Utility of R0 as a predictor of disease invasion in structured populations

Early theoretical work on disease invasion typically assumed large and well-mixed host populations. Many human and wildlife systems, however, have small groups with limited movement among groups. In these situations, the basic reproductive number, R0, is likely to be a poor predictor of a disease pandemic because it typically does not account for group structure and movement of individuals among groups. We extend recent work by combining the movement of hosts, transmission within groups, recovery from infection and the recruitment of new susceptibles into a stochastic model of disease in a host metapopulation. We focus on how recruitment of susceptibles affects disease invasion and how population structure can affect the frequency of superspreading events (SSEs). We show that the frequency of SSEs may decrease with the reduced movement and the group sizes due to the limited number of susceptible individuals available. Classification tree analysis of the model results illustrates the hierarchical nature of disease invasion in host metapopulations. First, the pathogen must effectively transmit within a group (R0>1), and then the pathogen must persist within a group long enough to allow for movement among the groups. Therefore, the factors affecting disease persistence--such as infectious period, group size and recruitment of new susceptibles--are as important as the local transmission rates in predicting the spread of pathogens across a metapopulation.     

Not just a migration problem: Metapopulations,habitat shifts,and gene flow are also important for fishway science and management

Worldwide, fishways are increasingly criticized for failing to meet conservation goals. We argue that this is largely due to the dominance of diadromous species of the Northern Hemisphere (e.g., Salmonidae) in the research that underpins the concepts and methods of fishway science and management. With highly diverse life histories, swimming abilities and spatial ecologies, most freshwater fish species do not conform to the stereotype imposed by this framework. This is leading to a global proliferation of fishways that are often unsuitable for native species. The vast majority of fish populations do not undertake extensive migrations between clearly separated critical habitats, yet the movement of individuals and the genetic information they carry is critically important for population viability. We briefly review some of the latest advances in spatial ecological modelling for dendritic networks to better define what it means to achieve effective fish passage at a barrier. Through a combination of critical habitat assessment and the modelling of metapopulations, climate change‐driven habitat shifts, and adaptive gene flow, we recommend a conceptual and methodological framework for fishway target‐setting and monitoring suitable for a wide range of species. In the process, we raise a number of issues that should contribute to the ongoing debate about fish passage research and the design and monitoring of fishways.     

LINKING RIVER MANAGEMENT TO SPECIES CONSERVATION USING DYNAMIC LANDSCAPE‐SCALE MODELS

Efforts to conserve stream and river biota could benefit from tools that allow managers to evaluate landscape‐scale changes in species distributions in response to water management decisions. We present a framework and methods for integrating hydrology, geographic context and metapopulation processes to simulate effects of changes in streamflow on fish occupancy dynamics across a landscape of interconnected stream segments. We illustrate this approach using a 482 km² catchment in the southeastern US supporting 50 or more stream fish species. A spatially distributed, deterministic and physically based hydrologic model is used to simulate daily streamflow for sub‐basins composing the catchment. We use geographic data to characterize stream segments with respect to channel size, confinement, position and connectedness within the stream network. Simulated streamflow dynamics are then applied to model fish metapopulation dynamics in stream segments, using hypothesized effects of streamflow magnitude and variability on population processes, conditioned by channel characteristics. The resulting time series simulate spatially explicit, annual changes in species occurrences or assemblage metrics (e.g. species richness) across the catchment as outcomes of management scenarios. Sensitivity analyses using alternative, plausible links between streamflow components and metapopulation processes, or allowing for alternative modes of fish dispersal, demonstrate large effects of ecological uncertainty on model outcomes and highlight needed research and monitoring. Nonetheless, with uncertainties explicitly acknowledged, dynamic, landscape‐scale simulations may prove useful for quantitatively comparing river management alternatives with respect to species conservation. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.     

Long‐term (37 years) impacts of low‐head dams on freshwater shrimp habitat connectivity in northeastern Puerto Rico

Freshwater migratory shrimp in Puerto Rico depend on watershed connectivity, from stream headwaters to the ocean, to complete their life cycle. Moreover, shrimp populations in different watersheds are known to be connected in an island‐wide metapopulation. However, low‐head dams paired with water intakes on streams draining the El Yunque National Forest (EYNF) reduce streamflow. Here, we examine the cumulative effects of low‐head dams on shrimp habitat connectivity over 37 years across seven EYNF watersheds. We calculate total and refugia habitat connectivity (where refugia habitat is defined as predator‐free upstream reaches above waterfalls >5 m in height) at a monthly time step using a habitat‐weighted index of longitudinal riverine connectivity, which incorporates location and operation of water intakes and streamflow variability. Findings indicate total and refugia habitat connectivity declined over 37 years (by 27% and 16%, respectively) as additional water intakes have been placed in lower reaches of watersheds. On a monthly time step, the proportion of streamflow withdrawn has the largest effect on habitat connectivity, with the result that connectivity is ~17% lower during drought years than in nondrought years and ~7% lower in dry compared with wet seasons. Our analysis of this long‐term dataset highlights how cumulative effects of low‐head dams paired with water intakes have reduced shrimp habitat connectivity. These results underscore the importance of reducing existing withdrawal rates in EYNF, and locating intakes where effects on connectivity are minimal, if conserving shrimp habitat is a management objective.     

BINOMIAL AUTOREGRESSIVE PROCESSES WITH DENSITY‐DEPENDENT THINNING

We present an elaboration of the usual binomial AR(1) process on {0,1, … ,N}that allows the thinning probabilities to depend on the current state N only through the ‘density’ n ∕ N, a natural assumption in many real contexts. We derive some basic properties of the model and explore approaches to parameter estimation. Some special cases are considered that allow for overdispersion and underdispersion, as well as positive and negative autocorrelations. We derive a law of large numbers and a central limit theorem, which provide useful large‐N approximations for various quantities of interest.     

