Metapopulations with habitat modification

Across the tree of life, organisms modify their local environment, rendering it more or less hospitable for other species. Despite the ubiquity of these processes, simple models that can be used to develop intuitions about the consequences of widespread habitat modification are lacking. Here, we extend the classic Levins metapopulation model to a setting where each of n species can colonize patches connected by dispersal, and when patches are vacated via local extinction, they retain a “memory” of the previous occupant—modeling habitat modification. While this model can exhibit a wide range of dynamics, we draw several overarching conclusions about the effects of modification and memory. In particular, we find that any number of species may potentially coexist, provided that each is at a disadvantage when colonizing patches vacated by a conspecific. This notion is made precise through a quantitative stability condition, which provides a way to unify and formalize existing conceptual models. We also show that when patch memory facilitates coexistence, it generically induces a positive relationship between diversity and robustness (tolerance of disturbance). Our simple model provides a portable, tractable framework for studying systems where species modify and react to a shared landscape.

Low parasite connectivity among three malaria hotspots in Thailand

Identifying sources and sinks of malaria transmission is critical for designing effective intervention strategies particularly as countries approach elimination. The number of malaria cases in Thailand decreased 90% between 2012 and 2020, yet elimination has remained a major public health challenge with persistent transmission foci and ongoing importation. There are three main hotspots of malaria transmission in Thailand: Ubon Ratchathani and Sisaket in the Northeast; Tak in the West; and Yala in the South. However, the degree to which these hotspots are connected via travel and importation has not been well characterized. Here, we develop a metapopulation model parameterized by mobile phone call detail record data to estimate parasite flow among these regions. We show that parasite connectivity among these regions was limited, and that each of these provinces independently drove the malaria transmission in nearby provinces. Overall, our results suggest that due to the low probability of domestic importation between the transmission hotspots, control and elimination strategies can be considered separately for each region.

Modelling the geographical spread of HIV among MSM in Guangdong, China: a metapopulation model considering the impact of pre-exposure prophylaxis

Men who have sex with men (MSM) make up the majority of new human immunodeficiency virus (HIV) diagnoses among young people in China. Understanding HIV transmission dynamics among the MSM population is, therefore, crucial for the control and prevention of HIV infections, especially for some newly reported genotypes of HIV. This study presents a metapopulation model considering the impact of pre-exposure prophylaxis (PrEP) to investigate the geographical spread of a hypothetically new genotype of HIV among MSM in Guangdong, China. We use multiple data sources to construct this model to characterize the behavioural dynamics underlying the spread of HIV within and between 21 prefecture-level cities (i.e. Guangzhou, Shenzhen, Foshan, etc.) in Guangdong province: the online social network via a gay social networking app, the offline human mobility network via the Baidu mobility website, and self-reported sexual behaviours among MSM. Results show that PrEP initiation exponentially delays the occurrence of the virus for the rest of the cities transmitted from the initial outbreak city; hubs on the movement network, such as Guangzhou, Shenzhen, and Foshan are at a higher risk of ‘earliest’ exposure to the new HIV genotype; most cities acquire the virus directly from the initial outbreak city while others acquire the virus from cities that are not initial outbreak locations and have relatively high betweenness centralities, such as Guangzhou, Shenzhen and Shantou. This study provides insights in predicting the geographical spread of a new genotype of HIV among an MSM population from different regions and assessing the importance of prefecture-level cities in the control and prevention of HIV in Guangdong province. This article is part of the theme issue ‘Data science approach to infectious disease surveillance’.

