2013/08/03 by Ling Xue, Xue, Ling, Caterina Scoglio +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #COVID-19 epidemiological studies #Evolution and Genetic Dynamics #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1308.0718
openalex publication_date 2013/08/03 · arxiv created 2013/08/06 · arxiv updated 2013/08/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation of infectious diseases. Relationships between the 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 the relationships may always exist and proposing a mathematical problem of proving their existences in general. Moreover, numerical simulations show that the reproduction number is not monotonically increasing or decreasing 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.