One of the primary goals in developing countries as Senegal consist in identifying outbreaks of endemic and communicable diseases, and preventing their spreading in the country and neighboring countries, without having a major health surveillance system. A possibility, exploited in the current work, is to analyze call records to infer mobility patterns and then the natural flow of epidemic contagion between individuals. The analysis is applicable in the full range of scales, from individuals to regions, providing a proxy for monitoring outbreaks and prevent their spreading. Our proposal consists in a memory-driven mobility model that captures the mobility patterns beyond the state of the art, by assigning high resolved probabilities to transitions between different arrondissements. Moreover, we complement the model with a game theoretical approach to the dilemma faced by individuals affording counter-measures to the epidemic spreading. Our results allow an accurate tracking of an epidemic outbreak, and provides enlightening control parameters to reduce the incidence of the spreading process based on cost reduction and social reinforcement.
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Maps of Senegal arrondissements color-coded by different information, namely population, mobile phone activity and Twitter activity.
Multilayer visualization (done with muxviz) of mobility and communication (calls and tweets) patterns in Senegal. Links between pairs of arrondissements indicate the existence of a significant mobility or communication flow between them. Our mobility model coupled to spreading dynamics and social dilemma can be also coupled to communication patterns from multivariate channels (e.g. CDR, online social networks, etc) to identify key arrondissements for information dissemination using multilayer centrality.
Mobility models built from a representative sequence of mobile phone calls (SSSCCCCSSSSBBBBBCCCBB) made by an individual during travels between three American cities, namely Chicago (C), San Antonio (S) and Baltimore (B). The first-order and second-order models fail to capture evident returning patterns, whereas the adaptive memory approach, introduced in this work, correctly identify such patterns.
Interactions between susceptible and infected individuals in a meta-population. The SEIR transmission model involves four different compartments, with individuals being in one compartment or another depending at which stage of the disease they are (susceptible, exposed, infected, recovered or removed). In the first-order mobility model (A), susceptible individuals in the compartment S can be infected by individuals in the compartment I within the same physical node. In the adaptive memory mobility model (B) susceptible individuals in each state-node can be infected by interactions (here indicated by dotted arrows) with individual belonging to the compartment I of any other state-node within the same physical node.
Mobility flow among a sub-set of Senegal's arrondissements using two different models, first-order (A) and adaptive memory (B). This circular visualization is suitable for identifying mobility patterns. The size of the flow is proportional to the width of the link and different colors are assigned to different links. The direction of the flow is encoded by the gap between link and circle segment at destination: links closer (farther) to the circle indicate origin (destination).
Evolution over time of mobility descriptors using first-order (FO) and adaptive memory (AM) modeling. Coverage (A) averaged over all nodes, mean return time (B) averaged over all nodes and global mean first passage time (C), obtained by averaging over all mean first passage times -- excluding return times. The error bars indicate the standard deviation from the mean. The difference between the curves corresponding to the two models tends to rapidly increase over time. (Note that the temporal axis is in logarithmic scale). The coverage and the mean return time are also calculated in each arrondissement separately and a scatter plot between their ranks obtained using FO and AM mobility models are shown in panels D and E, respectively. Color codes the relative difference between the values obtained from the two models, size is proportional to the population of the Department including the corresponding arrondissement as sub-administrative unit. In panel F is shown the relative difference between the mean first passage times obtained using FO and AM mobility models (color-coded), for each origin-destination pair.
Simulated spreading of an infective disease in Senegal. The spatial incidence at arrondissement level after 1~day is shown for for the first-order (A) and the adaptive memory plus adoption dilemma (B) models, where the color gradient is proportional to the number of infected individuals. The temporal evolution of the number of infected arrondissements obtained from both models is shown in panel C, whereas we show their relative difference in panel D. The percentage of infected individuals per arrondissement with respect to the arrondissement's population is calculated and the median of the resulting distribution is shown in panel E, whereas the relative difference between the two models is shown in panel F.
Comparison between the temporal evolution of a spreading process not accounting (A) and accounting (B) for social dilemma dynamics. The fraction of susceptible, exposed, infected and recovered individuals in the whole country is shown for each model versus time. Non-adopter individuals get infected with probability betaNegA=0.07, whereas adopter individuals get infected with probability betaA=0.0007. The cost of the adoption (c) is considered to be 1 per cent of the penalty for being infected P. The absolute difference between adoption and non-adoption dynamical processes is shown in panel C.
Summarizing, we have presented a model that improves significantly our prediction of the incidence of epidemics based on mobility patterns inferred from call detail records. The basic idea is to account for roundtrips by storing information about (memory) departure and arrival inferred from CDR and to take advantage of such information to infer mobility tracks. The adaptive memory model is complemented with a social dilemma that allows to explore initiatives based on social reinforcement, tax reduction, etc. to alleviate the cost (economic, cultural, social, etc.) of individuals who adopt countermeasures suggested by policy makers against epidemic processes. The results of our model are accurate enough to design targeted campaigns, using mobile phone communication channels, to widespread social action for weakening the incidence of an epidemics. In the case of Senegal, we were able to map with high resolution, at the level of arrondissements, the predicted incidence of the disease after a specific outbreak. These results could be of capital importance in helping policy-makers to simulate and forecast the outcome of their interventions in the health system. We devise that the current results can be enhanced by i) using transition matrices at tower level instead of district level; ii) considering the temporal evolution of the mobility matrices; and iii) including in the model additional layers of information awareness. All these facts makes the current work not a final method but an innovative starting point for new developments in social sensing and forecasting methods, where more high-quality social data from other sources (e.g. Twitter, Facebook) can be accounted for in a multilayer framework to ameliorate health policies devoted to predict, contain and eradicate contagion spreading.