Abstract
The COVID-19 pandemic forced authorities worldwide to implement moderate to severe restrictions in order to slow down or suppress the spread of the disease. It has been observed in several countries that a significant number of people fled a city or a region just before strict lockdown measures were implemented. This behavior carries the risk of seeding a large number of infections all at once in regions with otherwise small number of cases. In this work, we investigate the effect of fleeing on the size of an epidemic outbreak in the region under lockdown, and also in the region of destination. We propose a mathematical model that is suitable to describe the spread of an infectious disease over multiple geographic regions. Our approach is flexible to characterize the transmission of different viruses. As an example, we consider the COVID-19 outbreak in Italy. Projection of different scenarios shows that (i) timely and stricter intervention could have significantly lowered the number of cumulative cases in Italy, and (ii) fleeing at the time of lockdown possibly played a minor role in the spread of the disease in the country.
Highlights
A novel coronavirus (SARS-CoV-2) causing the severe acute respiratory illness COVID-19 appeared in China at the end of 2019
The proposed approach extends the known S-E-I-R model for disease dynamics[12], and is suitable to describe the spread of several infectious diseases, though we shall talk about COVID-19 later
We have established a model for the spread of an epidemic outbreak considering the effects of an exodus of large masses of people from infected areas before restrictive control measures are introduced
Summary
A novel coronavirus (SARS-CoV-2) causing the severe acute respiratory illness COVID-19 appeared in China at the end of 2019. Lau et al.[9], Lai et al.[10], Boldog et al.11) investigate the association between the domestic/international travel load and the number of cases exported from Wuhan to other regions in China These studies, do not seem to consider the large exodus induced by the lockdown measures. We formulate and study a compartmental epidemic model for the spread of an infectious disease in the two different geographic regions, establishing a new type of intervention-dependent final size relation. The latter can be used to estimate the final epidemic size even in the case of a change in the population size due to the migration just before the lockdown. The approach presented in this study can be adapted to describe the spread of an infectious disease over multiple geographic regions or to describe the transmission of viruses others than SARS-CoV-2
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