Elementary time-delay dynamics of COVID-19 disease

Jose Menendez

It is apparent that Eq. (2) will not apply to times during which zoonotic transmission is ongoing and community spread is not generalized. During this period the evolution of the disease depends on random events and geographical peculiarities that cannot be modeled without the introduction of several more parameters and categories. To avoid these complications, the initial time t = 0 is taken as the time at which the total number of cases has reached 500, and the data is fitted for t > 0 using , and as adjustable parameters. Since at earlier times , one can further simplify Eq. (2) to and adjust the solution to the data using only and as adjustable parameters. In a subsequent stage of the fit, the solution can be extended to longer times by adjusting the time . The dashed lines in Figure 1 and 2 show the fits for China and South Korea, respectively, and the corresponding parameters are on Table I . For China, there is a well-known discontinuity in the reported data that makes the fit somewhat challenging. For South Korea, seemed to be growing linearly as a function of time as this paper was written. This behavior is not captured by Eq. (4), and the fit "reacts" by yielding a higher value of relative to China and an adjusted value of that is somewhat smaller than the total number of cases already reported. This could be fixed by assuming that the transmission rate in Eq. (4) approaches an asymptotic residual value rather than becoming exactly zero. On the other hand, the total number of cases does seem to saturate to a maximum value in China, in nearly perfect agreement with Eq. (4) . Accordingly, the origin of the late linear growth in South Korea may be an artifact, or a consequence of the discovery of new cases due the reportedly unrelenting COVID-19 testing in this country.