disease-free equilibrium is globally asymptotically stable. We conclude that in the case of ρ(FV−1) < 1 the Z-matrix A is a non-singular M-matrix and the disease-free equilibrium is globally asymptotically stable. The peak prevalence of the subsequent outbreak is reduced due to the presence of recovered animals at the beginning of the outbreak This behavior results in a damped oscillations of recurrent outbreaks with decreasing peak prevalence, which approaches an endemic equilibrium.
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