No Arabic abstract
Mathematical and computational modeling approaches are increasingly used as quantitative tools in the analysis and forecasting of infectious disease epidemics. The growing need for realism in addressing complex public health questions is however calling for accurate models of the human contact patterns that govern the disease transmission processes. Here we present a data-driven approach to generate effective descriptions of population-level contact patterns by using highly detailed macro (census) and micro (survey) data on key socio-demographic features. We produce age-stratified contact matrices for 277 sub-national administrative regions of countries covering approximately 3.5 billion people and reflecting the high degree of cultural and societal diversity of the focus countries. We use the derived contact matrices to model the spread of airborne infectious diseases and show that sub-national heterogeneities in human mixing patterns have a marked impact on epidemic indicators such as the reproduction number and overall attack rate of epidemics of the same etiology. The contact patterns derived here are made publicly available as a modeling tool to study the impact of socio-economic differences and demographic heterogeneities across populations on the epidemiology of infectious diseases.
We explore the application of probability generating functions (PGFs) to invasive processes, focusing on infectious disease introduced into large populations. Our goal is to acquaint the reader with applications of PGFs, moreso than to derive new results. PGFs help predict a number of properties about early outbreak behavior while the population is still effectively infinite, including the probability of an epidemic, the size distribution after some number of generations, and the cumulative size distribution of non-epidemic outbreaks. We show how PGFs can be used in both discrete-time and continuous-time settings, and discuss how to use these results to infer disease parameters from observed outbreaks. In the large population limit for susceptible-infected-recovered (SIR) epidemics PGFs lead to survival-function based models that are equivalent the the usual mass-action SIR models but with fewer ODEs. We use these to explore properties such as the final size of epidemics or even the dynamics once stochastic effects are negligible. We target this tutorial to biologists and public health researchers who want to learn how to apply PGFs to invasive diseases, but it could also be used in an introductory mathematics course on PGFs. We include many exercises to help demonstrate concepts and to give practice applying the results. We summarize our main results in a few tables. Additionally we provide a small python package which performs many of the relevant calculations.
Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control policies, but may be hindered by incomplete data in some regions of the world. Here we explore the opportunity of using proxy data or models for individual mobility to describe commuting movements and predict the diffusion of infectious disease. We consider three European countries and the corresponding commuting networks at different resolution scales obtained from official census surveys, from proxy data for human mobility extracted from mobile phone call records, and from the radiation model calibrated with census data. Metapopulation models defined on the three countries and integrating the different mobility layers are compared in terms of epidemic observables. We show that commuting networks from mobile phone data well capture the empirical commuting patterns, accounting for more than 87% of the total fluxes. The distributions of commuting fluxes per link from both sources of data - mobile phones and census - are similar and highly correlated, however a systematic overestimation of commuting traffic in the mobile phone data is observed. This leads to epidemics that spread faster than on census commuting networks, however preserving the order of infection of newly infected locations. Match in the epidemic invasion pattern is sensitive to initial conditions: the radiation model shows higher accuracy with respect to mobile phone data when the seed is central in the network, while the mobile phone proxy performs better for epidemics seeded in peripheral locations. Results suggest that different proxies can be used to approximate commuting patterns across different resolution scales in spatial epidemic simulations, in light of the desired accuracy in the epidemic outcome under study.
How can we model influence between individuals in a social system, even when the network of interactions is unknown? In this article, we review the literature on the influence model, which utilizes independent time series to estimate how much the state of one actor affects the state of another actor in the system. We extend this model to incorporate dynamical parameters that allow us to infer how influence changes over time, and we provide three examples of how this model can be applied to simulated and real data. The results show that the model can recover known estimates of influence, it generates results that are consistent with other measures of social networks, and it allows us to uncover important shifts in the way states may be transmitted between actors at different points in time.
The contact structure of a population plays an important role in transmission of infection. Many ``structured models capture aspects of the contact structure through an underlying network or a mixing matrix. An important observation in such models, is that once a fraction $1-1/mathcal{R}_0$ has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunizing higher-risk individuals who play a greater role in transmission. Therefore, a limited ``first wave may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we systematically analyse a number of mean-field models for networks and other structured populations to address issues relevant to the Covid-19 pandemic. In particular, we consider herd-immunity under several scenarios. We confirm that, in networks with high degree heterogeneity, the first wave confers herd-immunity with significantly fewer infections than equivalent models with lower degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect might become more subtle. Indeed, modifying the structure can shield highly connected nodes from becoming infected during the first wave and make the second wave more substantial. We confirm this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. We find that results regarding herd immunity levels are strongly dependent on the model, the duration of lockdown and how lockdown is implemented.
Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations that often involve privacy issues, e.g., tracking mobile phone locations, or by estimations from models. Typically, such models build on accurate knowledge of the population size at each location. However, when this information is not readily available, their applicability is rather limited. As mobile phones are ubiquitous, our aim is to investigate if mobility patterns can be inferred from aggregated mobile phone call data alone. Using data released by Orange for Ivory Coast, we show that human mobility is well predicted by a simple model based on the frequency of mobile phone calls between two locations and their geographical distance. We argue that the strength of the model comes from directly incorporating the social dimension of mobility. Furthermore, as only aggregated call data is required, the model helps to avoid potential privacy problems.