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Example of a metapopulation with two patches, both having the same average connectivity ⟨k⟩ = 5. The first is a heterogeneous patch with resident individuals of connectivity 1 or 20, and the second is a homogeneous patch in which all residents have the same connectivity 5.
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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 mobil...
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Citations
... In this area, the inclusion of contact tracing strategies and not only symptomatic detection could be of particular interest. This approach could also be applied to reaction-diffusion processes that simultaneously incorporate mobility flows and contact patterns [33], paving the way for the identification of optimal distributions of detection resources [34,35]. In addition, the lockdown that complements detection has been implemented in a stylized way, i.e. starting from the beginning of the epidemic way rather than being applied in subsequent times. ...
Compartmental models are the most widely used framework for modeling infectious diseases. These models have been continuously refined to incorporate all the realistic mechanisms that can shape the course of an epidemic outbreak. Building on a compartmental model that accounts for early detection and isolation of infectious individuals through testing, in this article we focus on the viability of detection processes under limited availability of testing resources, and we study how the latter impacts on the detection rate. Our results show that, in addition to the well-known epidemic transition at R0=1, a second transition occurs at R0★>1 pinpointing the collapse of the detection system and, as a consequence, the switch from a regime of mitigation to a regime in which the pathogen spreads freely. We characterize the epidemic phase diagram of the model as a function of the relevant control parameters: the basic reproduction number, the maximum detection capacity of the system, and the fraction of individuals in shelter. Our analysis thus provides a valuable tool for estimating the detection resources and the level of confinement needed to face epidemic outbreaks.
... Human mobility, being a geospatiotemporal phenomenon [17,43,70,71], can be better modeled using meta-population multi-patch models [4,34,39,40,42,44], as traditional homogeneous compartmental models are incapable of capturing such a strong heterogeneous human behavior [15,17,34,51]. Once such models have been constructed, a wide spectrum of quantitative analyses leading to a deeper understanding of the relationship between mobility and the spread of infectious diseases can be conducted. ...
... Human mobility, being a geospatiotemporal phenomenon [17,43,70,71], can be better modeled using meta-population multi-patch models [4,34,39,40,42,44], as traditional homogeneous compartmental models are incapable of capturing such a strong heterogeneous human behavior [15,17,34,51]. Once such models have been constructed, a wide spectrum of quantitative analyses leading to a deeper understanding of the relationship between mobility and the spread of infectious diseases can be conducted. ...
Most studies modeling population mobility and the spread of infectious diseases, particularly those using meta-population multi-patch models, tend to focus on the theoretical properties and numerical simulation of such models. As such, there is relatively scant literature focused on numerical fit, inference, and uncertainty quantification of epidemic models with population mobility. In this research, we use three estimation techniques to solve an inverse problem and quantify its uncertainty for a human-mobility-based multi-patch epidemic model using mobile phone sensing data and confirmed COVID-19-positive cases in Hermosillo, Mexico. First, we utilize a Brownian bridge model using mobile phone GPS data to estimate the residence and mobility parameters of the epidemic model. In the second step, we estimate the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian-inspired evolutionary algorithm (EA)—that is, a genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification in the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results demonstrate that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from the HMC method yield large credible intervals, improving their coverage for the observed and predicted daily incidences. Furthermore, we observe that the use of a multi-patch model with mobility yields improved predictions when compared to a single-patch model.
... Developments in epidemiological research have confirmed that traditional compartmental epidemic models are deficient in modeling strong heterogeneous disease spread, as they were formulated with the assumption of interaction of a well-mixed homogeneous population [15,32,33]. It is widely recognized that humans do not exhibit homogeneous mobility patterns, [15], which highlights the importance of incorporating heterogeneous population behavioral responses in epidemiological models as emphasized by [34]. The literature is replete with a plethora of proposed models for capturing human heterogeneous mobility and dispersal and most of them are mostly geo-meta-population-multi-patched based, as can be seen in [e.g., 26,27,34-42]. ...
... Human mobility, being a geo-spatio-temporal phenomena [17,43,69,70], can be modelled by meta-population-multi-patched models [4,34,39,40,42,44], as traditional homogeneous compartmental models are incapable of capturing such a strong heterogeneous human behaviour [15,17,34,51]. Once such models have been constructed, a wide spectrum of quantitative analysis that leads to deep understanding of the reciprocity of mobility and the spread of infectious diseases can be conducted. ...
... Human mobility, being a geo-spatio-temporal phenomena [17,43,69,70], can be modelled by meta-population-multi-patched models [4,34,39,40,42,44], as traditional homogeneous compartmental models are incapable of capturing such a strong heterogeneous human behaviour [15,17,34,51]. Once such models have been constructed, a wide spectrum of quantitative analysis that leads to deep understanding of the reciprocity of mobility and the spread of infectious diseases can be conducted. ...
