A Bayesian approach for studying COVID-19 contagion dynamics in Algeria using a Poisson autoregressive (PAR) model

Global emphasis has been focused on tracking the trends of the COVID-19 pandemic. Numerous techniques have been developed or utilized for this purpose. In this study, we seek to present and evaluate a model that, in our opinion, has not received adequate attention, using Algeria as a case study. We developed two distinct Poisson autoregressive (PAR) models using the Monte Carlo Markov Chain (MCMC) simulation method and the Bayesian method: one based solely on short-term dependence and the other incorporating both short- and long-term dependence. The study aimed to apply these models to enhance the prediction of new infections and determine whether the disease is spreading or declining. This information can guide decisions on implementing or relaxing containment measures. Our findings suggest that Algeria's epidemiological state was relatively stable at the end of the study period, with the combined long-term and short-term dependence factors being less than 1 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mo>=</mml:mo><mml:mn>0.994</mml:mn><mml:mo>)</mml:mo></mml:math>. This indicates that while the epidemic is in decline, the infection rates are not expected to drop significantly in the near future. Furthermore, the short-term dependence parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi><mml:mo>=</mml:mo><mml:mn>0.987</mml:mn></mml:math>constitutes a significant portion (99%) of the total dependence. This high value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> suggest that the COVID-19 epidemic in Algeria is experiencing a strong decline, though the rate of new infections is expected to persist at a lower level for the foreseeable future. Given these findings, it is recommended that authorities remain vigilant and continue public health measures, including educational campaigns and awareness efforts, to promote COVID-19 vaccination and adherence to health guidelines.