Comparing metapopulation dynamics of infectious diseases under different models of human movement

The spread of the Delta variant in Catalonia during summer 2021: Modelling and interpretation

BACKGROUND

The emergence of highly transmissible SARS-CoV-2 variants has posed significant challenges to public health efforts worldwide. During the summer of 2021, the Delta variant (B.1.617.2) rapidly displaced the Alpha variant (B.1.1.7) in Catalonia, Spain, leading to a resurgence in infections despite ongoing vaccination campaigns. Understanding the epidemiological drivers of this outbreak is critical for refining future mitigation strategies.

METHODS

We employed a Bayesian age-stratified epidemiological model, incorporating vaccination status and variant-specific transmission dynamics, to analyze the outbreak in Catalonia. The model was calibrated using daily reported cases, hospitalizations, sequencing data, and vaccination coverage across age groups. We inferred contact patterns dynamically to assess their role in the epidemic resurgence and estimated the transmission advantage of the Delta variant over Alpha.

RESULTS

Our analysis revealed that increased social interactions among younger, less vaccinated populations significantly contributed to the surge in infections. The long weekend of Sant Joan (June 23-24) coincided with a peak in contact rates, driving a rise in the reproduction number, particularly among individuals aged 20-29. We estimated that the Delta variant had a 40-60.

CONCLUSIONS

Our findings underscore the critical role of vaccination coverage in mitigating the impact of emerging variants. The combination of increased social interactions and uneven vaccine distribution exacerbated the Delta-driven resurgence. NPIs alone proved insufficient in controlling transmission, highlighting the necessity of targeted vaccination strategies to achieve robust epidemic control. This study provides a framework for assessing future variant-specific threats and informing tailored public health interventions.

Multi-region infectious disease prediction modeling based on spatio-temporal graph neural network and the dynamic model

Human mobility between different regions is a major factor in large-scale outbreaks of infectious diseases. Deep learning models incorporating infectious disease transmission dynamics for predicting the spread of multi-regional outbreaks due to human mobility have become a hot research topic. In this study, we incorporate the Graph Transformer Neural Network and graph learning mechanisms into a metapopulation SIR model to build a hybrid framework, Metapopulation Graph Transformer Neural Network (M-Graphormer), for high-dimensional parameter estimation and multi-regional epidemic prediction. The framework effectively solves the problem that existing models may lose some hidden spatial dependencies in the data when dealing with the dynamic graph structure of the network due to human mobility. We performed multi-wave infectious disease prediction in multiple regions based on real epidemic data. The results show that the framework is capable of performing high-dimensional parameter estimation and accurately predicting epidemic transmission dynamics in multiple regions even with low data quality. In addition, we retrospectively extrapolate the temporal evolution patterns of contact rate under different interventions implemented in different regions, reflecting the dynamics of intervention intensity and the need for flexibility in adjusting interventions in different regions. To provide early warning of infectious disease transmission, we retrospectively predicted the arrival time of infectious diseases using data from the early stages of outbreaks.

Unexpected Transmission Dynamics in a University Town: Lessons from COVID-19

Institutions of higher education faced a number of challenges during the COVID-19 pandemic. Chief among them was whether or not to re-open during the second wave of COVID-19 in the fall of 2020, which was controversial because incidence in young adults was on the rise. The migration of students back to campuses worried many that transmission within student populations would spread into surrounding communities. In light of this, many colleges and universities implemented mitigation strategies, with varied degrees of success. Washington State University (WSU), located in the city of Pullman in Whitman County, WA, is an example of this type of university-community co-location, where the role of students returning to the area for the fall 2020 semester was contentious. Using COVID-19 incidence reported to Whitman County, we retrospectively study the transmission dynamics that occurred between the student and community subpopulations in fall 2020. We develop a two-population ordinary differential equation mechanistic model to infer transmission rates within and across the university student and community subpopulations. We use results from Bayesian parameter estimation to determine if sustained transmission of COVID-19 occurred in Whitman County and the magnitude of cross-transmission from students to community members. We find these results are consistent with estimation of the time-varying reproductive number and conclude that the students returning to WSU-Pullman did not place the surrounding community at disproportionate risk of COVID-19 during fall 2020 when mitigation efforts were in place.