COVID-19 in Scottish care homes: A metapopulation model of spread among residents and staff

Care homes in the UK were disproportionately affected by the first wave of the COVID-19 pandemic, accounting for almost half of COVID-19 deaths over the course of the period from 6th March – 15th June 2020. Understanding how infectious diseases establish themselves throughout vulnerable communities is crucial for minimising deaths and lowering the total stress on the National Health Service (NHS Scotland). We model the spread of COVID-19 in the health-board of NHS Lothian, Scotland over the course of the first wave of the pandemic with a compartmental Susceptible - Exposed - Infected reported - Infected unreported - Recovered - Dead (SEIARD), metapopulation model. Care home residents, care home workers and the rest of the population are modelled as subpopulations, interacting on a network describing their mixing habits. We explicitly model the outbreak’s reproduction rate and care home visitation level over time for each subpopulation, and execute a data fit and sensitivity analysis, focusing on parameters responsible for intra-subpopulation mixing: staff sharing, staff shift patterns and visitation. The results suggest that hospital discharges were not predominantly responsible for the early outbreak in care homes, and that only a few such cases led to infection seeding in care homes by the 6th of March Sensitivity analysis show the main mode of entry into care homes are infections by staff interacting with the general population. Visitation (before cancellation) and staff sharing were less significant in affecting outbreak size. Focusing on the protection and monitoring of staff, followed by reductions in staff sharing and quick cancellations of visitation can significantly reduce future infection attack rates of COVID-19 in care homes.Author SummaryCOVID-19 has spread throughout care homes in the UK, leading to many deaths of those most vulnerable in our population. This has sparked the need for further understanding of how infectious diseases spread throughout vulnerable communities such as care homes. We developed a model focused on the first wave in the Scottish health board of Lothian, which indicated pathways most likely leading to COVID-19 establishment within care homes. We found that care home visitation and hospital discharges did not significantly affect total COVID-19 cases in care home residents. The most significant route of entry for COVID-19 into care homes was through staff infections from the general population. We suggest to prioritise minimising infections in this pathway to reduce the number of outbreaks in care homes. Our model indicated that care homes were three weeks behind the general population in reducing the reproduction rate of COVID-19. This delay emphasises the need for more planning and support for care homes in organising effective responses to emerging pandemics.

Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

Stability analysis of the coexistence equilibrium of a balanced metapopulation model

We analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.

Signatures of the Venezuelan Humanitarian Crisis in the First Wave of COVID-19: Fuel Shortages and Border Migration

Testing and isolation have been crucial for controlling the COVID-19 pandemic. Venezuela has one of the weakest testing infrastructures in Latin America and the low number of reported cases in the country has been attributed to substantial underreporting. However, the Venezuelan epidemic seems to have lagged behind other countries in the region, with most cases occurring within the capital region and four border states. Here, we describe the spatial epidemiology of COVID-19 in Venezuela and its relation to the population mobility, migration patterns, non-pharmaceutical interventions and fuel availability that impact population movement. Using a metapopulation model of SARS-CoV-2 transmission dynamics, we explore how movement patterns could have driven the observed distribution of cases. Low within-country connectivity most likely delayed the onset of the epidemic in most states, except for those bordering Colombia and Brazil, where high immigration seeded outbreaks. NPIs slowed early epidemic growth and subsequent fuel shortages appeared to be responsible for limiting the spread of COVID-19 across the country.

Environment driven oscillation in an off-lattice May–Leonard model

Cyclic dominance of competing species is an intensively used working hypothesis to explain biodiversity in certain living systems, where the evolutionary selection principle would dictate a single victor otherwise. Technically the May–Leonard models offer a mathematical framework to describe the mentioned non-transitive interaction of competing species when individual movement is also considered in a spatial system. Emerging rotating spirals composed by the competing species are frequently observed character of the resulting patterns. But how do these spiraling patterns change when we vary the external environment which affects the general vitality of individuals? Motivated by this question we suggest an off-lattice version of the tradition May–Leonard model which allows us to change the actual state of the environment gradually. This can be done by introducing a local carrying capacity parameter which value can be varied gently in an off-lattice environment. Our results support a previous analysis obtained in a more intricate metapopulation model and we show that the well-known rotating spirals become evident in a benign environment when the general density of the population is high. The accompanying time-dependent oscillation of competing species can also be detected where the amplitude and the frequency show a scaling law of the parameter that characterizes the state of the environment. These observations highlight that the assumed non-transitive interaction alone is insufficient condition to maintain biodiversity safely, but the actual state of the environment, which characterizes the general living conditions, also plays a decisive role on the evolution of related systems.