How heterogeneous susceptibility and recovery rates affect the spread of epidemics on networks

Infectious Disease Modeling with Socio-Viral Behavioral Aspects-Lessons Learned from the Spread of SARS-CoV-2 in a University

When it comes to understanding the spread of COVID-19, recent studies have shown that pathogens can be transmitted in two ways: direct contact and airborne pathogens. While the former is strongly related to the distancing behavior of people in society, the latter are associated with the length of the period in which the airborne pathogens remain active. Considering those facts, we constructed a compartmental model with a time-dependent transmission rate that incorporates the two sources of infection. This paper provides an analytical and numerical study of the model that validates trivial insights related to disease spread in a responsive society. As a case study, we applied the model to the COVID-19 spread data from a university environment, namely, the Institut Teknologi Bandung, Indonesia, during its early reopening stage, with a constant number of students. The results show a significant fit between the rendered model and the recorded cases of infections. The extrapolated trajectories indicate the resurgence of cases as students' interaction distance approaches its natural level. The assessment of several strategies is undertaken in this study in order to assist with the school reopening process.

Characterizing tuberculosis transmission dynamics in high-burden urban and rural settings

Mycobacterium tuberculosis transmission dynamics in high-burden settings are poorly understood. Growing evidence suggests transmission may be characterized by extensive individual heterogeneity in secondary cases (i.e., superspreading), yet the degree and influence of such heterogeneity is largely unknown and unmeasured in high burden-settings. We conducted a prospective, population-based molecular epidemiology study of TB transmission in both an urban and rural setting of Botswana, one of the highest TB burden countries in the world. We used these empirical data to fit two mathematical models (urban and rural) that jointly quantified both the effective reproductive number, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R$$\end{document}R, and the propensity for superspreading in each population. We found both urban and rural populations were characterized by a high degree of individual heterogeneity, however such heterogeneity disproportionately impacted the rural population: 99% of secondary transmission was attributed to only 19% of infectious cases in the rural population compared to 60% in the urban population and the median number of incident cases until the first outbreak of 30 cases was only 32 for the rural model compared to 791 in the urban model. These findings suggest individual heterogeneity plays a critical role shaping local TB epidemiology within subpopulations.

Mitigating bias in estimating epidemic severity due to heterogeneity of epidemic onset and data aggregation

Outbreaks of infectious diseases, such as influenza, are a major societal burden. Mitigation policies during an outbreak or pandemic are guided by the analysis of data of ongoing or preceding epidemics. The reproduction number, R0, defined as the expected number of secondary infections arising from a single individual in a population of susceptibles is critical to epidemiology. For typical compartmental models such as the Susceptible-Infected-Recovered (SIR) R0 represents the severity of an epidemic. It is an estimate of the early-stage growth rate of an epidemic and is an important threshold parameter used to gain insights into the spread or decay of an outbreak. Models typically use incidence counts as indicators of cases within a single large population; however, epidemic data are the result of a hierarchical aggregation, where incidence counts from spatially separated monitoring sites (or sub-regions) are pooled and used to infer R0. Is this aggregation approach valid when the epidemic has different dynamics across the regions monitored? We characterize bias in the estimation of R0 from a merged data set when the epidemics of the sub-regions, used in the merger, exhibit delays in onset. We propose a method to mitigate this bias, and study its efficacy on synthetic data as well as real-world influenza and COVID-19 data.

Effect of time-dependent infectiousness on epidemic dynamics

In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive numbers and epidemic dynamics for a model incorporating time-dependent infectiousness and a standard SIR (susceptible-infected-recovered) model for both fully mixed and category-mixed populations. We find that the reproductive number depends only on the total infectious exposure and the largest eigenvalue of the mixing matrix and that these two effects are independent of each other. When we compare our time-dependent mean-field model to the SIR model with equivalent rates, the epidemic peak is advanced, and modifying the infection rate function has a strong effect on the time dynamics of the epidemic. We also observe behavior akin to a traveling wave as individuals transition through infectious states.

Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number [Formula: see text] on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life face-to-face contact networks. These results suggest that the hardest hit areas, such as New York City, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

Impact of the distribution of recovery rates on disease spreading in complex networks

We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heterogeneity. Our analytical solution is able to predict the shift in the critical properties induced by heterogeneous recovery rates. We find that the critical value of infectivity tends to be smaller than the one predicted by quenched mean-field approaches in the homogeneous case and that it can be linked to the variance of the recovery rates. Our findings also illustrate the role of dynamical-structural correlations, where we allow a power-law network to dynamically behave as a homogeneous structure by an appropriate tuning of its recovery rates. Overall, our results demonstrate that heterogeneity in the recovery rates, eventually in all dynamical parameters, is as important as the structural heterogeneity.

Spreading of computer viruses on time-varying networks

Social networks are the prime channel for the spreading of computer viruses. Yet the study of their propagation neglects the temporal nature of social interactions and the heterogeneity of users' susceptibility. Here, we introduce a theoretical framework that captures both properties. We study two realistic types of viruses propagating on temporal networks featuring Q categories of susceptibility and derive analytically the invasion threshold. We found that the temporal coupling of categories might increase the fragility of the system to cyber threats. Our results show that networks' dynamics and their interplay with users' features are crucial for the spreading of computer viruses.

Disease persistence on temporal contact networks accounting for heterogeneous infectious periods

The infectious period of a transmissible disease is a key factor for disease spread and persistence. Epidemic models on networks typically assume an identical average infectious period for all individuals, thus allowing an analytical treatment. This simplifying assumption is, however, often unrealistic, as hosts may have different infectious periods, due, for instance, to individual host-pathogen interactions or inhomogeneous access to treatment. While previous work accounted for this heterogeneity in static networks, a full theoretical understanding of the interplay of varying infectious periods and time-evolving contacts is still missing. Here, we consider a susceptible-infectious-susceptible epidemic on a temporal network with host-specific average infectious periods, and develop an analytical framework to estimate the epidemic threshold, i.e. the critical transmissibility for disease spread in the host population. Integrating contact data for transmission with outbreak data and epidemiological estimates, we apply our framework to three real-world case studies exploring different epidemic contexts-the persistence of bovine tuberculosis in southern Italy, the spread of nosocomial infections in a hospital, and the diffusion of pandemic influenza in a school. We find that the homogeneous parametrization may cause important biases in the assessment of the epidemic risk of the host population. Our approach is also able to identify groups of hosts mostly responsible for disease diffusion who may be targeted for prevention and control, aiding public health interventions.