M. Heuvelink G, Wu C, Yang J, Ruktanonchai NW, Qader SH, Ruktanonchai CW, Cleary E, Yao Y, Liu J, Nnanatu CC, Wesolowski A, Cummings DA, Tatem AJ, Lai S. Optimizing the detection of emerging infections using mobility-based spatial sampling

Timely and precise detection of emerging infections is imperative for effective outbreak management and disease control. Human mobility significantly influences the spatial transmission dynamics of infectious diseases. Spatial sampling, integrating the spatial structure of the target, holds promise as an approach for testing allocation in detecting infections, and leveraging information on individuals' movement and contact behavior can enhance targeting precision. This study introduces a spatial sampling framework informed by spatiotemporal analysis of human mobility data, aiming to optimize the allocation of testing resources for detecting emerging infections. Mobility patterns, derived from clustering point-of-interest and travel data, are integrated into four spatial sampling approaches at the community level. We evaluate the proposed mobility-based spatial sampling by analyzing both actual and simulated outbreaks, considering scenarios of transmissibility, intervention timing, and population density in cities. Results indicate that leveraging inter-community movement data and initial case locations, the proposed Case Flow Intensity (CFI) and Case Transmission Intensity (CTI)-informed spatial sampling enhances community-level testing efficiency by reducing the number of individuals screened while maintaining a high accuracy rate in infection identification. Furthermore, the prompt application of CFI and CTI within cities is crucial for effective detection, especially in highly contagious infections within densely populated areas. With the widespread use of human mobility data for infectious disease responses, the proposed theoretical framework extends spatiotemporal data analysis of mobility patterns into spatial sampling, providing a cost-effective solution to optimize testing resource deployment for containing emerging infectious diseases.

Study protocol: improving response to malaria in the Amazon through identification of inter-community networks and human mobility in border regions of Ecuador, Peru and Brazil

INTRODUCTION

Understanding human mobility's role in malaria transmission is critical to successful control and elimination. However, common approaches to measuring mobility are ill-equipped for remote regions such as the Amazon. This study develops a network survey to quantify the effect of community connectivity and mobility on malaria transmission.

METHODS

We measure community connectivity across the study area using a respondent driven sampling design among key informants who are at least 18 years of age. 45 initial communities will be selected: 10 in Brazil, 10 in Ecuador and 25 in Peru. Participants will be recruited in each initial node and administered a survey to obtain data on each community's mobility patterns. Survey responses will be ranked and the 2-3 most connected communities will then be selected and surveyed. This process will be repeated for a third round of data collection. Community network matrices will be linked with each country's malaria surveillance system to test the effects of mobility on disease risk.

ETHICS AND DISSEMINATION

This study protocol has been approved by the institutional review boards of Duke University (USA), Universidad San Francisco de Quito (Ecuador), Universidad Peruana Cayetano Heredia (Peru) and Universidade Federal Minas Gerais (Brazil). Results will be disseminated in communities by the end of the study.

Vector-borne disease models with Lagrangian approach

We develop a multi-group and multi-patch model to study the effects of population dispersal on the spatial spread of vector-borne diseases across a heterogeneous environment. The movement of host and/or vector is described by Lagrangian approach in which the origin or identity of each individual stays unchanged regardless of movement. The basic reproduction number [Formula: see text] of the model is defined and the strong connectivity of the host-vector network is succinctly characterized by the residence times matrices of hosts and vectors. Furthermore, the definition and criterion of the strong connectivity of general infectious disease networks are given and applied to establish the global stability of the disease-free equilibrium. The global dynamics of the model system are shown to be entirely determined by its basic reproduction number. We then obtain several biologically meaningful upper and lower bounds on the basic reproduction number which are independent or dependent of the residence times matrices. In particular, the heterogeneous mixing of hosts and vectors in a homogeneous environment always increases the basic reproduction number. There is a substantial difference on the upper bound of [Formula: see text] between Lagrangian and Eulerian modeling approaches. When only host movement between two patches is concerned, the subdivision of hosts (more host groups) can lead to a larger basic reproduction number. In addition, we numerically investigate the dependence of the basic reproduction number and the total number of infected hosts on the residence times matrix of hosts, and compare the impact of different vector control strategies on disease transmission.

Network Profile: Improving Response to Malaria in the Amazon through Identification of Inter-Community Networks and Human Mobility in Border Regions of Ecuador, Peru, and Brazil

Objectives

Understanding human mobility's role on malaria transmission is critical to successful control and elimination. However, common approaches to measuring mobility are ill-equipped for remote regions such as the Amazon. This study develops a network survey to quantify the effect of community connectivity and mobility on malaria transmission.

Design

A community-level network survey.

Setting

We collect data on community connectivity along three river systems in the Amazon basin: the Pastaza river corridor spanning the Ecuador-Peru border; and the Amazon and Javari river corridors spanning the Brazil-Peru border.

