Figure 1 shows the simulated daily number of PCR-positive diagnosed cases in the scenario that PCR positivity measures true active infection presence in the population compared to the actually-observed scenario in presence of the prolonged PCR positivity. There is a lag of 10 days between the true peak in infection incidence and the actually-observed peak in infection incidence when R0 is 1.6, and a lag of 5 days when R0 is 3.0. Moreover, the scenario incorporating the prolonged PCR positivity results in more cases being diagnosed than the scenario in which infected individuals are PCR positive only during active infection.
Figure 2 shows the ratio of the proportion of tests that are PCR positive (“positivity rate”) in presence of the prolonged PCR positivity divided by the proportion of tests that are PCR positive assuming no prolonged PCR positivity. This ratio is shown assuming a prolonged PCR positivity duration of 2, 3, 4, or 6 weeks. Prior to the epidemic peak, the proportion of tests that are PCR positive in presence of the prolonged PCR positivity is 2-fold higher than that assuming no prolonged PCR positivity. Meanwhile, after the epidemic peak, the ratio of the two proportions steadily increases and is higher the longer is the prolonged PCR positivity—that is more and more of the infections are diagnosed not during active infection, but during the prolonged PCR positivity stage. These results were generated assuming an R0 of 1.6, and the results assuming an R0 of 3.0 show the same pattern (Appendix Figure S2).
Figure 3 presents the difference in days between the epidemic peak as measured in presence of the prolonged PCR positivity and the epidemic peak based on true incidence of active infection in the population, assuming a prolonged PCR positivity duration of 2, 3, 4, or 6 weeks. The delay between the true epidemic peak and the observed epidemic peak increased as the duration of prolonged PCR positivity increased. This delay ranged from 7.5 days up to 16.5 days at an R0 of 1.6, and from 4.5 days up to 8.0 days at an R0 of 3.0.
Figure 4 and Figure S3 of the Appendix illustrate the change throughout the epidemic in the proportion of those who test positive by PCR and are latently infected, infectious, or post-infectious (that is in the prolonged PCR positivity stage) for \({R_0}=1.6\) and \({R_0}=3.0\), respectively. For \({R_0}=1.6\), prior to the epidemic peak, approximately half of those who test positive by PCR are in the prolonged PCR positivity stage (that is already recovered from the infection). After the epidemic peak, this proportion rises steeply as the epidemic begins to decline. A similar pattern is seen for \({R_0}=3.0\) (Figure S3 of the Appendix).
Figure S4 of the Appendix shows the estimated R0 as derived from the epidemic curve of diagnosed cases in presence and in absence of the prolonged PCR positivity. Two scenarios are presented, the first for an R0 of 1.6, and the second for an R0 of 3.0, and each factoring a prolonged PCR positivity duration of 2, 3, 4, or 6 weeks. The estimated R0 from the actually-observed diagnosed cases is always lower than that estimated from the true (active infection) diagnosed cases, but the difference is small, particularly so for the case of R0 of 1.6, and is not much affected by the duration of the prolonged PCR positivity.
Figure 5 shows the trend in the true prevalence of ever infection in the population versus the actually-observed seroprevalence factoring the 3 weeks average delay in the development of detectable antibodies [7, 8]. Two scenarios are presented, the first for an R0 of 1.6 and the second for an R0 of 3.0. There is a time delay in the actually-observed seroprevalence reaching the true prevalence of ever infection in the population, and this delay varies with time reflecting the epidemic phase (particularly closeness to the epidemic peak) and the intensity of the epidemic (value of R0).