Modelling fatality curves of COVID-19 and the effectiveness of intervention strategies

Giovani L. Vasconcelos; Antônio M. S. Macêdo; Raydonal Ospina; Francisco A. G. Almeida; Gerson C. Duarte-Filho; Inês C. L. Souza

In this paper we use the Richards growth model (RGM) [14] to study the fatality curves, represented by the cumulative number of deaths as a function of time, of COVID-19 for different countries that are at different stages of the epidemics. We show that the RGM describes reasonably well the fatality curves of all selected countries analysed in this study. We also introduce a theoretical framework, within the context of the RGM model, to calculate the efficiency of interventions. Here an intervention strategy is modelled by assuming that its net result is to alter the parameters of the RGM after a given time t 0 , so that the full epidemics dynamics is then described in terms of two RGM models: one before and the other after the time t 0 , where certain 'matching conditions' are imposed at t 0 . In this way, we are able to derive an analytical formula for the efficiency of the corresponding intervention as a function of the adoption time t 0 . We show, in particular, that the intervention efficiency quickly decays past a critical adoption time, thus showing that time is really of essence in containing an outbreak.