Extinction pathways and outbreak vulnerability in a stochastic Ebola model

Extinction in host-vector infection models and the role of heterogeneity

For infections that become endemic in a population, the process may appear stable over a long time scale, but stochastic fluctuations can lead to eventual disease extinction. We consider the effects of model parameters and of population heterogeneities upon the expected time to extinction for host-vector disease systems. We find that non-homogeneous host selection by vectors increases persistence times relative to the homogeneous case, and that the effect becomes even more marked when there are strong associations between particular groups of vectors and hosts. Heterogeneity in vector lifespans, in contrast, is found to decrease persistence times relative to the homogeneous case. Neither the basic reproduction number R0, nor the endemic prevalence level in the corresponding deterministic model, is found to be sufficient to predict (for a given population size) time to extinction. The endemic level, in particular, proves a very unreliable guide to the duration of long-term persistence.

Controlling epidemic extinction using early warning signals

As the recent COVID-19 pandemic has shown us, there is a critical need to develop new approaches to monitoring the outbreak and spread of infectious disease. Improvements in monitoring will enable a timely implementation of control measures, including vaccine and quarantine, to stem the spread of disease. One such approach involves the use of early warning signals to detect when critical transitions are about to occur. Although the early detection of a stochastic transition is difficult to predict using the generic indicators of early warning signals theory, the changes detected by the indicators do tell us that some type of transition is taking place. This observation will serve as the foundation of the method described in the article. We consider a susceptible–infectious–susceptible epidemic model with reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0>1$$\end{document}R0>1 so that the deterministic endemic equilibrium is stable. Stochastically, realizations will fluctuate around this equilibrium for a very long time until, as a rare event, the noise will induce a transition from the endemic state to the extinct state. In this article, we describe how metric-based indicators from early warning signals theory can be used to monitor the state of the system. By measuring the autocorrelation, return rate, skewness, and variance of the time series, it is possible to determine when the system is in a weakened state. By applying a control that emulates vaccine/quarantine when the system is in this weakened state, we can cause the disease to go extinct earlier than it otherwise would without control. We also demonstrate that applying a control at the wrong time (when the system is in a non-weakened, highly resilient state) can lead to a longer extinction time than if no control had been applied. This feature underlines the importance of determining the system’s state of resilience before attempting to affect its behavior through control measures.

Characterizing outbreak vulnerability in a stochastic SIS model with an external disease reservoir

In this article, we take a mathematical approach to the study of population-level disease spread, performing a quantitative and qualitative investigation of an SISκ model which is a susceptible-infectious-susceptible ( SIS ) model with exposure to an external disease reservoir. The external reservoir is non-dynamic, and exposure from the external reservoir is assumed to be proportional to the size of the susceptible population. The full stochastic system is modelled using a master equation formalism. A constant population size assumption allows us to solve for the stationary probability distribution, which is then used to investigate the predicted disease prevalence under a variety of conditions. By using this approach, we quantify outbreak vulnerability by performing the sensitivity analysis of disease prevalence to changing population characteristics. In addition, the shape of the probability density function is used to understand where, in parameter space, there is a transition from disease free, to disease present, and to a disease endemic system state. Finally, we use Kullback–Leibler divergence to compare our semi-analytical results for the SISκ model with more complex susceptible-infectious-recovered ( SIR ) and susceptible-exposed-infectious-recovered ( SEIR ) models.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

A key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general, this question requires the use of stochastic models which recognize the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable; however, their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective ‘birth–death’ description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth–death framework. We show that these predictions agree very well with the results of stochastic models by analysing the simplified susceptible–infected–susceptible (SIS) dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).

STEM: An Open Source Tool for Disease Modeling

The Spatiotemporal Epidemiologic Modeler (STEM) is an open source software project supported by the Eclipse Foundation and used by a global community of researchers and public health officials working to track and, when possible, control outbreaks of infectious disease in human and animal populations. STEM is not a model or a tool designed for a specific disease; it is a flexible, modular framework supporting exchange and integration of community models, reusable plug-in components, and denominator data, available to researchers worldwide at www.eclipse.org/stem. A review of multiple projects illustrates its capabilities. STEM has been used to study variations in transmission of seasonal influenza in Israel by strains; evaluate social distancing measures taken to curb the H1N1 epidemic in Mexico City; study measles outbreaks in part of London and inform local policy on immunization; and gain insights into H7N9 avian influenza transmission in China. A multistrain dengue fever model explored the roles of the mosquito vector, cross-strain immunity, and antibody response in the frequency of dengue outbreaks. STEM has also been used to study the impact of variations in climate on malaria incidence. During the Ebola epidemic, a weekly conference call supported the global modeling community; subsequent work modeled the impact of behavioral change and tested disease reintroduction via animal reservoirs. Work in Germany tracked salmonella in pork from farm to fork; and a recent doctoral dissertation used the air travel feature to compare the potential threats posed by weaponizing infectious diseases. Current projects include work in Great Britain to evaluate control strategies for parasitic disease in sheep, and in Germany and Hungary, to validate the model and inform policy decisions for African swine fever. STEM Version 4.0.0, released in early 2019, includes tools used in these projects and updates technical aspects of the framework to ease its use and re-use.

