Stochastic Metapopulation Research Articles

How migration changes dynamic patterns in a stochastic metapopulation model with Allee effect

How migration changes dynamic patterns in a stochastic metapopulation model with Allee effect

Stability of ecologically scaffolded traits during evolutionary transitions in individuality

Evolutionary transitions in individuality are events in the history of life leading to the emergence of new levels of individuality. Recent studies have described an ecological scaffolding scenario of such transitions focused on the evolutionary consequences of an externally imposed renewing meta-population structure with limited dispersal. One difficulty for such a scenario has been explaining the stability of collective-level traits when scaffolding conditions no longer apply. Here, we show that the stability of scaffolded traits can rely on evolutionary hysteresis: even if the environment is reverted to an ancestral state, collectives do not return to ancestral phenotypes. We describe this phenomenon using a stochastic meta-population model and adaptive dynamics. Further, we show that ecological scaffolding may be limited to Goldilocks zones of the environment. We conjecture that Goldilocks zones—even if they might be rare—could act as initiators of evolutionary transitions and help to explain the near ubiquity of collective-level individuality.

Modelling African swine fever introduction in diverse Australian feral pig populations

African swine fever (ASF) is a viral disease that affects domestic and feral pigs. While not currently present in Australia, ASF outbreaks have been reported nearby in Indonesia, Timor-Leste, and Papua New Guinea. Feral pigs are found in all Australian states and territories and are distributed in a variety of habitats. To investigate the impacts of an ASF introduction event in Australia, we used a stochastic network-based metapopulation feral pig model to simulate ASF outbreaks in different regions of Australia. Outbreak intensity and persistence in feral pig populations was governed by local pig recruitment rates, population size, carcass decay period, and, if applicable, metapopulation topology. In Northern Australia, the carcass decay period was too short for prolonged persistence, while endemic transmission could possibly occur in cooler southern areas. Populations in Macquarie Marshes in New South Wales and in Namadgi National Park in the Australian Capital Territory had the highest rates of persistence. The regions had different modes of transmission that led to long-term persistence. Endemic Macquarie Marshes simulations were characterised by rapid transmission caused by high population density that required a fragmented metapopulation to act as a bottleneck to slow transmission. Endemic simulations in Namadgi, with low density and relatively slow transmission, relied on large, well-connected populations coupled with long carcass decay times. Despite the potential for endemic transmission, both settings required potentially unlikely population sizes and dynamics for prolonged disease survival.

Temporal variations in international air travel: implications for modelling the spread of infectious diseases.

The international flight network creates multiple routes by which pathogens can quickly spread across the globe. In the early stages of infectious disease outbreaks, analyses using flight passenger data to identify countries at risk of importing the pathogen are common and can help inform disease control efforts. A challenge faced in this modelling is that the latest aviation statistics (referred to as contemporary data) are typically not immediately available. Therefore, flight patterns from a previous year are often used (referred to as historical data). We explored the suitability of historical data for predicting the spatial spread of emerging epidemics. We analysed monthly flight passenger data from the International Air Transport Association to assess how baseline air travel patterns were affected by outbreaks of Middle East respiratory syndrome (MERS), Zika and severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) over the past decade. We then used a stochastic discrete time susceptible-exposed-infected-recovered (SEIR) metapopulation model to simulate the global spread of different pathogens, comparing how epidemic dynamics differed in simulations based on historical and contemporary data. We observed local, short-term disruptions to air travel from South Korea and Brazil for the MERS and Zika outbreaks we studied, whereas global and longer-term flight disruptions occurred during the SARS-CoV-2 pandemic. For outbreak events that were accompanied by local, small and short-term changes in air travel, epidemic models using historical flight data gave similar projections of the timing and locations of disease spread as when using contemporary flight data. However, historical data were less reliable to model the spread of an atypical outbreak such as SARS-CoV-2, in which there were durable and extensive levels of global travel disruption. The use of historical flight data as a proxy in epidemic models is an acceptable practice, except in rare, large epidemics that lead to substantial disruptions to international travel.

