Spreading Processes in Multiplex Metapopulations Containing Different Mobility Networks

Abstract

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.

A mathematical model for the spatiotemporal epidemic spreading of COVID19

“…We propose a tailored model for the epidemic spread of COVID-19. We use a previous framework for the study of epidemics in structured metapopulations, with heterogeneous agents, subjected to recurrent mobility patterns [18][19][20]31].To understand the geographical diffusion of the disease, as a result of human-human interactions in small geographical patches, one has to combine the contagion process with the long-range disease propagation due to human mobility across different spatial scales. For the case of epidemic modeling, the metapopulation scenario is as follows.…”

“…Here, we propose mathematical model particularly designed to capture the main ingredients characterising the propagation of SARS-CoV-2 and the clinical characteristics reported for the cases of COVID-19. To this aim, we rely on previous metapopulation models by the authors [18][19][20][21] including the spatial demographical distribution and recurrent mobility patterns, and develop a more refined epidemic model that incorporates the stratification of population by age in order to consider the different epidemiological and clinical features associated to each group age that have been reported so far. The mathematical formulation of these models rely on the Microscopic Markov Chain Approach formulation for epidemic spreading in complex networks [22][23][24][25][26][27].…”

“…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.…”

Derivation of the effective reproduction number ℛ for COVID-19 in relation to mobility restrictions and confinement

“…It is precisely the inclusion of social, demographic and mobility data in the expression of R(t) what makes this expression a fundamental tool to evaluate and anticipate the effects of confinement and the reduction of mobility. Containment measures are implemented in the model in the spirit of Maier et al 17 . In this line, the containment measures confine a fraction κ 0 of the population at a given time t. The confinement leads to a reduction in the number of daily contacts to the household size and mobility.…”

A model for epidemic dynamics in a community with visitor subpopulation

“…In the past couple of decades, most papers related to theoretical/mathematical studies of the global spread of transmissible diseases were focused on the mobility of humans over various populations or patches (see Arino and van den Driessche, 2006;Colizza and Vespignani, 2008;Gong and Small, 2018;Saito et al, 2018;Soriano-Paños et al, 2018;Wang and Wu, 2018 and references therein). Frequently, such movements correspond to migration as opposed to temporary visits for a finite period as we consider in our case, or to human transportation on a large spatial scale during relatively long trips.…”