Network-level reproduction number and extinction threshold for vector-borne diseases
The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic rep...
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AIMS Press
2014-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.565 |
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| author | Ling Xue Caterina Scoglio |
| author_facet | Ling Xue Caterina Scoglio |
| author_sort | Ling Xue |
| collection | DOAJ |
| description | The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases. |
| format | Article |
| id | doaj-art-916f6df233ea4f788d5db7ef338f9511 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-916f6df233ea4f788d5db7ef338f95112025-01-24T02:31:53ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-12-0112356558410.3934/mbe.2015.12.565Network-level reproduction number and extinction threshold for vector-borne diseasesLing Xue0Caterina Scoglio1Kansas State Epicenter, Department of Electrical & Computer Engineering, Kansas State University, Manhattan, KS 66506Kansas State Epicenter, Department of Electrical & Computer Engineering, Kansas State University, Manhattan, KS 66506The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.565branching processbasic reproduction numbervector-borne diseases.extinction thresholdsnetwork |
| spellingShingle | Ling Xue Caterina Scoglio Network-level reproduction number and extinction threshold for vector-borne diseases Mathematical Biosciences and Engineering branching process basic reproduction number vector-borne diseases. extinction thresholds network |
| title | Network-level reproduction number and extinction threshold for vector-borne diseases |
| title_full | Network-level reproduction number and extinction threshold for vector-borne diseases |
| title_fullStr | Network-level reproduction number and extinction threshold for vector-borne diseases |
| title_full_unstemmed | Network-level reproduction number and extinction threshold for vector-borne diseases |
| title_short | Network-level reproduction number and extinction threshold for vector-borne diseases |
| title_sort | network level reproduction number and extinction threshold for vector borne diseases |
| topic | branching process basic reproduction number vector-borne diseases. extinction thresholds network |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.565 |
| work_keys_str_mv | AT lingxue networklevelreproductionnumberandextinctionthresholdforvectorbornediseases AT caterinascoglio networklevelreproductionnumberandextinctionthresholdforvectorbornediseases |