Stochastic metapopulation dynamics of a threatened amphibian to improve water delivery

AbstractWater extraction and climate change are altering the availability of surface water globally, thereby contributing to amphibian population declines. The managed delivery of water to benefit environmental values (environmental watering) is a promising conservation technique that can support amphibian recruitment and maintain viable populations. Environmental water can be delivered in various spatial patterns and with different frequencies, but comparing the effectiveness of competing strategies is complicated by variable and interactive environmental processes. We built a spatially explicit, stochastic, hydroecological metapopulation model to compare the effects of five environmental‐watering scenarios on the probability of persistence of threatened southern bell frogs (Litoria raniformis) in a major river reach in southern Australia. We compared a no‐intervention control to two managed watering frequencies (moderate and frequent) delivered in two spatial designs (managed wetlands grouped or spread across the reach). More frequent water provision to intervention sites improved the reach‐wide (metapopulation) probability of persistence, and spreading intervention sites across the reach improved persistence more than grouping intervention sites together. When re‐examined under severe drought conditions, L. raniformis had a 0.04 probability of persistence without intervention, which improved to 0.56 with high watering frequency. Model‐guided environmental water provision can improve reach‐wide persistence of amphibian metapopulations by guiding spatial and temporal delivery patterns to reduce the risk of extinction.

Treatment of sheep prior to movement: its contribution to an effective scab (psoroptic mange) management strategy

BackgroundOvine psoroptic mange (sheep scab) is an important disease of sheep worldwide caused by the parasitic mite, Psoroptes ovis. It has a negative impact on animal welfare and leads to significant economic losses for the sheep industry. Effective and targeted management is required to limit its transmission.MethodsA stochastic metapopulation model of sheep scab transmission is used to investigate the contribution of the treatment of sheep prior to movements to sales, gatherings (predominantly markets) and away grazing to the reduction of prevalence of farms with scab in Great Britain.ResultsTreatment prior to movement to gatherings resulted in an 86% reduction in the overall prevalence of farms with scab and was more effective at reducing the overall prevalence of farms with scab than treatment before other categories of movements. The relative risk of farms having scab infection was inversely related to the percentage of farms which treated, but this relationship was not linear, with the biggest declines in the prevalence of farms with scab being achieved by small percentages of farms treating; a 50% relative reduction in the farm prevalence was achieved with only 15% of farms treating prior to gathering movements.ConclusionsThe results suggest that pre-movement treatment of sheep could make an important contribution to national scab control and, in practice, the approach could be more highly targeted if used in conjunction with known geographic and management risk factors for scab.Graphical

Bayesian spatial modelling of localised SARS-CoV-2 transmission through mobility networks across England.

In the early phases of growth, resurgent epidemic waves of SARS-CoV-2 incidence have been characterised by localised outbreaks. Therefore, understanding the geographic dispersion of emerging variants at the start of an outbreak is key for situational public health awareness. Using telecoms data, we derived mobility networks describing the movement patterns between local authorities in England, which we have used to inform the spatial structure of a Bayesian BYM2 model. Surge testing interventions can result in spatio-temporal sampling bias, and we account for this by extending the BYM2 model to include a random effect for each timepoint in a given area. Simulated-scenario modelling and real-world analyses of each variant that became dominant in England were conducted using our BYM2 model at local authority level in England. Simulated datasets were created using a stochastic metapopulation model, with the transmission rates between different areas parameterised using telecoms mobility data. Different scenarios were constructed to reproduce real-world spatial dispersion patterns that could prove challenging to inference, and we used these scenarios to understand the performance characteristics of the BYM2 model. The model performed better than unadjusted test positivity in all the simulation-scenarios, and in particular when sample sizes were small, or data was missing for geographical areas. Through the analyses of emerging variant transmission across England, we found a reduction in the early growth phase geographic clustering of later dominant variants as England became more interconnected from early 2022 and public health interventions were reduced. We have also shown the recent increased geographic spread and dominance of variants with similar mutations in the receptor binding domain, which may be indicative of convergent evolution of SARS-CoV-2 variants.

Marginal effects of public health measures and COVID-19 disease burden in China: A large-scale modelling study.

China had conducted some of the most stringent public health measures to control the spread of successive SARS-CoV-2 variants. However, the effectiveness of these measures and their impacts on the associated disease burden have rarely been quantitatively assessed at the national level. To address this gap, we developed a stochastic age-stratified metapopulation model that incorporates testing, contact tracing and isolation, based on 419 million travel movements among 366 Chinese cities. The study period for this model began from September 2022. The COVID-19 disease burden was evaluated, considering 8 types of underlying health conditions in the Chinese population. We identified the marginal effects between the testing speed and reduction in the epidemic duration. The findings suggest that assuming a vaccine coverage of 89%, the Omicron-like wave could be suppressed by 3-day interval population-level testing (PLT), while it would become endemic with 4-day interval PLT, and without testing, it would result in an epidemic. PLT conducted every 3 days would not only eliminate infections but also keep hospital bed occupancy at less than 29.46% (95% CI, 22.73-38.68%) of capacity for respiratory illness and ICU bed occupancy at less than 58.94% (95% CI, 45.70-76.90%) during an outbreak. Furthermore, the underlying health conditions would lead to an extra 2.35 (95% CI, 1.89-2.92) million hospital admissions and 0.16 (95% CI, 0.13-0.2) million ICU admissions. Our study provides insights into health preparedness to balance the disease burden and sustainability for a country with a population of billions.

Metapopulation dynamics of SARS-CoV-2 transmission in a small-scale Amazonian society.

The severity of infectious disease outbreaks is governed by patterns of human contact, which vary by geography, social organization, mobility, access to technology and healthcare, economic development, and culture. Whereas globalized societies and urban centers exhibit characteristics that can heighten vulnerability to pandemics, small-scale subsistence societies occupying remote, rural areas may be buffered. Accordingly, voluntary collective isolation has been proposed as one strategy to mitigate the impacts of COVID-19 and other pandemics on small-scale Indigenous populations with minimal access to healthcare infrastructure. To assess the vulnerability of such populations and the viability of interventions such as voluntary collective isolation, we simulate and analyze the dynamics of SARS-CoV-2 infection among Amazonian forager-horticulturalists in Bolivia using a stochastic network metapopulation model parameterized with high-resolution empirical data on population structure, mobility, and contact networks. Our model suggests that relative isolation offers little protection at the population level (expected approximately 80% cumulative incidence), and more remote communities are not conferred protection via greater distance from outside sources of infection, due to common features of small-scale societies that promote rapid disease transmission such as high rates of travel and dense social networks. Neighborhood density, central household location in villages, and household size greatly increase the individual risk of infection. Simulated interventions further demonstrate that without implausibly high levels of centralized control, collective isolation is unlikely to be effective, especially if it is difficult to restrict visitation between communities as well as travel to outside areas. Finally, comparison of model results to empirical COVID-19 outcomes measured via seroassay suggest that our theoretical model is successful at predicting outbreak severity at both the population and community levels. Taken together, these findings suggest that the social organization and relative isolation from urban centers of many rural Indigenous communities offer little protection from pandemics and that standard control measures, including vaccination, are required to counteract effects of tight-knit social structures characteristic of small-scale populations.

Genetic rescue from protected areas is modulated by migration, hunting rate, and timing of harvest.

In terrestrial and marine ecosystems, migrants from protected areas may buffer the risk of harvest-induced evolutionary changes in exploited populations that face strong selective harvest pressures. Understanding the mechanisms favoring genetic rescue through migration could help ensure evolutionarily sustainable harvest outside protected areas and conserve genetic diversity inside those areas. We developed a stochastic individual-based metapopulation model to evaluate the potential for migration from protected areas to mitigate the evolutionary consequences of selective harvest. We parameterized the model with detailed data from individual monitoring of two populations of bighorn sheep subjected to trophy hunting. We tracked horn length through time in a large protected and a trophy-hunted populations connected through male breeding migrations. We quantified and compared declines in horn length and rescue potential under various combinations of migration rate, hunting rate in hunted areas and temporal overlap in timing of harvest and migrations, which affects the migrants' survival and chances to breed within exploited areas. Our simulations suggest that the effects of size-selective harvest on male horn length in hunted populations can be dampened or avoided if harvest pressure is low, migration rate is substantial, and migrants leaving protected areas have a low risk of being shot. Intense size-selective harvest impacts the phenotypic and genetic diversity in horn length, and population structure through changes in proportions of large-horned males, sex ratio and age structure. When hunting pressure is high and overlaps with male migrations, effects of selective removal also emerge in the protected population, so that instead of a genetic rescue of hunted populations, our model predicts undesirable effects inside protected areas. Our results stress the importance of a landscape approach to management, to promote genetic rescue from protected areas and limit ecological and evolutionary impacts of harvest on both harvested and protected populations.

Modelling the impact of interventions on imported, introduced and indigenous malaria infections in Zanzibar, Tanzania

Malaria cases can be classified as imported, introduced or indigenous cases. The World Health Organization’s definition of malaria elimination requires an area to demonstrate that no new indigenous cases have occurred in the last three years. Here, we present a stochastic metapopulation model of malaria transmission that distinguishes between imported, introduced and indigenous cases, and can be used to test the impact of new interventions in a setting with low transmission and ongoing case importation. We use human movement and malaria prevalence data from Zanzibar, Tanzania, to parameterise the model. We test increasing the coverage of interventions such as reactive case detection; implementing new interventions including reactive drug administration and treatment of infected travellers; and consider the potential impact of a reduction in transmission on Zanzibar and mainland Tanzania. We find that the majority of new cases on both major islands of Zanzibar are indigenous cases, despite high case importation rates. Combinations of interventions that increase the number of infections treated through reactive case detection or reactive drug administration can lead to substantial decreases in malaria incidence, but for elimination within the next 40 years, transmission reduction in both Zanzibar and mainland Tanzania is necessary.

A real-time regional model for COVID-19: Probabilistic situational awareness and forecasting.

The COVID-19 pandemic is challenging nations with devastating health and economic consequences. The spread of the disease has revealed major geographical heterogeneity because of regionally varying individual behaviour and mobility patterns, unequal meteorological conditions, diverse viral variants, and locally implemented non-pharmaceutical interventions and vaccination roll-out. To support national and regional authorities in surveilling and controlling the pandemic in real-time as it unfolds, we here develop a new regional mathematical and statistical model. The model, which has been in use in Norway during the first two years of the pandemic, is informed by real-time mobility estimates from mobile phone data and laboratory-confirmed case and hospitalisation incidence. To estimate regional and time-varying transmissibility, case detection probabilities, and missed imported cases, we developed a novel sequential Approximate Bayesian Computation method allowing inference in useful time, despite the high parametric dimension. We test our approach on Norway and find that three-week-ahead predictions are precise and well-calibrated, enabling policy-relevant situational awareness at a local scale. By comparing the reproduction numbers before and after lockdowns, we identify spatially heterogeneous patterns in their effect on the transmissibility, with a stronger effect in the most populated regions compared to the national reduction estimated to be 85% (95% CI 78%-89%). Our approach is the first regional changepoint stochastic metapopulation model capable of real time spatially refined surveillance and forecasting during emergencies.

Eco-hydrological modelling of channel network dynamics-part 2: application to metapopulation dynamics.

Temporal variations in the configuration of the flowing portion of stream networks are observed in the large majority of rivers worldwide. However, the ecological implications of river network expansions/retractions remain poorly understood, owing to the lack of computationally efficient modelling tools conceived for the long-term simulation of river network dynamics. Here, we couple a stochastic approach for the simulation of channel network expansion and retraction (described in a companion paper) with a dynamic version of a stochastic occupancy metapopulation model. The coupled eco-hydrological model is used to analyse the impact of pulsing river networks on species persistence under different hydroclimatic scenarios. Our results unveil the existence of a climate-dependent detrimental effect of network dynamics on species spread and persistence. This effect is enhanced by dry climates, where flashy expansions and retractions of the flowing channels induce metapopulation extinction. Survival probabilities are particularly reduced in settings where the spatial heterogeneity of network connectivity is pronounced. The analysis indicates that accounting for the temporal variability of the flowing river network and its connectivity is a fundamental prerequisite for analysing in-stream metapopulation dynamics.

Assessing the effectiveness of prophylactic treatment strategies for sheep scab

Ovine psoroptic mange (sheep scab) is a condition caused by a hypersensitivity response to the ectoparasitic mite, Psoroptes ovis. It is an animal welfare concern and causes extensive economic losses to the sheep industry worldwide. More effective scab management is required to limit increases in infection prevalence, particularly given growing concerns over acaricide resistance. Here, a stochastic metapopulation model is used to explore the effectiveness of a range of prophylactic acaricide treatment strategies in comparison to no intervention. Over a simulated one-year period, movement control, based on the prophylactic treatment of animals being moved in sales, followed by farm biosecurity of bought in animals, was shown to be the most effective at reducing scab risk and more cost-effective than no intervention. Localised targeting of prophylaxis in areas of high scab prevalence was more effective than using prophylaxis at random, however, this localised effect declined post-treatment because of the import of infected animals. The analysis highlights the role of the movement of infected animals in maintaining high levels of scab infection and the importance of reducing this route of transmission to allow localised management to be effective.

Comparing sources of mobility for modelling the epidemic spread of Zika virus in Colombia.

Timely, accurate, and comparative data on human mobility is of paramount importance for epidemic preparedness and response, but generally not available or easily accessible. Mobile phone metadata, typically in the form of Call Detail Records (CDRs), represents a powerful source of information on human movements at an unprecedented scale. In this work, we investigate the potential benefits of harnessing aggregated CDR-derived mobility to predict the 2015-2016 Zika virus (ZIKV) outbreak in Colombia, when compared to other traditional data sources. To simulate the spread of ZIKV at sub-national level in Colombia, we employ a stochastic metapopulation epidemic model for vector-borne diseases. Our model integrates detailed data on the key drivers of ZIKV spread, including the spatial heterogeneity of the mosquito abundance, and the exposure of the population to the virus due to environmental and socio-economic factors. Given the same modelling settings (i.e. initial conditions and epidemiological parameters), we perform in-silico simulations for each mobility network and assess their ability in reproducing the local outbreak as reported by the official surveillance data. We assess the performance of our epidemic modelling approach in capturing the ZIKV outbreak both nationally and sub-nationally. Our model estimates are strongly correlated with the surveillance data at the country level (Pearson's r = 0.92 for the CDR-informed network). Moreover, we found strong performance of the model estimates generated by the CDR-informed mobility networks in reproducing the local outbreak observed at the sub-national level. Compared to the CDR-informed networks, the performance of the other mobility networks is either comparatively similar or substantially lower, with no added value in predicting the local epidemic. This suggests that mobile phone data captures a better picture of human mobility patterns. This work contributes to the ongoing discussion on the value of aggregated mobility estimates from CDRs data that, with appropriate data protection and privacy safeguards, can be used for social impact applications and humanitarian action.

Integrating climate change and management scenarios in population models to guide the conservation of marine turtles

The globally significant green turtle (Chelonia mydas) population in the northern Great Barrier Reef is threatened by anthropogenic pressures, including climate change, habitat degradation, and indigenous harvest. Evidence suggesting the population is producing an extreme proportion of females due to increasing temperatures, coupled with temperature-dependent sex determination, is concerning. In response, and to explore management options, we developed two density-independent, stochastic stage-structured metapopulation models: a “Moderate Climate Model” and an “Extreme Climate Model”. The models differ based on climate change projections by incorporating increased female hatchling sex ratios due to global warming and loss of nesting habitat due to sea level rise. The models were based on demographic data from field studies at major rookeries and regional foraging grounds and allowed for variation in operational sex ratios, management actions, and levels of indigenous harvest. Under the Moderate Climate Model, population size increased but could be vulnerable to overharvest of adult females. If overharvest was indicated, the harvest of a proportion of subadults rather than only adult females reduced population declines. Under the Extreme Climate Model, there was a steep population decline even without any harvest, and harvesting subadults accelerated population decline due to the inclusion of subadult males. In the Extreme Climate Model, reversal of population decline depended on male turtles mating with an increased number of females, or management actions to substantially increase the number of male hatchlings produced.