Participants

We interviewed key informants in Brazil, Ecuador, and Peru, including from indigenous communities: Shuar, Achuar, Shiwiar, Kichwa, Ticuna, and Yagua. Key informants are at least 18 years of age and are considered community leaders.

Primary outcome

Weekly, community-level malaria incidence during the study period.

Methods

We measure community connectivity across the study area using a respondent driven sampling design. Forty-five communities were initially selected: 10 in Brazil, 10 in Ecuador, and 25 in Peru. Participants were recruited in each initial node and administered a survey to obtain data on each community's mobility patterns. Survey responses were ranked and the 2-3 most connected communities were then selected and surveyed. This process was repeated for a third round of data collection. Community network matrices will be linked with eadch country's malaria surveillance system to test the effects of mobility on disease risk.

Findings

To date, 586 key informants were surveyed from 126 communities along the Pastaza river corridor. Data collection along the Amazon and Javari river corridors is ongoing. Initial results indicate that network sampling is a superior method to delineate migration flows between communities.

Conclusions

Our study provides measures of mobility and connectivity in rural settings where traditional approaches are insufficient, and will allow us to understand mobility's effect on malaria transmission.

Travel distance, frequency of return, and the spread of disease

Human mobility is a key driver of infectious disease spread. Recent literature has uncovered a clear pattern underlying the complexity of human mobility in cities: [Formula: see text], the product of distance traveled r and frequency of return f per user to a given location, is invariant across space. This paper asks whether the invariant [Formula: see text] also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable [Formula: see text]. We use two large-scale datasets of individual human mobility to show that there is in fact a simple relation between r and f and both speed and spatial dispersion of disease spread. This discovery could assist in modeling spread of disease and inform travel policies in future epidemics-based not only on travel distance r but also on frequency of return f.

CDC (Cindy and David's Conversations) game: Advising President to survive pandemic

Ongoing debates on anti-COVID19 policies have been focused on coexistence-with versus zero-out (virus) strategies, which can be simplified as "always open (AO)" versus "always closed (AC)." We postulate that a middle ground, dubbed LOHC (low-risk-open and high-risk-closed), is likely favorable, precluding obviously irrational HOLC (high-risk-open and low-risk-closed). From a meta-strategy perspective, these four policies cover the full spectrum of anti-pandemic policies. By emulating the reality of anti-pandemic policies today, the study aims to identify possible cognitive gaps and traps by harnessing the power of evolutionary game-theoretic analysis and simulations, which suggest that (1) AO and AC seem to be "high-probability" events (0.412-0.533); (2) counter-intuitively, the middle ground-LOHC-seems to be small-probability event (0.053), possibly mirroring its wide adoptions but broad failures. Besides devising specific policies, an equally important challenge seems to deal with often hardly avoidable policy transitions along the process from emergence, epidemic, through pandemic, to endemic state.

Genomic assessment of invasion dynamics of SARS-CoV-2 Omicron BA.1

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants of concern (VOCs) now arise in the context of heterogeneous human connectivity and population immunity. Through a large-scale phylodynamic analysis of 115,622 Omicron BA.1 genomes, we identified >6,000 introductions of the antigenically distinct VOC into England and analyzed their local transmission and dispersal history. We find that six of the eight largest English Omicron lineages were already transmitting when Omicron was first reported in southern Africa (22 November 2021). Multiple datasets show that importation of Omicron continued despite subsequent restrictions on travel from southern Africa as a result of export from well-connected secondary locations. Initiation and dispersal of Omicron transmission lineages in England was a two-stage process that can be explained by models of the country's human geography and hierarchical travel network. Our results enable a comparison of the processes that drive the invasion of Omicron and other VOCs across multiple spatial scales.

Risk averse reproduction numbers improve resurgence detection

The effective reproduction number R is a prominent statistic for inferring the transmissibility of infectious diseases and effectiveness of interventions. R purportedly provides an easy-to-interpret threshold for deducing whether an epidemic will grow (R>1) or decline (R<1). We posit that this interpretation can be misleading and statistically overconfident when applied to infections accumulated from groups featuring heterogeneous dynamics. These groups may be delineated by geography, infectiousness or sociodemographic factors. In these settings, R implicitly weights the dynamics of the groups by their number of circulating infections. We find that this weighting can cause delayed detection of outbreak resurgence and premature signalling of epidemic control because it underrepresents the risks from highly transmissible groups. Applying E-optimal experimental design theory, we develop a weighting algorithm to minimise these issues, yielding the risk averse reproduction number E. Using simulations, analytic approaches and real-world COVID-19 data stratified at the city and district level, we show that E meaningfully summarises transmission dynamics across groups, balancing bias from the averaging underlying R with variance from directly using local group estimates. An E>1generates timely resurgence signals (upweighting risky groups), while an E<1ensures local outbreaks are under control. We propose E as an alternative to R for informing policy and assessing transmissibility at large scales (e.g., state-wide or nationally), where R is commonly computed but well-mixed or homogeneity assumptions break down.

