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 $R_0\sim 3.0$, 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 $\mathcal{R}(t)$, 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 $\mathcal{R}<1$. We find an analytical expression connecting $\mathcal{R}$ 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 $\mathcal{R}$ should assist policymakers to evaluate the epidemics’ response to actions, such as enforcing or relaxing confinement and social distancing.

The increasing agglomeration of people in dense urban areas coupled with the existence of efficient modes of transportation connecting such centers, make cities particularly vulnerable to the spread of epidemics. Here we develop a data-driven approach combines with a meta-population modeling to capture the interplay between population density, mobility and epidemic spreading. We study 163 cities, chosen from four different continents, and report a global trend where the epidemic risk induced by human mobility increases consistently in those cities where mobility flows are predominantly between high population density centers. We apply our framework to the spread of SARS-CoV-2 in the United States, providing a plausible explanation for the observed heterogeneity in the spreading process across cities. Based on this insight, we propose realistic mitigation strategies (less severe than lockdowns), based on modifying the mobility in cities. Our results suggest that an optimal control strategy involves an asymmetric policy that restricts flows entering the most vulnerable areas but allowing residents to continue their usual mobility patterns.

We propose a theoretical framework for the study of spreading processes in structured metapopulations, with heterogeneous agents, subjected to different recurrent mobility patterns. We propose to represent the heterogeneity in the composition of the metapopulations as layers in a multiplex network, where nodes would correspond to geographical areas and layers account for the mobility patterns of agents of the same class. We analyze classical epidemic models within this framework and obtain an excellent agreement with extensive Monte Carlo simulations. This agreement allows us to derive analytical expressions of the epidemic threshold and to face the challenge of characterizing a real multiplex metapopulation, the city of Medellín in Colombia, where different recurrent mobility patterns are observed depending on the socioeconomic class of the agents. Our framework allows us to unveil the geographical location of those patches that trigger the epidemic state at the critical point. A careful exploration reveals that social mixing between classes and mobility crucially determines these critical patches and, more importantly, it can produce abrupt changes of the critical properties of the epidemic onset.

An outbreak of a novel coronavirus, named SARS-CoV-2, that provokes the COVID-19 disease, was first reported in Hubei, mainland China on 31 December 2019. As of 20 March 2020, cases have been reported in 166 countries/regions, including cases of human-to-human transmission around the world. The proportions of this epidemics is probably one of the largest challenges faced by our interconnected modern societies. According to the current epidemiological reports, the large basic reproduction number, R ₀ ∼ 2.3, number of secondary cases produced by an infected individual in a population of susceptible individuals, as well as an asymptomatic period (up to 14 days) in which infectious individuals are undetectable without further analysis, pave the way for a major crisis of the national health capacity systems. Recent scientific reports have pointed out that the detected cases of COVID19 at young ages is strikingly short and that lethality is concentrated at large ages. Here we adapt a Microscopic Markov Chain Approach (MMCA) metapopulation mobility model to capture the spread of COVID-19. We propose a model that stratifies the population by ages, and account for the different incidences of the disease at each strata. The model is used to predict the incidence of the epidemics in a spatial population through time, permitting investigation of control measures. The model is applied to the current epidemic in Spain, using the estimates of the epidemiological parameters and the mobility and demographic census data of the national institute of statistics (INE). The results indicate that the peak of incidence will happen in the first half of April 2020 in absence of mobility restrictions. These results can be refined with improved estimates of epidemiological parameters, and can be adapted to precise mobility restrictions at the level of municipalities. The current estimates largely compromises the Spanish health capacity system, in particular that for intensive care units, from the end of March. However, the model allows for the scrutiny of containment measures that can be used for health authorities to forecast with accuracy their impact in prevalence of COVID–19. Here we show by testing different epidemic containment scenarios that we urge to enforce total lockdown to avoid a massive collapse of the Spanish national health system.

Vector-borne epidemics are progressively becoming a global burden, especially those related to flaviviruses, and the effects of different factors such as climate change or the increase of human mobility can sensibly increase the population at risk worldwide. Such outbreaks are the result of the combination of different factors including crossed contagions between humans and vectors, their demographic distribution and human mobility among others. The current availability of information about all those ingredients demands their incorporation into current mathematical models for vector-borne disease transmission. Here, relying on a Markovian formulation of the metapopulation dynamics, we propose a framework that explicitly includes human-vector interactions, mobility, and demography. The analysis of the framework allows us not only to derive an expression of the epidemic threshold capturing the conditions for the onset of the epidemics but also to highlight some unseen features of vector-borne epidemics, such as abrupt changes in the unfolding patterns of the disease for small variations of the degree of mobility. Finally, driven by these insights, we obtain a prevalence indicator to rank populations according to their risk of being affected by a vector-borne disease. We illustrate the utility of this indicator by reproducing the spatial distribution Dengue cases reported in the city of Santiago de Cali (Colombia) from 2015 to 2016.