109 results on '"Joel C. Miller"'
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2. A primer on the use of probability generating functions in infectious disease modeling
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Joel C. Miller
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Infectious and parasitic diseases ,RC109-216 - Abstract
We explore the application of probability generating functions (PGFs) to invasive processes, focusing on infectious disease introduced into large populations. Our goal is to acquaint the reader with applications of PGFs, moreso than to derive new results. PGFs help predict a number of properties about early outbreak behavior while the population is still effectively infinite, including the probability of an epidemic, the size distribution after some number of generations, and the cumulative size distribution of non-epidemic outbreaks. We show how PGFs can be used in both discrete-time and continuous-time settings, and discuss how to use these results to infer disease parameters from observed outbreaks. In the large population limit for susceptible-infected-recovered (SIR) epidemics PGFs lead to survival-function based models that are equivalent to the usual mass-action SIR models but with fewer ODEs. We use these to explore properties such as the final size of epidemics or even the dynamics once stochastic effects are negligible. We target this primer at biologists and public health researchers with mathematical modeling experience who want to learn how to apply PGFs to invasive diseases, but it could also be used in an applications-based mathematics course on PGFs. We include many exercises to help demonstrate concepts and to give practice applying the results. We summarize our main results in a few tables. Additionally we provide a small python package which performs many of the relevant calculations.
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- 2018
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3. Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes
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Joel C. Miller
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Infectious and parasitic diseases ,RC109-216 - Abstract
The emergence of Zika and Ebola demonstrates the importance of understanding the role of sexual transmission in the spread of diseases with a primarily non-sexual transmission route. In this paper, we develop low-dimensional models for how an SIR disease will spread if it transmits through a sexual contact network and some other transmission mechanism, such as direct contact or vectors. We show that the models derived accurately predict the dynamics of simulations in the large population limit, and investigate â0 and final size relations.
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- 2017
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4. Correction: Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics.
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Erik M. Volz, Joel C. Miller, Alison Galvani, and Lauren Ancel Meyers
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Biology (General) ,QH301-705.5 - Published
- 2011
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5. Epidemic Percolation Networks, Epidemic Outcomes, and Interventions
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Eben Kenah and Joel C. Miller
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Infectious and parasitic diseases ,RC109-216 - Abstract
Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies.
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- 2011
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6. Ethical frameworks should be applied to computational modelling of infectious disease interventions.
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Cameron Zachreson, Julian Savulescu, Freya M Shearer, Michael J Plank, Simon Coghlan, Joel C Miller, Kylie E C Ainslie, and Nicholas Geard
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Biology (General) ,QH301-705.5 - Abstract
This perspective is part of an international effort to improve epidemiological models with the goal of reducing the unintended consequences of infectious disease interventions. The scenarios in which models are applied often involve difficult trade-offs that are well recognised in public health ethics. Unless these trade-offs are explicitly accounted for, models risk overlooking contested ethical choices and values, leading to an increased risk of unintended consequences. We argue that such risks could be reduced if modellers were more aware of ethical frameworks and had the capacity to explicitly account for the relevant values in their models. We propose that public health ethics can provide a conceptual foundation for developing this capacity. After reviewing relevant concepts in public health and clinical ethics, we discuss examples from the COVID-19 pandemic to illustrate the current separation between public health ethics and infectious disease modelling. We conclude by describing practical steps to build the capacity for ethically aware modelling. Developing this capacity constitutes a critical step towards ethical practice in computational modelling of public health interventions, which will require collaboration with experts on public health ethics, decision support, behavioural interventions, and social determinants of health, as well as direct consultation with communities and policy makers.
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- 2024
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7. Mobile Messaging as Surveillance Tool during Pandemic (H1N1) 2009, Mexico
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Martín Lajous, Leon Danon, Ruy López-Ridaura, Christina M. Astley, Joel C. Miller, Scott F. Dowell, Justin J. O’Hagan, Edward Goldstein, and Marc Lipsitch
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Influenza ,cell phone ,surveillance ,mobile messaging ,survey ,viruses ,Medicine ,Infectious and parasitic diseases ,RC109-216 - Published
- 2010
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8. Early Real-Time Estimation of the Basic Reproduction Number of Emerging Infectious Diseases
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Bahman Davoudi, Joel C. Miller, Rafael Meza, Lauren Ancel Meyers, David J. D. Earn, and Babak Pourbohloul
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Physics ,QC1-999 - Abstract
When an infectious disease strikes a population, the number of newly reported cases is often the only available information during the early stages of the outbreak. An important goal of early outbreak analysis is to obtain a reliable estimate for the basic reproduction number, R_{0}. Over the past few years, infectious disease epidemic processes have gained attention from the physics community. Much of the work to date, however, has focused on the analysis of an epidemic process in which the disease has already spread widely within a population; conversely, very little attention has been paid, in the physics literature or elsewhere, to formulating the initial phase of an outbreak. Careful analysis of this phase is especially important as it could provide policymakers with insight on how to effectively control an epidemic in its initial stage. We present a novel method, based on the principles of network theory, that enables us to obtain a reliable real-time estimate of the basic reproduction number at an early stage of an outbreak. Our method takes into account the possibility that the infectious period has a wide distribution and that the degree distribution of the underlying contact network is heterogeneous. We validate our analytical framework with numerical simulations.
