Predicting epidemic evolution on contact networks from partial observations

The massive employment of computational models in network epidemiology calls for the development of improved inference methods for epidemic forecast. For simple compartment models, such as the Susceptible-Infected-Recovered model, Belief Propagation was proved to be a reliable and efficient method to identify the origin of an observed epidemics. Here we show that the same method can be applied to predict the future evolution of an epidemic outbreak from partial observations at the early stage of the dynamics. The results obtained using Belief Propagation are compared with Monte Carlo direct sampling in the case of SIR model on random (regular and power-law) graphs for different observation methods and on an example of real-world contact network. Belief Propagation gives in general a better prediction that direct sampling, although the quality of the prediction depends on the quantity under study (e.g. marginals of individual states, epidemic size, extinction-time distribution) and on the actual number of observed nodes that are infected before the observation time

Impact of Diffusion on synchronization pattern of epidemics in nonidentical metapopulation networks

In a prior study, a novel deterministic compartmental model known as the SEIHRK model was introduced, shedding light on the pivotal role of test kits as an intervention strategy for mitigating epidemics. Particularly in heterogeneous networks, it was empirically demonstrated that strategically distributing a limited number of test kits among nodes with higher degrees substantially diminishes the outbreak size. The network's dynamics were explored under varying values of infection rate. In this research, we expand upon these findings to investigate the influence of migration on infection dynamics within distinct communities of the network. Notably, we observe that nodes equipped with test kits and those without tend to segregate into two separate clusters when coupling strength is low, but beyond a critical threshold coupling coefficient, they coalesce into a unified cluster. Building on this clustering phenomenon, we develop a reduced equation model and rigorously validate its accuracy through comprehensive simulations. We show that this property is observed in both complete and random graphs.Comment: 8 figures, 15 pages including citation

Heterogeneous network epidemics: real-time growth, variance and extinction of infection

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process. We find closed-form analytic expressions for the mean and variance of the number of infectious individuals as a function of time and the degree of the initially infected individual(s), and write down a system of differential equations for the probability of extinction by time t that are numerically fast compared to Monte Carlo simulation. We show that these quantities are all sensitive to the degree distribution—in particular we confirm that the mean prevalence of infection depends on the first two moments of the degree distribution and the variance in prevalence depends on the first three moments of the degree distribution. In contrast to most existing analytic approaches, the accuracy of these results does not depend on having a large number of infectious individuals, meaning that in the large population limit they would be asymptotically exact even for one initial infectious individual

Belief Propagation approach to epidemics prediction on networks

In my thesis I study the problem of predicting the evolution of the epidemic spreading on networks when incomplete information, in form of a partial observation, is available. I focus on the irreversible process described by the discrete time version of the Susceptible-Infected-Recovered (SIR) model on networks. Because of its intrinsic stochasticity, forecasting the SIR process is very difficult, even if the structure of individuals contact pattern is known. In today's interconnected and interdependent society, infectious diseases pose the threat of a worldwide epidemic spreading, hence governments and public health systems maintain surveillance programs to report and control the emergence of new disease event ranging from the seasonal influenza to the more severe HIV or Ebola. When new infection cases are discovered in the population it is necessary to provide real-time forecasting of the epidemic evolution. However the incompleteness of accessible data and the intrinsic stochasticity of the contagion pose a major challenge. The idea behind the work of my thesis is that the correct inference of the contagion process before the detection of the disease permits to use all the available information and, consequently, to obtain reliable predictions. I use the Belief Propagation approach for the prediction of SIR epidemics when a partial observation is available. In this case the reconstruction of the past dynamics can be efficiently performed by this method and exploited to analyze the evolution of the disease. Although the Belief Propagation provides exact results on trees, it turns out that is still a good approximation on general graphs. In this cases Belief Propagation may present convergence related issues, especially on dense networks. Moreover, since this approach is based on a very general principle, it can be adapted to study a wide range of issues, some of which I analyze in the thesis

Use of Epidemiological and Geostatistical Methods to Understand the Epidemic of Homicides in Baltimore, 2005 to 2017

Violence is widely recognized as a public health problem. Baltimore, Maryland, a city 45 miles north of Washington, DC, has experienced homicide rates several times higher than those experienced by the United States as a country since at least 1975. Since 2015, Baltimore City has experienced an epidemic of homicides, with an average homicide rate of over 50 homicides per 100,000 residents. We analyzed the individual social characteristics of the victims of homicide in Baltimore City between 2005 and 2017. We used descriptive epidemiology to understand the distribution of social risk factors for victimization in individuals. We also used information on the location of homicides in this time period — along with socioeconomic information on Community Statistical Areas (CSA) — to understand the association between neighborhood environmental characteristics and the homicide rates in those CSAs. We finally took inventory of violence prevention programs existing in Baltimore City as of 2017, and we compared the goals of those programs with the findings from the analysis of victims and the victim location. Through the use of epidemiological and geostatistical methods, we found that not all segments of the population of Baltimore City experienced the same levels of homicide victimization. African American men between the ages of 15 and 34 made up over 61% of the homicide victims between 2005 and 2017 in Baltimore City. Most of the homicides showed spatial clustering around CSAs with elevated levels of poverty and disorder (e.g. broken street lights). Hot spot analysis using person, place, and time showed that hot spots tended to appear or disappear depending on the year of the homicides. The government and civil society in Baltimore City are working in different ways to address violence. Existing programs would do well to expand into the emerging hot spots of homicides, while other programs would probably have a greater impact on violence if they combined efforts and focused on a specific segment of the population. Finally, there is a great opportunity for healthcare providers to treat violence with the same approaches as other public health problems

Extinction Times of Epidemic Outbreaks in Networks

In the Susceptible–Infectious–Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold