Determining the effects of transplacental and direct transmission on the probability of persistence in a bluetongue virus model in temperate and tropical regions

Results in Applied Mathematics

Joseph Y.T. Mugisha¹  Obiora C. Collins²  Kevin J. Duffy³  Francis Mugabi³ 

[1] Corresponding author.;Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda;Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban, 4000, South Africa;

关键词: Bluetongue virus;    Transplacental transmission;    Direct transmission;    Persistence;    Overwintering;   

DOI  :  

来源: DOAJ

【 摘 要 】

Bluetongue virus (BTV) is an important concern for the ruminant livestock industry owing to its high morbidity rate. It is mainly transmitted by a midge to a host (vectorial transmission) but even though its replication in the midge ceases during winter in temperate countries, outbreaks re-emerge in the next season. Transplacental and direct transmission have been proposed as mechanisms that facilitate its overwintering (persistence), but to date, their effects on the probability of BTV persistence are not fully understood. In addition, the effects of these mechanisms on the probability of BTV persistence in tropical regions where the virus is endemic are not clear. A deterministic model that accounts for BTV transmission to cattle is formulated and analysed. Using the next generation approach the basic reproduction number (R0) is determined. When R0<1, the model exhibits a backward bifurcation indicating that the virus persists. When R0>1, a continuous-time Markov chain (CTMC) model derived from the deterministic model is used to estimate the probability of BTV persistence. By approximating the CTMC model with a multitype Galton–Watson branching process, it is shown that both mechanisms can have a high and a low positive effect on the probability of BTV persistence in temperate and tropical regions, respectively. These results indicate the importance of transplacental and direct transmission for BTV persistence in temperate regions, but not in tropical regions where vectorial transmission is the dominant mechanism as expected.

【 授权许可】

Unknown