Infectious disease dynamics in metapopulations with heterogeneous transmission and recurrent mobility

Human mobility, contact patterns, and their interplay are key aspects of our social behavior that shape the spread of infectious diseases across different regions. In the light of new evidence and data sets about these two elements, epidemic models should be refined to incorporate both the heterogeneity of human contacts and the complexity of mobility patterns. Here, we propose a theoretical framework that allows accommodating these two aspects in the form of a set of Markovian equations. We validate these equations with extensive mechanistic simulations and derive analytically the epidemic threshold. The expression of this critical value allows us to evaluate its dependence on the specific demographic distribution, the structure of mobility flows, and the heterogeneity of contact patterns, thus shedding light on the microscopic mechanisms responsible for the epidemic detriment driven by recurrent mobility patterns reported in the literature.

Modeling the Spatiotemporal Epidemic Spreading of COVID-19 and the Impact of Mobility and Social Distancing Interventions

On 31 December, 2019, an outbreak of a novel coronavirus, SARS-CoV-2, that causes the COVID-19 disease, was first reported in Hubei, mainland China. This epidemics' health threat is probably one of the biggest challenges faced by our interconnected modern societies. According to the epidemiological reports, the large basic reproduction number R-0 similar to 3.0, together with a huge fraction of asymptomatic infections, paved the way for a major crisis of the national health capacity systems. Here, we develop an age-stratified mobility-based metapopulation model that encapsulates the main particularities of the spreading of COVID-19 regarding (i) its transmission among individuals, (ii) the specificities of certain demographic groups with respect to the impact of COVID-19, and (iii) the human mobility patterns inside and among regions. The full dynamics of the epidemic is formalized in terms of a microscopic Markov chain approach that incorporates the former elements and the possibility of implementing containment measures based on social distancing and confinement. With this model, we study the evolution of the effective reproduction number R(t), the key epidemiological parameter to track the evolution of the transmissibility and the effects of containment measures, as it quantifies the number of secondary infections generated by an infected individual. The suppression of the epidemic is directly related to this value and is attained when R < 1. We find an analytical expression connecting R. with nonpharmacological interventions, and its phase diagram is presented. We apply this model at the municipality level in Spain, successfully forecasting the observed incidence and the number of fatalities in the country at each of its regions. The expression for R should assist policymakers to evaluate the epidemics' response to actions, such as enforcing or relaxing confinement and social distancing.