2015/06/10 by Daniel Antunes Maciel Villela, Villela, Daniel A. M.
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.1506.03339
openalex publication_date 2015/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Testing symptomatic individuals for a disease can deliver treatment\nresources, if tests' results turn positive, which speeds up their treatment and\nmight also decrease individuals' contacts to other ones. An imperfect test,\nhowever, might incorrectly consider susceptible individuals to be infected\n(false positives). In this case, testing reduces the epidemic in the expense of\npotentially misclassifying individuals. We present a mathematical model that\ndescribes the dynamics of an infectious disease and its testing. Susceptible\nindividuals turn to "susceptible but deemed infected" at rate \θ.\nInfected individuals go to a state "infected and tested positive" at rate\n\α. Both of these rates are functions of test's sensitivity and\nspecificity. Analysis of the model permits us to derive an expression for R0\nand to find the conditions for reaching R0<1, i.e., when the disease--free\nequilibrium is stable. We find that under certain conditions it is possible to\nget R0<1, when originally, i.e., without testing, we would have R0>1. We\nalso present numerical results to cover interesting scenarios such as using\ndifferent tests and to compare these results.\n