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Optimal control analysis of bluetongue virus transmission in patchy environments connected by host and wind-aided midge movements

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Abstract

Bluetongue, a midge-borne disease of ruminants caused by the bluetongue virus (BTV) can rapidly spread from one region (patch) to another by host and/or midge movements, making its control difficult. A multi-patch deterministic model for BTV is formulated and analysed to evaluate the effectiveness of vaccination, quarantine, insecticide spraying and the use of repellent control strategies in reducing the within and between-patches transmission. By using optimal control theory, the effectiveness of these strategies is established. Incremental cost-effectiveness ratios are calculated to determine the most cost-effective strategy. In a single patch, vaccination, insecticide spraying and the use of repellents are all highly effective in minimising transmission, but the most cost-effective is vaccination. In patches connected by host and midge movements, if any of these controls is applied in a high-risk patch, a disease-free status is achieved in both patches, but if implemented in a low-risk patch, it is not attained in any patch. If hosts and midges move, quarantine has no effect, but for no midge movement, the effect can be large in a low-risk patch if it’s internally imposed.

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Funding

This work is based on research supported in part by the National Research Foundation of South Africa (Grant Number 131604) and an Institute of Systems Science (DUT) Doctoral Scholarship.

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Authors and Affiliations

  1. Institute of Systems Science, Durban University of Technology, P. O. Box 1334, Durban, 4000, South Africa

    Francis Mugabi, Kevin J. Duffy & Obiora C. Collins

  2. Department of Mathematics, Makerere University, P. O. Box 7062, Kampala, Uganda

    Joseph Y. T. Mugisha

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  1. Francis Mugabi
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  2. Kevin J. Duffy
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  4. Obiora C. Collins
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Contributions

FM and JYTM conceptualised the project. FM analysed and drafted the content of the manuscript. KJD, JYTM and OCC supervised and assisted with the research and write up. All authors approved the final manuscript.

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Correspondence to Kevin J. Duffy.

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Mugabi, F., Duffy, K.J., Mugisha, J.Y.T. et al. Optimal control analysis of bluetongue virus transmission in patchy environments connected by host and wind-aided midge movements. J. Appl. Math. Comput. 68, 1949–1978 (2022). https://doi.org/10.1007/s12190-021-01596-9

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  • DOI: https://doi.org/10.1007/s12190-021-01596-9

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