Multiscaled causality of infections on viral testing volumes: The case of COVID-19 in Tunisia

Coronavirus disease (COVID-19) is one of the most detrimental pandemics that affected the humanity throughout the ages. The irregular historical progression of the virus over the first year of the pandemic was accompanied with far-reaching health and social damages. To prepare logistically against this worsening disaster, many public authorities around the world had set up screening and forecasting studies. This article aims to analyse the time-frequency co-evolution of the number of confirmed cases (NCC) in Tunisia and the related number of performed polymerase chain reaction (PCR) tests over the COVID-19 first year. Accurately predicting such a relationship allows Tunisian authorities to set up an effective health prevention plan.

In order to keep pace with the speed of evolution of the virus, we used uninterrupted daily time series from the Tunisian Ministry of Public Health (TMPH) recorded over the COVID-19 first year. The objective is to: (1) analyse the time-frequency progress of the NCC in relationship with the number of PCR tests, (2) identify a multi-scale two-factor stochastic model in order to develop a robust bivariate forecasting technique.

We assume a bivariate stochastic process which is projected onto a set of wavelet sub-spaces to investigate the scale-by-scale co-evolvement the NCC/PCR over the COVID-19 first year. A wavelet-based multiresolutional causality test is then performed.

The main results recommend the rejection of the null hypothesis of no instantaneous causality in both directions, while the statistics of the Granger test suggest failing to reject the null hypothesis of non-causality. However, by proceeding scale-by-scale, the Granger causality is proven significant in both directions over varying frequency bands.

It is important to include the NCC and PCR variables in any time series model intended to predict one of these variables. Such a bivariate and multi-scale model is supposed to better predict the needs of the public health sector in screening tests. On this basis, testing campaigns with multiple periodicities can be planned by the Tunisian authorities.