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- 2012
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9. Fast Variables Determine the Epidemic Threshold in the Pairwise Model with an Improved Closure.
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István Z. Kiss, Joel C. Miller, and Péter L. Simon
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- 2018
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10. Optimal timing of one-shot interventions for epidemic control.
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Francesco Di Lauro, István Z. Kiss, and Joel C. Miller
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- 2021
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11. Protective impacts of household-based tuberculosis contact tracing are robust across endemic incidence levels and community contact patterns.
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Joshua Havumaki, Ted Cohen, Chengwei Zhai, Joel C. Miller, Seth D. Guikema, Marisa C. Eisenberg, and Jon Zelner
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- 2021
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12. Concurrency measures in the era of temporal network epidemiology: A review.
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Naoki Masuda, Joel C. Miller, and Petter Holme
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- 2020
13. Analytic models for SIR disease spread on random spatial networks.
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John C. Lang, Hans De Sterck, Jamieson L. Kaiser, and Joel C. Miller
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- 2018
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14. Which lockdowns are the best lockdowns? Optimal interventions and the trolley problem in heterogeneous populations
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Pratyush K. Kollepara, Rebecca H. Chisholm, István Z. Kiss, and Joel C. Miller
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Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimises the attack rate of an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second-wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policy makers. This ethical dilemma is shown to be analogous to the trolley problem and we discuss how the dilemma can be avoided.
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- 2023
15. Complex contagions and hybrid phase transitions.
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Joel C. Miller
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- 2016
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16. Efficient Generation of Networks with Given Expected Degrees.
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Joel C. Miller and Aric A. Hagberg
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- 2011
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17. Seasonality in risk of pandemic influenza emergence.
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Spencer J. Fox, Joel C. Miller, and Lauren Ancel Meyers
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- 2017
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18. EoN (Epidemics on Networks): a fast, flexible Python package for simulation, analytic approximation, and analysis of epidemics on networks.
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Joel C. Miller and Tony Ting
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- 2019
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19. Quantifying the impact of individual and collective compliance with infection control measures for ethical public health policy
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Daniel Roberts, Euzebiusz Jamrozik, George S. Heriot, Anja C. Slim, Michael J. Selgelid, and Joel C. Miller
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Multidisciplinary - Abstract
Infectious disease control measures often require collective compliance of large numbers of individuals to benefit public health. This raises ethical questions regarding the value of the public health benefit created by individual and collective compliance. Answering these requires estimating the extent to which individual actions prevent infection of others. We develop mathematical techniques enabling quantification of the impacts of individuals or groups complying with three public health measures: border quarantine, isolation of infected individuals, and prevention via vaccination/prophylaxis. The results suggest that (i) these interventions exhibit synergy: they become more effective on a per-individual basis as compliance increases and (ii) There is often significant “overdetermination” of transmission: if a susceptible person contacts multiple infectious individuals, an intervention preventing one transmission may not change the ultimate outcome (thus risk imposed by some individuals may erode the benefits of others’ compliance). These results have implications for public health policy during epidemics.
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- 2021
20. The Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective
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Francesco Di Lauro, Istvan Z. Kiss, Luc Berthouze, Matthew D. Dorey, and Joel C. Miller
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Immunity, Herd ,Computer science ,General Mathematics ,Immunology ,Population ,Residual ,General Biochemistry, Genetics and Molecular Biology ,Herd immunity ,Econometrics ,Humans ,education ,Set (psychology) ,Epidemics ,Uncategorized ,General Environmental Science ,Network model ,Pharmacology ,Flexibility (engineering) ,education.field_of_study ,General Neuroscience ,Mathematical Concepts ,Models, Theoretical ,Computational Theory and Mathematics ,Transmission (telecommunications) ,Susceptible individual ,Epidemiological Models ,Original Article ,General Agricultural and Biological Sciences - Abstract
The contact structure of a population plays an important role in transmission of infection. Many ‘structured models’ capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction $$1-1/{\mathcal {R}}_0$$ 1 - 1 / R 0 has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunising higher-risk individuals who play a greater role in transmission. Therefore, a limited ‘first wave’ may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model.
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- 2021
21. Authority Rankings from HITS, PageRank, and SALSA: Existence, Uniqueness, and Effect of Initialization.
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Ayman Farahat, Thomas LoFaro, Joel C. Miller, Gregory Rae, and Lesley A. Ward
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- 2006
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22. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs.