Rubella metapopulation dynamics and importance of spatial coupling to the risk of congenital rubella syndrome in Peru

Rubella is generally a mild childhood disease, but infection during early pregnancy may cause spontaneous abortion or congenital rubella syndrome (CRS), which may entail a variety of birth defects. Consequently, understanding the age-structured dynamics of this infection has considerable public health value. Vaccination short of the threshold for local elimination of transmission will increase the average age of infection. Accordingly, the classic concern for this infection is the potential for vaccination to increase incidence in individuals of childbearing age. A neglected aspect of rubella dynamics is how age incidence patterns may be moulded by the spatial dynamics inherent to epidemic metapopulations. Here, we use a uniquely detailed dataset from Peru to explore the implications of this for the burden of CRS. Our results show that the risk of CRS may be particularly severe in small remote regions, a prediction at odds with expectations in the endemic situation, and with implications for the outcome of vaccination. This outcome results directly from the metapopulation context: specifically, extinction–re-colonization dynamics are crucial because they allow for significant leakage of susceptible individuals into the older age classes during inter-epidemic periods with the potential to increase CRS risk by as much as fivefold.     

The effect of population structure on the emergence of drug resistance during influenza pandemics.

The spread of H5N1 avian influenza and the recent high numbers of confirmed human cases have raised international concern about the possibility of a new pandemic. Therefore, antiviral drugs are now being stockpiled to be used as a first line of defence. The large-scale use of antivirals will however exert a strong selection pressure on the virus, and may lead to the emergence of drug-resistant strains. A few mathematical models have been developed to assess the emergence of drug resistance during influenza pandemics. These models, however, neglected the spatial structure of large populations and the stochasticity of epidemic and demographic processes. To assess the impact of population structure and stochasticity, we modify and extend a previous model of influenza epidemics into a metapopulation model which takes into account the division of large populations into smaller units, and develop deterministic and stochastic versions of the model. We find that the dynamics in a fragmented population is less explosive, and, as a result, prophylaxis will prevent more infections and lead to fewer resistant cases in both the deterministic and stochastic model. While in the deterministic model the final level of resistance during treatment is not affected by fragmentation, in the stochastic model it is. Our results enable us to qualitatively extrapolate the prediction of deterministic, homogeneous-mixing models to more realistic scenarios.     

Disease control across urban–rural gradients

Controlling the regional re-emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after its initial spread in ever-changing personal contact networks and disease landscapes is a challenging task. In a landscape context, contact opportunities within and between populations are changing rapidly as lockdown measures are relaxed and a number of social activities re-activated. Using an individual-based metapopulation model, we explored the efficacy of different control strategies across an urban–rural gradient in Wales, UK. Our model shows that isolation of symptomatic cases or regional lockdowns in response to local outbreaks have limited efficacy unless the overall transmission rate is kept persistently low. Additional isolation of non-symptomatic infected individuals, who may be detected by effective test-and-trace strategies, is pivotal to reducing the overall epidemic size over a wider range of transmission scenarios. We define an ‘urban–rural gradient in epidemic size'' as a correlation between regional epidemic size and connectivity within the region, with more highly connected urban populations experiencing relatively larger outbreaks. For interventions focused on regional lockdowns, the strength of such gradients in epidemic size increased with higher travel frequencies, indicating a reduced efficacy of the control measure in the urban regions under these conditions. When both non-symptomatic and symptomatic individuals are isolated or regional lockdown strategies are enforced, we further found the strongest urban–rural epidemic gradients at high transmission rates. This effect was reversed for strategies targeted at symptomatic individuals only. Our results emphasize the importance of test-and-trace strategies and maintaining low transmission rates for efficiently controlling SARS-CoV-2 spread, both at landscape scale and in urban areas.     

Control of equine influenza: scenario testing using a realistic metapopulation model of spread

We present a metapopulation model of the spread of equine influenza among thoroughbred horses parametrized with data from a 2003 outbreak in Newmarket, UK. The number of horses initially susceptible is derived from a threshold theorem and a published statistical model. Two simulated likelihood-based methods are used to find the within- and between-yard transmissions using both exponential and empirical latent and infectious periods. We demonstrate that the 2003 outbreak was largely locally driven and use the parametrized model to address important questions of control. The chance of a large epidemic is shown to be largely dependent on the size of the index yard. The impact of poor responders to vaccination is estimated under different scenarios. A small proportion of poor responders strongly influences the efficiency of vaccine policies, which increases risk further when the vaccine and infecting strains differ following antigenic drift. Finally, the use of vaccinating in the face of an outbreak is evaluated at a global and individual management group level. The benefits for an individual horse trainer are found to be substantial, although this is influenced by the behaviour of other trainers.     

融入迁移限制与双层集合种群网络的传染病模型

本文在斑块环境下基于易感–感染–易感模型(SIS模型)研究了感染者迁移限制对传染病传播的影响,其中迁移限制用双层网络进行表示,并提出了双层集合种群动态网络.子种群(即斑块)用双层网络上的节点表示,双层网络上的链接分别代表易感节点斑块和感染节点斑块间的迁移路径,易感染和感染节点分别通过双层网络上的链接随机游走.并提出了两种反应扩散方程分别作为易感染与感染节点的微分方程,分别计算其数值解,以评估每个斑块(节点)的感染风险.研究表明:在双层网络中,迁移限制会降低感染节点密度,将感染节点限制在中心节点(度值最高的子种群)中.感染节点密度高度依赖于双层网络结构.