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                <title xml:lang="en">On the true number of COVID-19 infections: Effect of the Sensitivity, Specificity and Number of Tests</title>
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                <term xml:lang="en">Policy-Making</term>
                <term xml:lang="en">Specificity</term>
                <term xml:lang="en">PCR</term>
                <term xml:lang="en">Virological Test</term>
                <term xml:lang="en">SerologicalTest</term>
                <term xml:lang="en">Number of Infections</term>
                <term xml:lang="en">Estimation</term>
                <term xml:lang="en">False Negative</term>
                <term xml:lang="en">Testing Campaigns.</term>
                <term xml:lang="en">Data Analysis</term>
                <term xml:lang="en">SARS-CoV-2</term>
                <term xml:lang="en">False Positive</term>
                <term xml:lang="en">Covid-19</term>
                <term xml:lang="en">Sensitivity</term>
                <term xml:lang="fr">Nombre d’infections</term>
                <term xml:lang="fr">Testsérologique</term>
                <term xml:lang="fr">Sensibilité</term>
                <term xml:lang="fr">Campagnes de tests.</term>
                <term xml:lang="fr">Elaboration de politiques</term>
                <term xml:lang="fr">Analyse de données</term>
                <term xml:lang="fr">Faux positifs</term>
                <term xml:lang="fr">Faux négatifs</term>
                <term xml:lang="fr">Estimation</term>
                <term xml:lang="fr">Test virologique</term>
                <term xml:lang="fr">PCR</term>
                <term xml:lang="fr">SARS-CoV-2</term>
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              <p>In this report, a formula for estimating the number of SARS-CoV-2 infections in a population is given. The formula is in terms of the test results and test parameters, i.e., probability of true positives (sensitivity) and the probability of true negatives (specificity). The motivation of this work lies on the fact that, depending on the sensitivity and specificity of the tests, the number of positive results might be drastically different to the number of infected individuals. From this perspective, counting the positive results is not a reliable information source for decision-makingor policy-making.  The relevance of the estimation presented in this work is that the precision increases with the number of tests. That is, large testing campaigns lead to a reliable estimation of the fraction of infected individuals in a population.  Two conclusions are drawn from this work.  First, in order to ensure that a reliable estimation is achieved, testing campaigns must be implemented with tests for which the sum of the sensitivity and the specificity is sufficiently different from one. Second, the key parameter for reducing the estimation error is the number of tests. For large number of tests, as long as the sum of the sensitivity and specificity do not add upto one, the exact values of these parameters have very little impact in the estimation error.</p>
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              <p>Ce rapport présente une formule mathématique pour estimer le nombre d’infectionsSARS-CoV-2 dans une population donnée.  La formule utilise les résultats et les paramètres des tests, c’est-à-dire la probabilité de vrais positifs (sensibilité) et de vrais négatifs (spécificité). Selon la sensibilité et la spécificité des tests, le nombre de résultats positifs peut être radicalement différent du nombre d’individus infectés. Ainsi, le nombre final de résultats rendus positifs n’est pas une source d’information fiable pour la prise de décision ou l’élaboration des directives.Deux conclusions sont tirées de ce travail; afin de garantir l’obtention d’une estimation fiable,des campagnes de tests doivent être mises en oeuvre avec des tests pour lesquels la somme de la sensibilité et de la spécificité est significativement différente de un. De plus, il est prouvé qu’un nombre important de tests conduit à une estimation plus précise du nombre d’infectés. Pour un grand nombre de tests, tant que la somme de la sensibilité et de la spécificité n’est pas égale à un, les valeurs exactes de ces paramètres ont très peu d’impact sur l’erreur d’estimation</p>
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