Abstract
The main objective of the present article is twofold: first, to model the fatality curves of the COVID-19 disease, as represented by the cumulative number of deaths as a function of time; and second, to use the corresponding mathematical model to study the effectiveness of possible intervention strategies. We applied the Richards growth model (RGM) to the COVID-19 fatality curves from several countries, where we used the data from the Johns Hopkins University database up to May 8, 2020. Countries selected for analysis with the RGM were China, France, Germany, Iran, Italy, South Korea, and Spain. The RGM was shown to describe very well the fatality curves of China, which is in a late stage of the COVID-19 outbreak, as well as of the other above countries, which supposedly are in the middle or towards the end of the outbreak at the time of this writing. We also analysed the case of Brazil, which is in an initial sub-exponential growth regime, and so we used the generalised growth model which is more appropriate for such cases. An analytic formula for the efficiency of intervention strategies within the context of the RGM is derived. Our findings show that there is only a narrow window of opportunity, after the onset of the epidemic, during which effective countermeasures can be taken. We applied our intervention model to the COVID-19 fatality curve of Italy of the outbreak to illustrate the effect of several possible interventions.
Highlights
The response interventions to the pandemic of the novel coronavirus disease (COVID-19) have varied from country to country
We show that the Richards growth model (RGM) describes reasonably well the fatality curves of all countries analysed in this study, except Brazil, which is in an early-to-intermediate stage of the epidemic
We adopted the following ad hoc procedure to obtain a smooth ‘empirical’ curve for China: we multiplied all data points prior to the revision date by a factor corresponding to the ratio between the numbers of deaths after and before the revision date, meaning that the excess deaths due to the data correction was uniformly redistributed by the same proportion for all dates before the revision. This is admittedly an arbitrary procedure, which is intended only as a numerical way of ‘welding’ the two sides of the curve at the jump. This ‘renormalised’ fatality curve for China is shown in Fig. 1, superimposed with the corresponding statistical fit of the RGM curve, where the fit parameters are shown in the inset of the figure
Summary
The response interventions to the pandemic of the novel coronavirus disease (COVID-19) have varied from country to country. Several countries, specially those first hit by the disease, have adopted a standard progressive protocol, from containment to mitigation to supression (WHO, 2020). Specially those first hit by the disease, have adopted a standard progressive protocol, from containment to mitigation to supression (WHO, 2020) As these strategies failed to deter the spread of the virus, government authorities introduced ever more stringent measures on their citizens’ movements in an attempt to suppress or sharply reduce the propagation of the virus. One difficulty in deciding the best approach to counter the spread of the novel coronavirus (SARS-CoV-2) is that the virus propagation dynamics is not yet well understood
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