Travel-related Importation and Exportation Risks of SARS-CoV-2 Omicron Variant in 367 Prefectures (Cities) - China, 2022.

IntroductionMinimizing the importation and exportation risks of coronavirus disease 2019 (COVID-19) is a primary concern for sustaining the “Dynamic COVID-zero” strategy in China. Risk estimation is essential for cities to conduct before relaxing border control measures.MethodsInformed by the daily number of passengers traveling between 367 prefectures (cities) in China, this study used a stochastic metapopulation model parameterized with COVID-19 epidemic characteristics to estimate the importation and exportation risks.ResultsUnder the transmission scenario (R0=5.49), this study estimated the cumulative case incidence of Changchun City, Jilin Province as 3,233 (95% confidence interval: 1,480, 4,986) before a lockdown on March 14, 2022, which is close to the 3,168 cases reported in real life by March 16, 2022. In a total of 367 prefectures (cities), 127 (35%) had high exportation risks according to the simulation and could transmit the disease to 50% of all other regions within a period from 17 to 94 days. The average time until a new infection arrives in a location in 1 of the 367 prefectures (cities) ranged from 26 to 101 days.ConclusionsEstimating COVID-19 importation and exportation risks is necessary for preparedness, prevention, and control measures of COVID-19 — especially when new variants emerge.

Sheep scab spatial distribution: the roles of transmission pathways

BackgroundOvine psoroptic mange (sheep scab) is a highly pathogenic contagious infection caused by the mite Psoroptes ovis. Following 21 years in which scab was eradicated in the UK, it was inadvertently reintroduced in 1972 and, despite the implementation of a range of control methods, its prevalence increased steadily thereafter. Recent reports of resistance to macrocyclic lactone treatments may further exacerbate control problems. A better understanding of the factors that facilitate its transmission are required to allow improved management of this disease. Transmission of infection occurs within and between contiguous sheep farms via infected sheep-to-sheep or sheep–environment contact and through long-distance movements of infected sheep, such as through markets.MethodsA stochastic metapopulation model was used to investigate the impact of different transmission routes on the spatial pattern of outbreaks. A range of model scenarios were considered following the initial infection of a cluster of highly connected contiguous farms.ResultsScab spreads between clusters of neighbouring contiguous farms after introduction but when long-distance movements are excluded, infection then self-limits spatially at boundaries where farm connectivity is low. Inclusion of long-distance movements is required to generate the national patterns of disease spread observed.ConclusionsPreventing the movement of scab infested sheep through sales and markets is essential for any national management programme. If effective movement control can be implemented, regional control in geographic areas where farm densities are high would allow more focussed cost-effective scab management.Graphical

Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading

Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.

Sheep scab transmission: a spatially explicit dynamic metapopulation model

Psoroptic mange (sheep scab), caused by the parasitic mite, Psoroptes ovis, is an important disease of sheep worldwide. It causes chronic animal welfare issues and economic losses. Eradication of scab has proved impossible in many sheep-rearing areas and recent reports of resistance to macrocyclic lactones, a key class of parasiticide, highlight the importance of improving approaches to scab management. To allow this, the current study aimed to develop a stochastic spatial metapopulation model for sheep scab transmission which can be adapted for use in any geographical region, exhibited here using data for Great Britain. The model uses agricultural survey and sheep movement data to geo-reference farms and capture realistic movement patterns. Reported data on sheep scab outbreaks from 1973 to 1991 were used for model fitting with Sequential Monte Carlo Approximate Bayesian Computation methods. The outbreak incidence predicted by the model was from the same statistical distribution as the reported outbreak data ({chi }^{2} = 115.3, p = 1) and the spatial location of sheep scab outbreaks predicted was positively correlated with the observed outbreak data by county (tau = 0.55, p < 0.001), confirming that the model developed is able to accurately capture the number of farms infected in a year, the seasonality of scab incidence and the spatial patterns seen in the data. This model gives insight into the transmission dynamics of sheep scab and will allow the exploration of more effective control strategies.