A simple SIS epidemic model with a backward bifurcation

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Endemic persistence or disease extinction: The effect of separation into sub-communities

Consider an infectious disease which is endemic in a population divided into several large sub-communities that interact. Our aim is to understand how the time to extinction is affected by the level of interaction between communities. We present two approximations of the expected time to extinction in a population consisting of a small number of large sub-communities. These approximations are described for an SIR epidemic model, with focus on diseases with short infectious period in relation to life length, such as childhood diseases. Both approximations are based on Markov jump processes. Simulations indicate that the time to extinction is increasing in the degree of interaction between communities. This behaviour can also be seen in our approximations in relevant regions of the parameter space.     

An SEIS epidemic model with transport-related infection

In this paper, an SEIS epidemic model is proposed to study the effect of transport-related infection on the spread and control of infectious disease. New result implies that traveling of the exposed (means exposed but not yet infectious) individuals can bring disease from one region to other regions even if the infectious individuals are inhibited from traveling among regions. It is shown that transportation among regions will change the disease dynamics and break infection out even if infectious diseases will go to extinction in each isolated region without transport-related infection. In addition, our analysis shows that transport-related infection intensifies the disease spread if infectious diseases break out to cause an endemic situation in each region, in the sense of that both the absolute and relative size of patients increase. This suggests that it is very essential to strengthen restrictions of passengers once we know infectious diseases appeared.     

Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Stochastic compartmental models of the SEIR type are often used to make inferences on epidemic processes from partially observed data in which only removal times are available. For many epidemics, the assumption of constant removal rates is not plausible. We develop methods for models in which these rates are a time-dependent step function. A reversible jump MCMC algorithm is described that permits Bayesian inferences to be made on model parameters, particularly those associated with the step function. The method is applied to two datasets on outbreaks of smallpox and a respiratory disease. The analyses highlight the importance of allowing for time dependence by contrasting the predictive distributions for the removal times and comparing them with the observed data.      

Rapid evolution and ecological host-parasite dynamics

Traditionally, the termination of parasite epidemics has been attributed to ecological causes: namely, the depletion of susceptible hosts as a result of mortality or acquired immunity. Here, we suggest that epidemics can also end because of rapid host evolution. Focusing on a particular host–parasite system, Daphnia dentifera and its parasite Metschnikowia bicuspidata , we show that Daphnia from lakes with recent epidemics were more resistant to infection and had less variance in susceptibility than Daphnia from lakes without recent epidemics. However, our studies revealed little evidence for genetic variation in infectivity or virulence in Metschnikowia . Incorporating the observed genetic variation in host susceptibility into an epidemiological model parameterized for this system reveals that rapid evolution can explain the termination of epidemics on time scales matching what occurs in lake populations. Thus, not only does our study provide rare evidence for parasite-mediated selection in natural populations, it also suggests that rapid evolution has important effects on short-term host–parasite dynamics.     

Avoidable errors in the modelling of outbreaks of emerging pathogens, with special reference to Ebola

As an emergent infectious disease outbreak unfolds, public health response is reliant on information on key epidemiological quantities, such as transmission potential and serial interval. Increasingly, transmission models fit to incidence data are used to estimate these parameters and guide policy. Some widely used modelling practices lead to potentially large errors in parameter estimates and, consequently, errors in model-based forecasts. Even more worryingly, in such situations, confidence in parameter estimates and forecasts can itself be far overestimated, leading to the potential for large errors that mask their own presence. Fortunately, straightforward and computationally inexpensive alternatives exist that avoid these problems. Here, we first use a simulation study to demonstrate potential pitfalls of the standard practice of fitting deterministic models to cumulative incidence data. Next, we demonstrate an alternative based on stochastic models fit to raw data from an early phase of 2014 West Africa Ebola virus disease outbreak. We show not only that bias is thereby reduced, but that uncertainty in estimates and forecasts is better quantified and that, critically, lack of model fit is more readily diagnosed. We conclude with a short list of principles to guide the modelling response to future infectious disease outbreaks.     

Early detection surveillance for an emerging plant pathogen: a rule of thumb to predict prevalence at first discovery

Emerging plant pathogens are a significant problem for conservation and food security. Surveillance is often instigated in an attempt to detect an invading epidemic before it gets out of control. Yet in practice many epidemics are not discovered until already at a high prevalence, partly due to a lack of quantitative understanding of how surveillance effort and the dynamics of an invading epidemic relate. We test a simple rule of thumb to determine, for a surveillance programme taking a fixed number of samples at regular intervals, the distribution of the prevalence an epidemic will have reached on first discovery (discovery-prevalence) and its expectation E(q*). We show that E(q*) = r/(N/Δ), i.e. simply the rate of epidemic growth divided by the rate of sampling; where r is the epidemic growth rate, N is the sample size and Δ is the time between sampling rounds. We demonstrate the robustness of this rule of thumb using spatio-temporal epidemic models as well as data from real epidemics. Our work supports the view that, for the purposes of early detection surveillance, simple models can provide useful insights in apparently complex systems. The insight can inform decisions on surveillance resource allocation in plant health and has potential applicability to invasive species generally.     

Ecological dynamics of emerging bat virus spillover

Viruses that originate in bats may be the most notorious emerging zoonoses that spill over from wildlife into domestic animals and humans. Understanding how these infections filter through ecological systems to cause disease in humans is of profound importance to public health. Transmission of viruses from bats to humans requires a hierarchy of enabling conditions that connect the distribution of reservoir hosts, viral infection within these hosts, and exposure and susceptibility of recipient hosts. For many emerging bat viruses, spillover also requires viral shedding from bats, and survival of the virus in the environment. Focusing on Hendra virus, but also addressing Nipah virus, Ebola virus, Marburg virus and coronaviruses, we delineate this cross-species spillover dynamic from the within-host processes that drive virus excretion to land-use changes that increase interaction among species. We describe how land-use changes may affect co-occurrence and contact between bats and recipient hosts. Two hypotheses may explain temporal and spatial pulses of virus shedding in bat populations: episodic shedding from persistently infected bats or transient epidemics that occur as virus is transmitted among bat populations. Management of livestock also may affect the probability of exposure and disease. Interventions to decrease the probability of virus spillover can be implemented at multiple levels from targeting the reservoir host to managing recipient host exposure and susceptibility.     

Success,failure and ambiguity of the dilution effect among competitors

It remains challenging to predict variation in the magnitude of disease outbreaks. The dilution effect seeks to explain this variation by linking multiple host species to disease transmission. It predicts that disease risk increases for a focal host when host species diversity declines. However, when an increase in species diversity does not reduce disease, we are often unable to diagnose why. Here, we increase mechanistic and predictive clarity of the dilution effect with a general trait‐based model of disease transmission in multi‐host communities. Then, we parameterise and empirically test our model with a multi‐generational case study of planktonic disease. The model‐experiment combination shows that hosts that vary in competitive ability (R*) and potential to spread disease (R₀) can produce three qualitatively disparate outcomes of dilution on disease: the dilution effect can succeed, fail, or be ambiguous/irrelevant.