**1. Motivation**

The spread of the COVID-19 virus at the beginning of 2020 caught many countries and governments by surprise and unveiled a widespread lack of pandemic preparedness at the global and national level.

Currently, given the absence of a vaccine and the incomplete information about several aspects of contagion, such as the role of different risk factors, the dynamics of transmission and the role of asymptomatic transmission, governments operate under significant uncertainty. Against this background, data from countries where the virus has initially spread (notably China) are a precious source of information for the countries that are fighting against the virus. The more data becomes available, the more policies can be formulated with the backing of evidence as regards the "curve" and the "peak" of the contagion.

Early attempts to model the contagion curve of the COVID-19 include (Danon et al. 2020), which predicted that the outbreak would peak 126 to 147 days (around 4 months) after the start of person-to-person transmission in England and Wales, at a time in which the virus had been found in just 25 countries; and (Kucharski et al. 2020), which combines a stochastic transmission model with four datasets on cases of COVID-19 originated in Wuhan to estimate how transmission varied over time, and calculate the probability that newly introduced cases might generate outbreaks in other areas. In Imperial College COVID-19 Response Team (2020), researchers modified an individual-based simulation model developed to support pandemic influenza planning to explore scenarios for COVID-19 in Great Britain.

Particularly relevant studies for our work are Gu et al. (2020) and Giordano et al. (2020) which, while mathematically expressing the current practices in the modelling on the global spread of diseases, draw policy making suggestions. We follow the same line of research, combining mathematical rigour with attention to drawing results that can be useful for policy makers. Specifically, our contribution is a new statistical model for disease spread which, by taking dependence between daily contagion counts into account, can better capture the contagion curve dynamics and, thus, can draw further light on the understanding of its possible future path.

Our approach is connected to the exponential growth models employed in the SIR literature (Biggerstaff et al. 2014), to which we contribute by including an autoregressive component in the growth dynamics.