Most studies modelling population mobility and the spread of infectious diseases, particularly using meta-population-multi-patched models, tend to focus on theoretical properties and numerical simulations of such models. There is relatively scanty literature published on fit, inference and uncertainty quantification on epidemic models with population mobility. In this research, we have used three estimation techniques to solve an inverse problem and quantify its uncertainty on a human mobility-based multi-patched epidemic model, using mobile phone sensing data and COVID-19 confirmed positive cases in Hermosillo, Mexico. First, we have utilized a Brownian bridge model using mobile phone GPS data to estimate residence and mobility parameters of the epidemic model. In the second step, we have estimated the optimal model epidemiological parameters by deterministically inverting the model using genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification on the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results show that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from HMC result into large credible intervals, improving their coverage for the observed and predicted daily incidences. We also observe improved predictions when using multi-patch model with mobility against the single-patch model.
... To introduce the human heterogeneous contacts, the epidemics in networks model (or reaction-diffusion models on meta population networks) have played an essential role in journals with a physics focus [13,12,54,47]. Nevertheless, the model inference, fit or selection, uses highly computing-intensive numeric methods such as MCMC or particle filtering based on Monte Carlo simulations. ...
Abstract
It is often necessary to introduce the main characteristics of population mobility dynamics to model critical social phenomena such as the economy, violence, transmission of information, or infectious diseases. In this work, we focus on modeling and inferring urban population mobility using the geospatial data of its inhabitants. The objective is to estimate mobility and times inhabitants spend in the areas of interest, such as zip codes and census geographical areas. The proposed method uses the Brownian bridge model for animal movement in ecology. We illustrate its possible applications using mobile phone GPS data in 2020 from the city of Hermosillo, Sonora, in Mexico. We incorporate the estimated residence-mobility matrix into a multi-patch compartmental SEIR model to assess the effect of mobility changes due to governmental interventions.
... Therefore, trips last less than one time step (i.e., day). This assumption is also consistent with recent studies [24], [53], [54], [55], [56]. ...
Understanding the feedback loop that links the spatiotemporal spread of infectious diseases and human behavior is an open problem. To study this problem, we develop a multiplex framework that couples epidemic spreading across subpopulations in a metapopulation network (i.e., physical layer) with the spreading of awareness about the epidemic in a communication network (i.e., virtual layer). We explicitly study the interactions between the mobility patterns across subpopulations and the awareness propagation among individuals. We analyze the coupled dynamics using microscopic Markov chains (MMCs) equations and validate the theoretical results via Monte Carlo (MC) simulations. We find that with the spreading of awareness, reducing human mobility becomes more effective in mitigating the large-scale epidemic. We also investigate the influence of varying topological features of the physical and virtual layers and the correlation between the connectivity and local population size per subpopulation. Overall the proposed modeling framework and findings contribute to the growing literature investigating the interplay between the spatiotemporal spread of epidemics and human behavior.
... Nowadays, some infectious diseases are still aimed at large populations [1,2]. ey are regarded as the potential causes of death, particularly in numerous developing countries [3,4]. ...
... Let the matrix function P(S, E, I) � diag(1, E/I, E/I), then P f P − 1 � diag(0, (E ′ /E) − (I ′ /I), (E ′ /E) − (I ′ /I)), matrix B � P f P − 1 + PJ[2] P − 1 can be written in the form ...
In the current study, a generalized SEIR epidemic model is studied. The generalized fractional-order SEIR model (susceptible-infected-recovered (SIR) epidemic) model differentiated the population into susceptible population, exposure population, infected population, and rehabilitation population and has fundamental mentoring importance for the forecast of the probable outburst of infectious ailments. The fundamental duplicated quantity R 0 is inferred. When R 0 < 1 , the disease-free equilibrium (DFE) is particular and tending towards stability. When R 0 > 1 , the endemic equilibrium is sole. In addition, certain circumstances are set up to make sure the local progressive stability of disease-free and endemic equilibrium. Considering the influence of the individual behavior, a broader SEIR epidemic model is raised, which classified the population into susceptible, exposure, infected, and rehabilitation. What is more, the basic reproduction number, that regulates whether the infection will die out or not, is obtained by the spectral radius of the next-generation matrix; moreover, the global stability of DFE and endemic equilibrium are analyzed by a geometry method.
... A common approach to simulate the role of human mobility is to introduce a reaction-diffusion process in the metapopulation model [15][16][17][18][19][20]. In the network, each node can represent a subpopulation consisting of many individuals, and edges indicate the mobility probabilities between different subpopulations. ...