The Spatiotemporal Epidemiologic Modeler (STEM) is an open source software project supported by the Eclipse Foundation and used by a global community of researchers and public health officials working to track and, when possible, control outbreaks of infectious disease in human and animal populations. STEM is not a model or a tool designed for a specific disease; it is a flexible, modular framework supporting exchange and integration of community models, reusable plug‐in components, and denominator data, available to researchers worldwide.

Recommendations for ‘The City in Need’

As the body first deteriorates and then reaches immunity against a disease, the city also first suffers and then becomes more resilient by the end of an outbreak event. The city may not become fully immune, but will be more experienced and prepared with a much enhanced resilience for the future.

Viral Infections in Pregnancy: A Focus on Ebola Virus

During gestation, the immune response of the placenta to viruses and other pathogens plays an important role in determining a pregnant woman's vulnerability toward infectious diseases. Located at the maternalfetal interface, trophoblast cells serve to minimize the spread of viruses between the host and developing fetus through an intricate system of innate antiviral immune signaling. Adverse pregnancy outcomes, ranging from learning disabilities to preterm birth and fetal death, are all documented results of a viral breach in the placental barrier. Viral infections during pregnancy can also be spread through blood and vaginal secretions, and during the post-natal period, via breast milk. Thus, even in the absence of vertical transmission of viral infection to the fetus, maternal health can still be compromised and threaten the pregnancy. The most common viral DNA isolates found in gestation are adenovirus, cytomegalovirus, and enterovirus. However, with the recent pandemic of Ebola virus, and the first documented case of a neonate to survive due to experimental therapies in 2017, it is becoming increasingly apparent that the changing roles and impacts of viral infection during pregnancy needs to be better understood, while strategies to minimize adverse pregnancy outcomes need to be identified. This review focuses on the adverse impacts of viral infection during gestation, with an emphasis on Ebola virus.

Degree Dispersion Increases the Rate of Rare Events in Population Networks

There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this Letter, we show that degree dispersion-the fact that the number of local connections in networks varies broadly-increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network's degree distribution over its mean squared.

Using control to shape stochastic escape and switching dynamics

We present a strategy to control the mean stochastic switching times of general dynamical systems with multiple equilibrium states subject to Gaussian white noise. The control can either enhance or abate the probability of escape from the deterministic region of attraction of a stable equilibrium in the presence of external noise. We synthesize a feedback control strategy that actively changes the system's mean stochastic switching behavior based on the system's distance to the boundary of the attracting region. With the proposed controller, we are able to achieve a desired mean switching time, even when the strength of noise in the system is not known. The control method is analytically validated using a one-dimensional system, and its effectiveness is numerically demonstrated for a set of dynamical systems of practical importance.

New perspectives for the prediction and statistical quantification of extreme events in high-dimensional dynamical systems

We discuss extreme events as random occurrences of strongly transient dynamics that lead to nonlinear energy transfers within a chaotic attractor. These transient events are the result of finite-time instabilities and therefore are inherently connected with both statistical and dynamical properties of the system. We consider two classes of problems related to extreme events and nonlinear energy transfers, namely (i) the derivation of precursors for the short-term prediction of extreme events, and (ii) the efficient sampling of random realizations for the fastest convergence of the probability density function in the tail region. We summarize recent methods on these problems that rely on the simultaneous consideration of the statistical and dynamical characteristics of the system. This is achieved by combining available data, in the form of second-order statistics, with dynamical equations that provide information for the transient events that lead to extreme responses. We present these methods through two high-dimensional, prototype systems that exhibit strongly chaotic dynamics and extreme responses due to transient instabilities, the Kolmogorov flow and unidirectional nonlinear water waves.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Stochastic dynamics of an epidemic with recurrent spillovers from an endemic reservoir

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Stochastic SIR with reservoir to describe the dynamics of pathogens in a host.

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Branching process approximations are provided.

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Recurrent spillover cause multiple outbreaks even for a pathogen barely contagious.

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Spillover and direct transmission have similar importance for pathogens dynamics.

Most emerging human infectious diseases have an animal origin. While zoonotic diseases originate from a reservoir, most theoretical studies have principally focused on single-host processes, either exclusively humans or exclusively animals, without considering the importance of animal to human transmission (i.e. spillover transmission) for understanding the dynamics of emerging infectious diseases. Here we aim to investigate the importance of spillover transmission for explaining the number and the size of outbreaks. We propose a simple continuous time stochastic Susceptible-Infected-Recovered model with a recurrent infection of an incidental host from a reservoir (e.g. humans by a zoonotic species), considering two modes of transmission, (1) animal-to-human and (2) human-to-human. The model assumes that (i) epidemiological processes are faster than other processes such as demographics or pathogen evolution and that (ii) an epidemic occurs until there are no susceptible individuals left. The results show that during an epidemic, even when the pathogens are barely contagious, multiple outbreaks are observed due to spillover transmission. Overall, the findings demonstrate that the only consideration of direct transmission between individuals is not sufficient to explain the dynamics of zoonotic pathogens in an incidental host.