An Immuno-Epidemiological Vector-Host Model with Within-Vector Viral\n Kinetics

2019/12/17 by Hayriye Gulbudak, Gulbudak, Hayriye
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)

paper · pdf · doi:10.48550/arxiv.1912.08312

openalex publication_date 2019/12/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

A current challenge for disease modeling and public health is understanding\npathogen dynamics across scales since their ecology and evolution ultimately\noperate on several coupled scales. This is particularly true for vector-borne\ndiseases, where within-vector, within-host, and between vector-host populations\nall play crucial roles in diversity and distribution of the pathogen. Despite\nrecent modeling efforts to determine the effect of within-host virus-immune\nresponse dynamics on between-host transmission, the role of within-vector viral\ndynamics on disease spread is overlooked. Here we formulate an\nage-since-infection structured epidemic model coupled to nonlinear ordinary\ndifferential equations describing within-host immune-virus dynamics and\nwithin-vector viral kinetics, with feedbacks across these scales. We first\ndefine the \within-host viral-immune response and within-vector viral\nkinetics dependent basic reproduction number mathcal R₀. Then we prove\nthat whenever mathcal R₀<1, the disease free equilibrium is locally\nasymptotically stable, and under certain biologically interpretable conditions,\nglobally asymptotically stable. Otherwise if mathcal R₀>1, it is unstable\nand the system has a unique positive endemic equilibrium. In the special case\nof constant vector to host inoculum size, we show the positive equilibrium is\nlocally asymptotically stable and the disease is weakly uniformly persistent.\nFurthermore numerical results suggest that within-vector-viral kinetics and\ndynamic inoculum size may play a substantial role in epidemics. Finally, we\naddress how the model can be utilized to better predict the success of control\nstrategies such as vaccination and drug treatment.\n

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