In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system’s necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate $$ \lambda $$ λ was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.

As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves, even when the community disease transmission rate $$\beta$$ β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, $$\beta > \beta _c$$ β > β c ) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, $$\beta < \beta _c$$ β < β c ) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with $$r(t) \approx 1$$ r ( t ) ≈ 1 hovering around its threshold value.

The initial exponential growth rate of an epidemic is an important measure that follows directly from data at hand, commonly used to infer the basic reproduction number. As the growth rates λ(t) of tested positive COVID-19 cases have crossed the threshold in many countries, with negative numbers as surrogate for disease transmission deceleration, lockdowns lifting are linked to the behavior of the momentary reproduction numbers r(t), often called R0. Important to note that this concept alone can be easily misinterpreted as it is bound to many internal assumptions of the underlying model and significantly affected by the assumed recovery period. Here we present our experience, as part of the Basque Country Modeling Task Force (BMTF), in monitoring the development of the COVID-19 epidemic, by considering not only the behaviour of r(t) estimated for the new tested positive cases - significantly affected by the increased testing capacities, but also the momentary growth rates for hospitalizations, ICU admissions, deceased and recovered cases, in assisting the Basque Health Managers and the Basque Government during the lockdown lifting measures. Two different data sets, collected and then refined during the COVID-19 responses, are used as an exercise to estimate the momentary growth rates and reproduction numbers over time in the Basque Country, and the implications of using those concepts to make decisions about easing lockdown and relaxing social distancing measures are discussed. These results are potentially helpful for task forces around the globe which are now struggling to provide real scientific advice for health managers and governments while the lockdown measures are relaxed.

The initial exponential growth rate of an epidemic is an important measure that follows directly from data at hand, commonly used to infer the basic reproduction number. As the growth rates λ(t) of tested positive COVID-19 cases have crossed the threshold in many countries, with negative numbers as surrogate for disease transmission deceleration, lockdowns lifting are linked to the behavior of the momentary reproduction numbers r(t), often called R 0. Important to note that this concept alone can be easily misinterpreted as it is bound to many internal assumptions of the underlying model and significantly affected by the assumed recovery period. Here we present our experience, as part of the Basque Country Modeling Task Force (BMTF), in monitoring the development of the COVID-19 epidemic, by considering not only the behaviour of r(t) estimated for the new tested positive casessignificantly affected by the increased testing capacities, but also the momentary growth rates for hospitalizations, ICU admissions, deceased and recovered cases, in assisting the Basque Health Managers and the Basque Government during the lockdown lifting measures. Two different data sets, collected and then refined during the COVID-19 responses, are used as an exercise to estimate the momentary growth rates and reproduction numbers over time in the Basque Country, and the implications of using those concepts to make decisions about easing lockdown and relaxing social distancing measures are discussed. These results are potentially helpful for task forces around the globe which are now struggling to provide real scientific advice for health managers and governments while the lockdown measures are relaxed.

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