A pandemic at the Tunisian scale. Mathematical modelling of reported and unreported COVID-19 infected cases

Starting from the city of Wuhan in China in late December 2019, the pandemic quickly spread to the rest of the world along the main intercontinental air routes. At the time of writing this article, there are officially about five million infections and more than 300 000 deaths. Statistics vary widely from country to country, revealing significant differences in anticipation and management of the crisis. We propose to examine the COVID-19 epidemic in Tunisia through mathematical models, which aim to determine the actual number of infected cases and to predict the course of the epidemic. As of May 11, 2020, there are officially 1032 COVID-19 infected cases in Tunisia. 45 people have died. Using a mathematical model based on the number of reported infected cases, the number of deaths, and the effect of the 18-day delay between infection and death, this study estimates the actual number of COVID-19 cases in Tunisia as 2555 cases. This paper analyses the evolution of the epidemic in Tunisia using population dynamics with an SEIR model combining susceptible cases S(t), asymptomatic infected cases A(t), reported infected cases V(t), and unreported infected cases U(t). This work measures the basic reproduction number [Formula], which is the average number of people infected by a COVID-19 infected person. The model predicts an [Formula]. Strict containment measures have led to a significant reduction in the reproduction rate. Contact tracing and respect for isolation have an impact: at the current time, we compute that Tunisia has an [Formula] (95% CI 0.14-0.70). These values depend on physical separation and can vary over time depending on the management of suspicious cases. Their objective estimation and the study of their evolution are however necessary to understand the pandemic and to reduce their unintended damage (due to an absence of symptoms, or the confusion of certain symptoms with less contagious diseases, or unavailable or unreliable tests).