The influence of transportation processes on the spread of epidemics has been extensively studied recently. However, the effect of origin-destination selection in different time and space is an overlooked issue. In this paper, we investigate a traffic-driven epidemic model in complex networks with non-uniform origin and destination selection. An analytic expression for the epidemic threshold is derived by expanding the generalized algorithm betweenness centrality into two forms that contain the roles of origin and destination, respectively. We find that both origin-destination selection patterns and routing protocols can significantly affect the spread of epidemics, mainly because they affect the frequency of use of hub nodes in the scale-free network. Regardless of the selection pattern, the efficient routing protocol is effective in suppressing the spread of epidemics. Besides, there exists an optimal value of routing parameter for each pattern, corresponding to the maximal epidemic threshold. This phenomenon can be explained by network properties and path lengths. Both numerical simulation and theoretical analysis reveal the incidence of epidemic spreading or the traffic flow varies at nodes with different degrees.
... This approach revealed that these two aspects are essential to assess the advisability of contention measures based on the restriction of mobility. This approach has been further generalized to include networks with multiple types of mobility 23,24 , the study of vector-borne diseases 25,26 , different permanence times on the destination 27 , the heterogeneous of different contact patterns 28 . Importantly, this Markovian framework has been used, after accounting for the particularities of SARS-CoV-2 transmission, to evaluate the evolution, and health systems impact, of COVID-19 in different countries [29][30][31] . ...
... Taking advantage of the definition of the mixing matrix M Eq. (28) can be written in a compact form as: i.e an eigenvalue problem. From all the possible solutions (eigenvectors) of Eq. (28) we are interested in the one corresponding to the minimum value of λ (as it defines the epidemic threshold of the metapopulation), that corresponds to the maximum eigenvalue of M. Thus, the epidemic threshold reads: ...
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents to alleviate analytical difficulties. Here, we address the impact that recurrent mobility patterns, and the spatial distribution of distinguishable agents, have on the unfolding of epidemics in large urban areas. We incorporate the distinguishable nature of agents regarding both, their residence, and their usual destination. The proposed model allows both a fast computation of the spatio-temporal pattern of the epidemic trajectory and. the analytical calculation of the epidemic threshold. This threshold is found as the spectral radius of a mixing matrix encapsulating the residential distribution, and the specific commuting patterns of agents. We prove that the simplification of indistinguishable individuals overestimates the value of the epidemic threshold.
... In recent times, several methods have been attempted to determine important nodes in a networked system [30][31][32][33][34][35][36][37][38][39]. However, there is no guarantee that the method of determining important nodes in a simple network is applicable because the metapopulation network includes hierarchical structures [15,27,40,41]. Moreover, there is still a lack of centrality to determine influential subpopulations in a metapopulation epidemic model based on a concrete mathematical background. ...
Identifying influential subpopulations in metapopulation epidemic models has far-reaching potential implications for surveillance and intervention policies of a global pandemic. However, there is a lack of methods to determine influential nodes in metapopulation models based on a rigorous mathematical background. In this study, we derive the message-passing theory for metapopulation modeling and propose a method to determine influential spreaders. Based on our analysis, we identify the most dangerous city as a potential seed of a pandemic when applied to real-world data. Moreover, we particularly assess the relative importance of various sources of heterogeneity at the subpopulation level, e.g., the number of connections and mobility patterns, to determine properties of spreading processes. We validate our theory with extensive numerical simulations on empirical and synthetic networks considering various mobility and transmission probabilities. We confirm that our theory can accurately predict influential subpopulations in metapopulation models.
... As Cota et al. recently noted, the unprecedented volume of digital data now available requires we -revisit epidemic models, in particular those studying the geographical spread of pathogens leveraging the mobility of hosts‖ (Cota et al., 2021). Here we take up that challenge through a focus on the Gravity Model in part because its two variables, population or mass and distance between two bodies, are central to many later models. ...
Wellness depends on health and that, in turn, depends on the absence of disease. Analogous models based on physical laws have long been utilized by researchers to understand epidemic expansion in urban communities. Perhaps the most significant of this class is the gravity model in which population size is equated with planetary mass and distance between cities to that separating planets. While the model assumes homogeneity among different bodies, cities or planets, in epidemiology the likelihood of disease spread may depend on other heterogeneous, non-constant factors. The study used a public dataset of H1N1 Influenza in 2009 as the focus. A natural log regression was applied in an attempt to sort the relative importance of gravity model variables as predictors of influenza occurrence and diffusion. It was found that while the model population size serves as a general predictor of disease expansion that distance failed as an indicator of disease dynamics. Furthermore, findings from the study show that disease progression was irregular and not, as one might expect from the gravity model, consistent in space or over time. The study concludes that the gravity model may serve only as a coarse predictor of disease expansion over time. By extension, this raises similar questions about other models in which homogeneity between populations or network of populations is assumed.