HM, Brady OJ, Guerra CA, García GA, Carter AR, Ferguson HM, Afolabi BE, Hay SI, Reiner RC, Kiware S, Smith DL. Spatial dynamics of malaria transmission

The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework-human population strata, patches, and aquatic habitats-interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the "vectorial capacity matrix," a human transmitting capacity distribution matrix, and threshold conditions. An [Formula: see text] package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems.

The Role of Permanently Resident Populations in the Two-Patches SIR Model with Commuters

We consider a two-patches SIR model where communication occurs through commuters, distinguishing explicitly permanently resident populations from commuters populations. We give an explicit formula of the reproduction number and show how the proportions of permanently resident populations impact it. We exhibit nonintuitive situations for which allowing commuting from a safe territory to another one where the transmission rate is higher can reduce the overall epidemic threshold and avoid an outbreak.

The transmission mechanism theory of disease dynamics: Its aims, assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process. Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history, dating back to over a century now, that knowledge has not yet been formalized into a scientific theory. In this article, we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system, disease dynamics is determined by transmission as the main dynamic disease process. Therefore, the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now. The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims, assumptions and limitations.

Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks

We examine how spatial heterogeneity combines with mobility network structure to influence vector-borne disease dynamics. Specifically, we consider a Ross-Macdonald-type disease model on n spatial locations that are coupled by host movement on a strongly connected, weighted, directed graph. We derive a closed form approximation to the domain reproduction number using a Laurent series expansion, and use this approximation to compute sensitivities of the basic reproduction number to model parameters. To illustrate how these results can be used to help inform mitigation strategies, as a case study we apply these results to malaria dynamics in Namibia, using published cell phone data and estimates for local disease transmission. Our analytical results are particularly useful for understanding drivers of transmission when mobility sinks and transmission hot spots do not coincide.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

An algebraic framework for structured epidemic modelling

Pandemic management requires that scientists rapidly formulate and analyse epidemiological models in order to forecast the spread of disease and the effects of mitigation strategies. Scientists must modify existing models and create novel ones in light of new biological data and policy changes such as social distancing and vaccination. Traditional scientific modelling workflows detach the structure of a model-its submodels and their interactions-from its implementation in software. Consequently, incorporating local changes to model components may require global edits to the code base through a manual, time-intensive and error-prone process. We propose a compositional modelling framework that uses high-level algebraic structures to capture domain-specific scientific knowledge and bridge the gap between how scientists think about models and the code that implements them. These algebraic structures, grounded in applied category theory, simplify and expedite modelling tasks such as model specification, stratification, analysis and calibration. With their structure made explicit, models also become easier to communicate, criticize and refine in light of stakeholder feedback. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimating SARS-CoV-2 variant fitness and the impact of interventions in England using statistical and geo-spatial agent-based models

The SARS-CoV-2 epidemic has been extended by the evolution of more transmissible viral variants. In autumn 2020, the B.1.177 lineage became the dominant variant in England, before being replaced by the B.1.1.7 (Alpha) lineage in late 2020, with the sweep occurring at different times in each region. This period coincided with a large number of non-pharmaceutical interventions (e.g. lockdowns) to control the epidemic, making it difficult to estimate the relative transmissibility of variants. In this paper, we model the spatial spread of these variants in England using a meta-population agent-based model which correctly characterizes the regional variation in cases and distribution of variants. As a test of robustness, we additionally estimated the relative transmissibility of multiple variants using a statistical model based on the renewal equation, which simultaneously estimates the effective reproduction number R. Relative to earlier variants, the transmissibility of B.1.177 is estimated to have increased by 1.14 (1.12-1.16) and that of Alpha by 1.71 (1.65-1.77). The vaccination programme starting in December 2020 is also modelled. Counterfactual simulations demonstrate that the vaccination programme was essential for reopening in March 2021, and that if the January lockdown had started one month earlier, up to 30 k (24 k-38 k) deaths could have been prevented. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Spatio-temporal spread of COVID-19: Comparison of the inhomogeneous SEPIR model and data from South Carolina