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Douglas Baldwin, ünal Göktas, Willy Hereman, Linda Hong, Ryan S. Martino, and Joel C. Miller
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- 2004
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23. Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics
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Robert R. Wilkinson, Joel C Miller, Adedapo Chris Loyinmi, Christopher E. Overton, and Kieran J. Sharkey
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QA75 ,Stochastic modelling ,General Mathematics ,Immunology ,Communicable Diseases ,Models, Biological ,General Biochemistry, Genetics and Molecular Biology ,Moment closure ,FOS: Mathematics ,Applied mathematics ,Humans ,Quantitative Biology - Populations and Evolution ,Epidemics ,General Environmental Science ,Mathematics ,Pharmacology ,Stochastic Processes ,General Neuroscience ,Probability (math.PR) ,Dynamics (mechanics) ,Populations and Evolution (q-bio.PE) ,State (functional analysis) ,Mathematical Concepts ,Distribution (mathematics) ,Computational Theory and Mathematics ,FOS: Biological sciences ,Ordinary differential equation ,Graph (abstract data type) ,General Agricultural and Biological Sciences ,Epidemic model ,Mathematics - Probability - Abstract
Deterministic approximations to stochastic Susceptible–Infectious–Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.
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- 2021
24. A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling
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Gergely Röst, Istvan Z. Kiss, Zsolt Vizi, and Joel C. Miller
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Distribution (number theory) ,Reproduction number ,Epidemic ,Monotonic function ,Network ,Pairwise model ,01 natural sciences ,Non-Markovian ,03 medical and health sciences ,0103 physical sciences ,Statistics ,90B10, 90B15, 92D30 ,Quantitative Biology::Populations and Evolution ,lcsh:Industry ,Quantitative Biology - Populations and Evolution ,010306 general physics ,QA ,030304 developmental biology ,Mathematics ,0303 health sciences ,Applied Mathematics ,lcsh:Mathematics ,Populations and Evolution (q-bio.PE) ,Variance (accounting) ,Infectious period ,lcsh:QA1-939 ,FOS: Biological sciences ,Epidemic outbreak ,Pairwise comparison ,lcsh:HD2321-4730.9 - Abstract
For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks.
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- 2019
25. Evaluating the contributions of strategies to prevent SARS-CoV-2 transmission in the healthcare setting: a modelling study
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William P. Hanage, Xueting Qiu, Joel C. Miller, and Derek R. MacFadden
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medicine.medical_specialty ,Infectious Disease Transmission, Patient-to-Professional ,Coronavirus disease 2019 (COVID-19) ,protocols & guidelines ,Health Personnel ,media_common.quotation_subject ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Force of infection ,01 natural sciences ,Article ,health & safety ,03 medical and health sciences ,0302 clinical medicine ,Health care ,Pandemic ,medicine ,Humans ,Infection control ,030212 general & internal medicine ,0101 mathematics ,Intensive care medicine ,Pandemics ,Personal Protective Equipment ,Personal protective equipment ,Health policy ,media_common ,030304 developmental biology ,0303 health sciences ,business.industry ,Transmission (medicine) ,Public health ,010102 general mathematics ,COVID-19 ,health policy ,General Medicine ,Models, Theoretical ,infection control ,3. Good health ,Medicine ,Psychological resilience ,Public Health ,business ,Delivery of Health Care - Abstract
SummaryBackgroundSince its onset, the COVID-19 pandemic has caused significant morbidity and mortality worldwide, with particularly severe outcomes in healthcare institutions and congregate settings. To mitigate spread, healthcare systems have been cohorting patients to limit contacts between uninfected patients and potentially infected patients or healthcare workers (HCWs). A major challenge in managing the pandemic is the presence of currently asymptomatic individuals capable of transmitting the virus, who could introduce COVID-19 into uninfected cohorts. The optimal combination of personal protective equipment (PPE) and testing approaches to prevent these events is unclear, especially in light of ongoing limitations in access to both.MethodsUsing stochastic simulations with an SEIR model we quantified and compared the impacts of PPE use, patient and HCWs testing, and cohorting.FindingsIn the base case without testing or PPE, the healthcare system was rapidly overwhelmed, and became a net contributor to the force of infection. We found that effective use of PPE by both HCWs and patients could prevent this scenario, while random testing of apparently asymptomatic individuals on a weekly basis was less effective. We also found that even imperfect use of PPE could provide substantial protection by decreasing the force of infection, and that creation of smaller patient/HCW subcohorts can provide additional resilience to outbreak development.InterpretationThese findings reinforce the importance of ensuring adequate PPE supplies even in the absence of testing, and provide support for strict subcohorting regimens to reduce outbreak potential in healthcare institutions.FundingNational Institute of General Medical Sciences, National Institutes of Health.Research in contextEvidence beforePreserving healthcare from outbreaks