A modified SEIR model to predict the COVID-19 outbreak in Spain: simulating control scenarios and multi-scale epidemics

Leonardo R Lopez; Xavier Rodo

We followed the approach of Peng et al. [6] and implemented a modified SEIR model that accounts for the spread of infection during the latent period. This novel capacity to significantly spread during the latent period is a distinctive feature of the current SARS-CoV-2 epidemic if compared to SARS in 2003. Therefore, many classical models such as SIR [9, 10, 11] , SEIR [11] and SEIJR [12] are not appropriate to describe the outbreak of SARS-CoV-2 in China and elsewhere. Thanks to new data on the average latent period and average time of treatment, this time delay process can be successfully incorporated in a novel dynamical system framework to describe this quite unique dynamics. It has been discussed that at times of ongoing epidemics, and due to errors and under reporting, accumulated numbers of diagnosed cases and even number of deaths might reflect more reliably the extent of epidemic progression than the daily reported new cases. Alternately, and as in Chen 2020 [9] and Peng et al. [6] we also employ the accumulated numbers in time as variables, as it was done also for modelling MERS-CoV in the recent past [13] . Isolating key segments of populations (e.g. vulnerable populations, workers providing essential services, or a territory with too fast growing incidences) to protect them from an uncontrolled epidemic progression, is under vivid discussion as the real extent of viral spread in the population is not well known. Both the limited diagnostic capacity and the lack of clear strategies and mechanisms to quarantine infectious individuals, stand as two of the main limitations to control disease spread. Countries such as South Korea [14, 15] and Taiwan [16, 17] rapidly deployed aggressive contact tracing and quarantine systems [18] , understanding that early deployment of resources to try to control initial seeding foci, often not only balances public health criteria but also economics. Given the differences in public health strategies and the varying capacity of the national health systems in each country to tackle the extent of the infection in the population, the growing proportions of undiagnosed infected that eventually show up, are seen to exert an elevated stress on the already saturated health's system capacities. It is therefore relevant to accurately evaluate the effects of the social distancing actions imposed by governments, such as the individual or territory isolation and interruption of labour activity and/or intra and inter-urban transportation. Such strong provisions of isolation for suspected cases and infection due to contact with undiagnosed individuals are also taken into account in our modelling approach. This same SEIR model has been utilised to compare the effects of lock-down of Hubei province on the transmission dynamics in Wuhan and Beijing [6] . The manuscript is organised as follows: in Section 2, we describe the dynamic model and datasets used to simulate the evolution of the outbreak of SARS-CoV-2 in Spain and in its 17 administrative regions (CCAA), as well as in Italy. The effect on the epidemic curves of the efficacy of the different intervention measures aggregated for Spain, is presented in Section 3.1. Section 3.2 provides estimates of the future number of diagnosed people, fatalities and recovered individuals for each individual CCAA prediction as of March 23 and the main active foci in Section 3.3. Section 3.4 addresses model uncertainties and limitations of our study, and we add results for It