Network inference from population-level observation of epidemics

The SAITS epidemic spreading model and its combinational optimal suppression control

In this paper, an SAITS epidemic model based on a single layer static network is proposed and investigated. This model considers a combinational suppression control strategy to suppress the spread of epidemics, which includes transferring more individuals to compartments with low infection rate and with high recovery rate. The basic reproduction number of this model is calculated and the disease-free and endemic equilibrium points are discussed. An optimal control problem is formulated to minimize the number of infections with limited resources. The suppression control strategy is investigated and a general expression for the optimal solution is given based on the Pontryagin's principle of extreme value. The validity of the theoretical results is verified by numerical simulations and Monte Carlo simulations.

Probabilistic predictions of SIS epidemics on networks based on population-level observations

We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erdős-Rényi and Barabási-Albert networks. It is known that the contact network influences the spread of an epidemic within a population. Therefore, observations of an epidemic, in this case at the population-level, contain information about the underlying network. This information, in turn, is useful for predicting the future course of an ongoing epidemic. To exploit this in a prediction framework, the exact high-dimensional stochastic model of an SIS epidemic on a network is approximated by a lower-dimensional surrogate model. The surrogate model is based on a birth-and-death process; the effect of the underlying network is described by a parametric model for the birth rates. We demonstrate empirically that the surrogate model captures the intrinsic stochasticity of the epidemic once it reaches a point from which it will not die out. Bayesian parameter inference allows for uncertainty about the model parameters and the class of the underlying network to be incorporated directly into probabilistic predictions. An evaluation of a number of scenarios shows that in most cases the resulting prediction intervals adequately quantify the prediction uncertainty. As long as the population-level data is available over a long-enough period, even if not sampled frequently, the model leads to excellent predictions where the underlying network is correctly identified and prediction uncertainty mainly reflects the intrinsic stochasticity of the spreading epidemic. For predictions inferred from shorter observational periods, uncertainty about parameters and network class dominate prediction uncertainty. The proposed method relies on minimal data at population-level, which is always likely to be available. This, combined with its numerical efficiency, makes the proposed method attractive to be used either as a standalone inference and prediction scheme or in conjunction with other inference and/or predictive models.

Asymptotic Absorption-Time Distributions in Extinction-Prone Markov Processes

We characterize absorption-time distributions for birth-death Markov chains with an absorbing boundary. For "extinction-prone" chains (which drift on average toward the absorbing state) the asymptotic distribution is Gaussian, Gumbel, or belongs to a family of skewed distributions. The latter two cases arise when the dynamics slow down dramatically near the boundary. Several models of evolution, epidemics, and chemical reactions fall into these classes; in each case we establish new results for the absorption-time distribution. Applications to African sleeping sickness are discussed.

First detection of threshold crossing events under intermittent sensing

The time taken by a random variable to cross a threshold for the first time, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional "sensor" monitoring the threshold crossing event is always active. In many realistic scenarios, the sensor monitoring the stochastic process works intermittently. Then, the relevant quantity of interest is the first detection time, which denotes the time when the sensor detects the random variable to be above the threshold for the first time. In this Letter, a birth-death process monitored by a random intermittent sensor is studied for which the first detection time distribution is obtained. In general, it is shown that the first detection time is related to and is obtainable from the first passage time distribution. Our analytical results display an excellent agreement with simulations. Furthermore, this framework is demonstrated in several applications-the susceptible infected susceptible compartmental and logistic models and birth-death processes with resetting. Finally, we solve the practically relevant problem of inferring the first passage time distribution from the first detection time.

Association of TNFRSF1A and IFNLR1 Gene Polymorphisms with the Risk of Developing Breast Cancer and Clinical Pathologic Features

Several genes have been associated with breast cancer (BC) susceptibility. The tumor necrosis factor receptor superfamily, member 1A (TNFRSF1A), and interferon lambda receptor 1 (IFNLR1) genes encode receptors that mediate the action of inflammatory cytokines. Previous studies have demonstrated the association of the variants rs1800693 (TNFRSF1A) and rs4649203 (IFNLR1) with some inflammatory diseases. The present study aimed to verify a possible association of these variants with BC, its clinical pathologic features, as well as epidemiological data in a Brazilian population. A total of 243 patients and 294 individuals without history of BC were genotyped for these polymorphisms through TaqMan® SNP genotyping assays by qPCR. For the TNFRSF1A gene, no significant results were found. For IFNLR1, the AA genotype (p = 0.008) and the A allele (p = 0.02) were significantly associated with a lower risk of developing BC. When analyzing the age, it was observed that each increase of one year contributes to the development of BC (p < 0.001). Also, the smoking habit (p < 0.001) and body mass index (p = 0.018) increase the risk of disease development. Analyzing progesterone receptor factor an association was found with the AA genotype of the IFNLR1 (p = 0.02). The findings suggest that polymorphism in the immune-related IFNLR1 gene contribute to BC susceptibility in a Brazilian population. These findings can contribute to the further understanding of the role this gene and pathways in BC development.

Network-inference-based prediction of the COVID-19 epidemic outbreak in the Chinese province Hubei

At the moment of writing, the future evolution of the COVID-19 epidemic is unclear. Predictions of the further course of the epidemic are decisive to deploy targeted disease control measures. We consider a network-based model to describe the COVID-19 epidemic in the Hubei province. The network is composed of the cities in Hubei and their interactions (e.g., traffic flow). However, the precise interactions between cities is unknown and must be inferred from observing the epidemic. We propose the Network-Inference-Based Prediction Algorithm (NIPA) to forecast the future prevalence of the COVID-19 epidemic in every city. Our results indicate that NIPA is beneficial for an accurate forecast of the epidemic outbreak.