of respiratory viruses is a longstanding concern, brought into sharp relief by the covid-19 pandemic. Early case series and numerous anecdotal reports suggest that health care workers (HCWs) and patients receiving treatment for conditions other than SARS-CoV-2 infection are at elevated risk of becoming infected, and the consequences of infections in long term care facilities are well known. In addition, the early stages of the pandemic have been marked by shortages of personal protective equipment (PPE) and diagnostic testing, but the most effective strategies for their use given the specific characteristics of SARS-CoV-2 transmission are unclear.Value addedOur research plainly shows the importance of presymptomatic transmission. Given reasonable estimates of this, random testing of currently asymptomatic staff and patients once a week is not able to prevent large outbreaks. We show that PPE is, as expected, the most effective intervention and moreover even suboptimal PPE use is highly beneficial. To further limit transmission, we show the benefit of sub-cohorting into smaller groups of HCWs and patients. When the force of infection in the community is low, this can entirely prevent the establishment of infection in a large fraction of healthcare.ImplicationsPPE should be used throughout healthcare, on the assumption that any patient or HCWs is potentially infected. Further work should determine the most effective means of PPE for the non-COVID cohort. If PPE resources are limited, whether in general or due to a second surge, we recommend subcohorting to limit the impact of introductions from the community.
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- 2021
26. Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control
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Antoine Allard, Hao Hu, Benjamin M. Althouse, Edward Allen Wenger, Laurent Hébert-Dufresne, Samuel V. Scarpino, and Joel C. Miller
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RNA viruses ,0301 basic medicine ,Viral Diseases ,Pulmonology ,Coronaviruses ,Epidemiology ,Psychological intervention ,Disease ,Disease Outbreaks ,law.invention ,Medical Conditions ,0302 clinical medicine ,law ,Pandemic ,Medicine and Health Sciences ,Poisson Distribution ,030212 general & internal medicine ,Biology (General) ,Pathology and laboratory medicine ,Virus Testing ,Coinfection ,General Neuroscience ,Medical microbiology ,Viral Load ,Infectious Diseases ,Transmission (mechanics) ,Viruses ,SARS CoV 2 ,Pathogens ,General Agricultural and Biological Sciences ,SARS coronavirus ,Coronavirus disease 2019 (COVID-19) ,Essay ,QH301-705.5 ,Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) ,Opportunistic Infections ,Biology ,Microbiology ,General Biochemistry, Genetics and Molecular Biology ,Respiratory Disorders ,03 medical and health sciences ,Diagnostic Medicine ,Virology ,Environmental health ,Humans ,Stochastic Processes ,Biology and life sciences ,General Immunology and Microbiology ,SARS-CoV-2 ,Organisms ,Viral pathogens ,COVID-19 ,Outbreak ,Covid 19 ,Microbial pathogens ,030104 developmental biology ,Medical Risk Factors ,Respiratory Infections ,Basic reproduction number ,Viral Transmission and Infection - Abstract
Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), the etiological agent of the Coronavirus Disease 2019 (COVID-19) disease, has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used—appropriately and less appropriately—to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, often dominated by a small number of individuals, and heavily influenced by superspreading events (SSEs). The distinct transmission features of SARS-CoV-2, e.g., high stochasticity under low prevalence (as compared to other pathogens, such as influenza), and the central role played by SSEs on transmission dynamics cannot be overlooked. Many explosive SSEs have occurred in indoor settings, stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, produce processing facilities, fish factories, cruise ships, family gatherings, parties, and nightclubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity to effectively contain outbreaks with targeted interventions to eliminate SSEs. Here, we describe the different types of SSEs, how they influence transmission, empirical evidence for their role in the COVID-19 pandemic, and give recommendations for control of SARS-CoV-2., This Essay discusses how the transmission of COVID-19 is dominated by superspreading events, proposing that finding ways to cut the long tail of secondary infections is important for controlling onward transmission.
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- 2020
27. Effects of Heterogeneous and Clustered Contact Patterns on Infectious Disease Dynamics.
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Erik M. Volz, Joel C. Miller, Alison P. Galvani, and Lauren Ancel Meyers
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- 2011
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28. Decision letter: Evidence for transmission of COVID-19 prior to symptom onset
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Joel C Miller, Marc Lipsitch, and Virginia E. Pitzer
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Pediatrics ,medicine.medical_specialty ,Transmission (mechanics) ,Coronavirus disease 2019 (COVID-19) ,business.industry ,law ,Medicine ,Symptom onset ,business ,law.invention - Published
- 2020
29. If long-term suppression is not possible, how do we minimize mortality for COVID-19 and other emerging infectious disease outbreaks?
