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

where C (t) = dC(t)/dt. Note that condition (8) takes into account, albeit indirectly, the fact that intervention measures take some time to affect the epidemic dynamics. In other words, the trend (i.e., the derivative) one sees at a given time t reflects in part the measures taken at some earlier time (or lack thereof). Thus, imposing continuity of the derivative of the epidemic curve at time t 0 in our 'intervention strategy' seeks to capture this delay effect. In our intervention model above, we assume that the net result of the action is to alter the parameters r and α of the Richards model at time t 0 . Of course, the difficult part is to estimate how a particular set of intervention measures (e.g., contact tracing and quarantine of contacts, social distancing, school closures, etc) would influence these parameters. Such an analysis is however beyond the scope of the present paper. Note furthermore that, as discussed above, the time t 0 is not the actual time of adoption of the intervention but rather the time at which the corresponding measures have started to affect the epidemics dynamics, as reflected in the number of cases. Nevertheless we shall for simplicity refer to t 0 as the intervention 'adoption time.' As defined in (6), an intervention strategy adopted at time t 0 can be viewed as a map (r, K, α, t c ) → (r , K , α , t c ) in the parameter space of the RGM, which results in the condition K /K < 1. Let us therefore define the intervention efficiency as the relative reduction in the total number of cases: η(t 0 ) = (K − K )/K, where it is assumed that η(t 0 ) > 0. Using conditions (7) and (8) in (3), one obtains that