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ARS Home » Plains Area » Manhattan, Kansas » Center for Grain and Animal Health Research » ABADRU » Research » Publications at this Location » Publication #300378
Title: Network-level reproduction number and extinction threshold for vector-borne diseases

Author
item XUE, LING - Kansas State University
item SCOGLIO, CATERINA - Kansas State University

Submitted to: Journal of Theoretical Biology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/4/2012
Publication Date: 8/7/2012
Citation: Xue, L., Scoglio, C. 2012. Network-level reproduction number and extinction threshold for vector-borne diseases. Journal of Theoretical Biology. https://doi.org/10.1016/j.jtbi.2012.04.029.
DOI: https://doi.org/10.1016/j.jtbi.2012.04.029

Interpretive Summary: The number of new cases originating from a single infected individual is considered the reproductive number of a disease and is an indicator of epidemic spread. If the number is less than one, than the disease will not spread and will move towards elimination. Therefore calculating this number is important to determine the optimal mitigation and possibly elimination strategies that most efficiently and rapidly end a vector-borne disease outbreak. The reproductive number and time to extinction are two key components of extinction thresholds and this paper uses simulations to connect the reproductive number to extinction probability and thresholds. This important connection will be necessary to predict the persistence of vector-borne diseases and to optimize control strategies.

Technical Abstract: The 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 network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding 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 of proving existence of the relationships in general. Moreover, numerical simulations show that the reproduction number does not monotonically increase or decrease with the extinction threshold. Key parameters in predicting uncertainty of extinction thresholds are identified using Latin Hypercube Sampling/Partial Rank Correlation Coefficient. 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.