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Isaac Chun-Hai Fung, Andreas Handel, Joel C. Miller, and Yang Ge
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medicine.medical_specialty ,Population level ,Coronavirus disease 2019 (COVID-19) ,Containment ,Immunity ,business.industry ,Social distance ,Psychological intervention ,medicine ,Emerging infectious disease ,Outbreak ,Intensive care medicine ,business - Abstract
As COVID-19 continues to spread, public health interventions are crucial to minimize its impact. The most desirable goal is to drive the pathogen quickly to extinction. This generally involves applying interventions as strongly as possible, which worked for SARS, but so far has failed for COVID-19. If fast eradication is not achievable, the next best goal is to delay the spread and minimize cases and burden on the health care system until suitable drugs or vaccines are available. This suppression approach also calls for strong interventions, potentially applied for a long time.
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- 2020
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30. The timing of one-shot interventions for epidemic control
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Joel C. Miller, Francesco Di Lauro, and Istvan Z. Kiss
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medicine.medical_specialty ,education.field_of_study ,One shot ,business.industry ,Growth phase ,Population ,Psychological intervention ,Harm ,Intervention (counseling) ,Pandemic ,medicine ,Intensive care medicine ,education ,business ,Epidemic control - Abstract
The interventions and outcomes in the ongoing SARS-CoV-2 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a “one-shot intervention”) on an epidemic and consider the impact of the intervention’s timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately. Author Summary Some interventions which help control a spreading epidemic have significant adverse effects on the population, and cannot be maintained long-term. The optimal timing of such an intervention will depend on the ultimate goal. Interventions to delay the epidemic while new treatments or interventions are developed are best implemented as soon as possible. Interventions to minimize the peak prevalence are best implemented partway through the growth phase allowing immunity to build up so that the eventual rebound is not larger than the initial peak. Interventions to minimize the total number of infections are best implemented late in the growth phase to minimize the amount of rebound. For a population with subcommunities which would have asynchronous outbreaks, similar results hold. Additionally, we find that it is best to target the intervention asynchronously to each subcommunity rather than synchronously across the population.
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- 2020
31. EoN (Epidemics on Networks): a fast, flexible Python package for simulation, analytic approximation, and analysis of epidemics on networks
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Tony Ting and Joel C. Miller
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0303 health sciences ,Physics - Physics and Society ,Complex contagion ,Computer science ,Distributed computing ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,Python (programming language) ,01 natural sciences ,Quantitative Biology - Quantitative Methods ,03 medical and health sciences ,FOS: Biological sciences ,0103 physical sciences ,Stochastic simulation ,010303 astronomy & astrophysics ,computer ,Quantitative Methods (q-bio.QM) ,030304 developmental biology ,computer.programming_language - Abstract
We provide a description of the Epidemics on Networks (EoN) python package designed for studying disease spread in static networks. The package consists of over $100$ methods available for users to perform stochastic simulation of a range of different processes including SIS and SIR disease, and generic simple or comlex contagions., Comment: This paper is available in a shorter form without examples at https://joss.theoj.org/papers/10.21105/joss.01731.pdf
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- 2020
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32. Modifications of Kleinberg's HITS Algorithm Using Matrix Exponentiation and WebLog Records.
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Joel C. Miller, Gregory Rae, and Fred Schaefer
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- 2001
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33. Mean-field models for non-Markovian epidemics on networks
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Konstantin B. Blyuss, Joel C. Miller, Istvan Z. Kiss, and Neil Sherborne
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Theoretical computer science ,Exponential distribution ,Time Factors ,Computer science ,Markov process ,01 natural sciences ,Communicable Diseases ,Models, Biological ,Article ,Mean-field models ,010305 fluids & plasmas ,symbols.namesake ,37N25 ,0103 physical sciences ,92D30 ,Humans ,Computer Simulation ,Statistical physics ,Fixed length ,010306 general physics ,QA ,Epidemics ,Probability ,Stochastic Processes ,Applied Mathematics ,Message passing ,Computational Biology ,Rigorous proof ,Mathematical Concepts ,Infectious period ,Agricultural and Biological Sciences (miscellaneous) ,Markov Chains ,Mean field theory ,Modeling and Simulation ,symbols ,Non-Markovian transmission and recovery ,Epidemics on networks ,Pairwise comparison - Abstract
This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission the message passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.