During the COVID-19 pandemic authorities have been striving to obtain reliable predictions for the spreading dynamics of the disease. We recently developed a multi-“sub-populations” (multi-compartments: susceptible, exposed, pre-symptomatic, infectious, recovered) model, that accounts for the spatial in-homogeneous spreading of the infection and shown, for a variety of examples, how the epidemic curves are highly sensitive to location of epicenters, non-uniform population density, and local restrictions. In the present work we test our model against real-life data from South Carolina during the period May 22 to July 22 (2020). During this period, minimal restrictions have been employed, which allowed us to assume that the local basic reproduction number is constant in time. We account for the non-uniform population density in South Carolina using data from NASA’s Socioeconomic Data and Applications Center (SEDAC), and predict the evolution of infection heat-maps during the studied period. Comparing the predicted heat-maps with those observed, we find high qualitative resemblance. Moreover, the Pearson’s correlation coefficient is relatively high thus validating our model against real-world data. We conclude that the model accounts for the major effects controlling spatial in-homogeneous spreading of the disease. Inclusion of additional sub-populations (compartments), in the spirit of several recently developed models for COVID-19, can be easily performed within our mathematical framework.

Reassessment of contact restrictions and testing campaigns against COVID-19 via spatio-temporal modeling

Since the earliest outbreak of COVID-19, the disease continues to obstruct life normalcy in many parts of the world. The present work proposes a mathematical framework to improve non-pharmaceutical interventions during the new normal before vaccination settles herd immunity. The considered approach is built from the viewpoint of decision makers in developing countries where resources to tackle the disease from both a medical and an economic perspective are scarce. Spatial auto-correlation analysis via global Moran's index and Moran's scatter is presented to help modulate decisions on hierarchical-based priority for healthcare capacity and interventions (including possible vaccination), finding a route for the corresponding deployment as well as landmarks for appropriate border controls. These clustering tools are applied to sample data from Sri Lanka to classify the 26 Regional Director of Health Services (RDHS) divisions into four clusters by introducing convenient classification criteria. A metapopulation model is then used to evaluate the intra- and inter-cluster contact restrictions as well as testing campaigns under the absence of confounding factors. Furthermore, we investigate the role of the basic reproduction number to determine the long-term trend of the regressing solution around disease-free and endemic equilibria. This includes an analytical bifurcation study around the basic reproduction number using Brouwer Degree Theory and asymptotic expansions as well as related numerical investigations based on path-following techniques. We also introduce the notion of average policy effect to assess the effectivity of contact restrictions and testing campaigns based on the proposed model's transient behavior within a fixed time window of interest.

Spatial scales in human movement between reservoirs of infection

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Simple, yet flexible, model of human movement patterns.

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Analytic formalism which can be used to derive important spatial scales.

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Introduces a novel drift–diffusion approximation for stochastic reservoirs.

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A new critical spatial scale predicted for helminth reservoirs of infection.

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The necessary data needed to test these predictions is outlined in detail.

The life cycle of parasitic organisms that are the cause of much morbidity in humans often depend on reservoirs of infection for transmission into their hosts. Understanding the daily, monthly and yearly movement patterns of individuals between reservoirs is therefore of great importance to implementers of control policies seeking to eliminate various parasitic diseases as a public health problem. This is due to the fact that the underlying spatial extent of the reservoir of infection, which drives transmission, can be strongly affected by inputs from external sources, i.e., individuals who are not spatially attributed to the region defined by the reservoir itself can still migrate and contribute to it. In order to study the importance of these effects, we build and examine a novel theoretical model of human movement between spatially-distributed focal points for infection clustered into regions defined as ‘reservoirs of infection’. Using our model, we vary the spatial scale of human moment defined around focal points and explicitly calculate how varying this definition can influence the temporal stability of the effective transmission dynamics – an effect which should strongly influence how control measures, e.g., mass drug administration (MDA), define evaluation units (EUs). Considering the helminth parasites as our main example, by varying the spatial scale of human movement, we demonstrate that a critical scale exists around infectious focal points at which the migration rate into their associated reservoir can be neglected for practical purposes. This scale varies by species and geographic region, but is generalisable as a concept to infectious reservoirs of varying spatial extents and shapes. Our model is designed to be applicable to a very general pattern of infectious disease transmission modified by the migration of infected individuals between clustered communities. In particular, it may be readily used to study the spatial structure of hosts for macroparasites with temporally stationary distributions of infectious focal point locations over the timescales of interest, which is viable for the soil-transmitted helminths and schistosomes. Additional developments will be necessary to consider diseases with moving reservoirs, such as vector-born filarial worm diseases.