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- 2017
34. Protective impacts of household-based tuberculosis contact tracing are robust across endemic incidence levels and community contact patterns
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Marisa C. Eisenberg, Chengwei Zhai, Ted Cohen, Joel C. Miller, Seth D. Guikema, Jon Zelner, and Joshua Havumaki
- Subjects
Bacterial Diseases ,Epidemiology ,Information Theory ,Tuberculosis Contact ,Psychological intervention ,Global Health ,law.invention ,Medical Conditions ,0302 clinical medicine ,Risk Factors ,law ,Drug Discovery ,Medicine and Health Sciences ,030212 general & internal medicine ,Biology (General) ,Randomized Controlled Trials as Topic ,Family Characteristics ,Ecology ,Incidence ,Mortality rate ,Incidence (epidemiology) ,Tuberculosis Drug Discovery ,Infectious Diseases ,Transmission (mechanics) ,Geography ,Computational Theory and Mathematics ,Modeling and Simulation ,Physical Sciences ,Disease Progression ,Tuberculosis Diagnosis and Management ,Algorithms ,Network Analysis ,Research Article ,Computer and Information Sciences ,Drug Research and Development ,Tuberculosis ,Death Rates ,QH301-705.5 ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Population Metrics ,Clustering Coefficients ,Diagnostic Medicine ,Environmental health ,Genetics ,medicine ,Humans ,Computer Simulation ,Molecular Biology ,Ecology, Evolution, Behavior and Systematics ,Disease burden ,Probability ,Public Health Informatics ,Pharmacology ,Population Biology ,Biology and Life Sciences ,Tropical Diseases ,medicine.disease ,030228 respiratory system ,Graph Theory ,Medical Risk Factors ,Contact Tracing ,Mathematics ,Contact tracing - Abstract
There is an emerging consensus that achieving global tuberculosis control targets will require more proactive case finding approaches than are currently used in high-incidence settings. Household contact tracing (HHCT), for which households of newly diagnosed cases are actively screened for additional infected individuals is a potentially efficient approach to finding new cases of tuberculosis, however randomized trials assessing the population-level effects of such interventions in settings with sustained community transmission have shown mixed results. One potential explanation for this is that household transmission is responsible for a variable proportion of population-level tuberculosis burden between settings. For example, transmission is more likely to occur in households in settings with a lower tuberculosis burden and where individuals mix preferentially in local areas, compared with settings with higher disease burden and more dispersed mixing. To better understand the relationship between endemic incidence levels, social mixing, and the impact of HHCT, we developed a spatially explicit model of coupled household and community transmission. We found that the impact of HHCT was robust across settings of varied incidence and community contact patterns. In contrast, we found that the effects of community contact tracing interventions were sensitive to community contact patterns. Our results suggest that the protective benefits of HHCT are robust and the benefits of this intervention are likely to be maintained across epidemiological settings., Author summary Screening household members of newly detected tuberculosis cases is an efficient method for finding previously undiagnosed cases in high-burden settings. Despite the intuitive appeal of this approach, randomized trials examining the population-level effects of these interventions in settings with sustained community transmission have shown mixed results. One explanation for these inconclusive findings is that household transmission is responsible for a varying proportion of overall tuberculosis burden between locations, with the impact of household transmission being a function of both the overall incidence and the relative intensity of disease-transmitting contacts in the community and the household. In this manuscript, we use an individual-based network model to explore how local incidence levels and patterns of community contact impact the effectiveness of household-based approaches for interrupting tuberculosis transmission. Our analyses suggest that protective benefits of household-based interventions are maintained across a wide range of epidemiological settings. Our findings provide evidence for the robustness of household-based interventions and suggest that variable results from trials may be primarily due to implementation challenges rather than inherent limitations of these interventions.
- Published
- 2021
35. A data-driven network model for the emerging COVID-19 epidemics in Wuhan, Toronto and Italy
- Author
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Ling Xue, Huafeng Li, Joel C. Miller, Jose G. Estrada-Franco, Wei Sun, Shuanglin Jing, James M. Hyman, and Huaiping Zhu
- Subjects
Control measures ,Basic Reproduction Number ,Mitigation strategies ,01 natural sciences ,Pandemic ,Regional science ,Network model ,Ontario ,0303 health sciences ,Applied Mathematics ,General Medicine ,Markov Chains ,3. Good health ,Italy ,Modeling and Simulation ,Quarantine ,symbols ,Coronavirus Infections ,General Agricultural and Biological Sciences ,Monte Carlo Method ,Algorithms ,Statistics and Probability ,China ,Physics - Physics and Society ,medicine.medical_specialty ,Pneumonia, Viral ,FOS: Physical sciences ,Physics and Society (physics.soc-ph) ,Models, Biological ,Article ,General Biochemistry, Genetics and Molecular Biology ,Betacoronavirus ,03 medical and health sciences ,symbols.namesake ,Modelling and Simulation ,0103 physical sciences ,Confidence Intervals ,medicine ,Humans ,Computer Simulation ,Epidemics ,Quantitative Biology - Populations and Evolution ,010306 general physics ,Pandemics ,030304 developmental biology ,General Immunology and Microbiology ,Markov chain ,SARS-CoV-2 ,Node (networking) ,Public health ,Populations and Evolution (q-bio.PE) ,COVID-19 ,Markov chain Monte Carlo ,Mathematical Concepts ,Megacity ,FOS: Biological sciences ,Heterogeneity ,Contact Tracing ,Basic reproduction number - Abstract
The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data for the COVID-19 epidemic in Wuhan (China), Toronto (Canada), and the Italian Republic using a Markov Chain Monte Carlo (MCMC) optimization algorithm. Our model fits all three regions well with narrow confidence intervals and could be adapted to simulate other megacities or regions. The model projections on the role of containment strategies can help inform public health authorities to plan control measures., Highlights • Predictive modelling and forecasting the epidemic trends for COVID-19 are essential for developing countermeasures to mitigate this pandemic. • We develop a network model, taking into account underlying social contact heterogeneity in the real world. • We derived explicit expressions of the basic reproduction number and final epidemic size. • Our model fitted the outbreaks for the three selected places very well with narrow confidence intervals and could be adapted to other megacities or other regions. • The model projections on the role of containment strategies can help inform public health authorities to plan control measures.
- Published
- 2020
36. Implementation and applications of EMOD, an individual-based multi-disease modeling platform
- Author
-
Jaline Gerardin, Kevin A. McCarthy, Kurt Frey, Philip A. Welkhoff, Edward Allen Wenger, Jillian S. Gauld, Jeffrey Steinkraus, Amanda S Izzo, Joel C. Miller, Thomas Fischle, Robert S Baker, Christian N Wiswell, Christopher W. Lorton, Guillaume Chabot-Couture, Anna Bershteyn, Jonathan Bloedow, Quirine A. ten Bosch, Hung-Fu Ting, Ye Chen, Dejan Lukacevic, Svetlana Titova, André Lin Ouédraogo, Daniel J. Klein, Daniel Bridenbecker, Bradley G. Wagner, T. Alex Perkins, and Hao Hu
- Subjects
Microbiology (medical) ,Computer science ,030231 tropical medicine ,Population ,Modularity ,Communicable Diseases ,03 medical and health sciences ,0302 clinical medicine ,Software ,Software Design ,Component (UML) ,Regression testing ,Immunology and Allergy ,Humans ,epidemiological modeling ,030212 general & internal medicine ,education ,Codebase ,education.field_of_study ,General Immunology and Microbiology ,business.industry ,software ,Software development ,mathematical modeling ,Computational Biology ,General Medicine ,Models, Theoretical ,Infectious Diseases ,Software design ,Disease Susceptibility ,Software engineering ,business ,Algorithms ,Research Article - Abstract
Individual-based models provide modularity and structural flexibility necessary for modeling of infectious diseases at the within-host and population levels, but are challenging to implement. Levels of complexity can exceed the capacity and timescales for students and trainees in most academic institutions. Here we describe the process and advantages of a multi-disease framework approach developed with formal software support. The epidemiological modeling software, EMOD, has undergone a decade of software development. It is structured so that a majority of code is shared across disease modeling including malaria, HIV, tuberculosis, dengue, polio and typhoid. In additional to implementation efficiency, the sharing increases code usage and testing. The freely available codebase also includes hundreds of regression tests, scientific feature tests and component tests to help verify functionality and avoid inadvertent changes to functionality during future development. Here we describe the levels of detail, flexible configurability and modularity enabled by EMOD and the role of software development principles and processes in its development., To address multi-scale questions in infectious disease transmission, a multi-disease modeling platform EMOD has been developed with modularity, code sharing across diseases, and formal software development and testing processes.
- Published
- 2018
37. Complex contagions and hybrid phase transitions
- Author
-
Joel C. Miller
- Subjects
Phase transition ,education.field_of_study ,Control and Optimization ,Complex contagion ,Computer Networks and Communications ,Computer science ,Applied Mathematics ,Population ,Poisson process ,INFECTIOUS PROCESS ,Management Science and Operations Research ,01 natural sciences ,010305 fluids & plasmas ,Computational Mathematics ,symbols.namesake ,Discrete time and continuous time ,0103 physical sciences ,symbols ,Statistical physics ,Threshold model ,010306 general physics ,education ,Cluster analysis - Abstract
A complex contagion is an infectious process in which individuals may require multiple transmissions before changing state. These are used to model behaviours if an individual only adopts a particular behaviour after perceiving a consensus among others. We may think of individuals as beginning inactive and becoming active once they are contacted by a sufficient number of active partners. These have been studied in a number of cases, but analytic models for the dynamic spread of complex contagions are typically complex. Here we study the dynamics of the Watts threshold model (WTM) assuming that transmission occurs in continuous time as a Poisson process, or in discrete time where individuals transmit to all partners in the time step following their infection. We adapt techniques developed for infectious disease modelling to develop an analyse analytic models for the dynamics of the WTM in configuration model networks and a class of random clustered (triangle-based) networks. The resulting model is relatively simple and compact. We use it to gain insights into the dynamics of the contagion. Taking the infinite population limit, we derive conditions under which cascades happen with an arbitrarily small initial proportion active, confirming a hypothesis of Watts for this case. We also observe hybrid phase transitions when cascades are not possible for small initial conditions, but occur for large enough initial conditions. We derive sufficient conditions for this hybrid phase transition to occur. We show that in many cases, if the hybrid phase transition occurs, then all individuals eventually become active. Finally, we discuss the role clustering plays in facilitating or impeding the spread and find that the hypothesis of Watts that was confirmed in configuration model networks does not hold in general. This approach allows us to unify many existing disparate observations and derive new results.
- Published
- 2015
38. Mathematics of Epidemics on Networks : From Exact to Approximate Models
- Author
-
István Z. Kiss, Joel C. Miller, Péter L. Simon, István Z. Kiss, Joel C. Miller, and Péter L. Simon
- Subjects
- Mathematical statistics, Mathematical models
- Abstract
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by:Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book;Presenting different mathematical approaches to formulate exact and solvable models;Identifying the concrete links between approximate models and their rigorous mathematical representation;Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity;Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks;Providing software that can solve differential equation models or directly simulate epidemics on networks.Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike.
- Published
- 2017
39. Seasonality in risk of pandemic influenza emergence
- Author
-
Joel C. Miller, Spencer J. Fox, and Lauren Ancel Meyers
- Subjects
0301 basic medicine ,RNA viruses ,Viral Diseases ,Influenza Viruses ,Pathology and Laboratory Medicine ,0302 clinical medicine ,Pandemic ,Medicine and Health Sciences ,Evolutionary Emergence ,030212 general & internal medicine ,lcsh:QH301-705.5 ,Northern Hemisphere ,Ecology ,Geography ,Transmission (medicine) ,virus diseases ,Agriculture ,3. Good health ,Infectious Diseases ,Computational Theory and Mathematics ,Medical Microbiology ,Modeling and Simulation ,Viral Pathogens ,Viruses ,Human mortality from H5N1 ,Seasons ,Pathogens ,Risk assessment ,Network Analysis ,Research Article ,Risk ,Computer and Information Sciences ,Evolutionary Processes ,Livestock ,Immunology ,Biology ,Models, Biological ,Microbiology ,03 medical and health sciences ,Cellular and Molecular Neuroscience ,Influenza, Human ,Genetics ,medicine ,Flu season ,Humans ,Molecular Biology ,Pandemics ,Microbial Pathogens ,Ecology, Evolution, Behavior and Systematics ,Heterosubtypic immunity ,Evolutionary Biology ,Pandemic influenza ,Immunity ,Organisms ,Computational Biology ,Biology and Life Sciences ,Seasonality ,medicine.disease ,Virology ,Influenza ,030104 developmental biology ,lcsh:Biology (General) ,13. Climate action ,Earth Sciences ,Geographic areas ,Demography ,Orthomyxoviruses - Abstract
Influenza pandemics can emerge unexpectedly and wreak global devastation. However, each of the six pandemics since 1889 emerged in the Northern Hemisphere just after the flu season, suggesting that pandemic timing may be predictable. Using a stochastic model fit to seasonal flu surveillance data from the United States, we find that seasonal flu leaves a transient wake of heterosubtypic immunity that impedes the emergence of novel flu viruses. This refractory period provides a simple explanation for not only the spring-summer timing of historical pandemics, but also early increases in pandemic severity and multiple waves of transmission. Thus, pandemic risk may be seasonal and predictable, with the accuracy of pre-pandemic and real-time risk assessments hinging on reliable seasonal influenza surveillance and precise estimates of the breadth and duration of heterosubtypic immunity., Author summary Influenza pandemics emerge via genomic reassortment between circulating human and animal strains. The risk of pandemic emergence should therefore be high during the flu season, when viruses are abundant and conditions favor transmission. However, the six pandemics on record since 1889 all emerged in the Northern Hemisphere following the flu season, suggesting that other forces may predictably constrain pandemic risk. We find that seasonal influenza epidemics leave a wake of immunity that impedes pandemic emergence. This transient refractory period is consistent with the spring-summer emergence, multiple wave dynamics of recent pandemics, and may cause initial underestimation of the viral transmission rate. These findings may improve pre-pandemic risk assessments and real-time situational awareness, particularly as we gain greater insight into the extent of immunity.
- Published
- 2017
40. Dynamic and adaptive networks
- Author
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Joel C. Miller, Péter L. Simon, and Istvan Z. Kiss
- Subjects
Structure (mathematical logic) ,Relation (database) ,Computer science ,Distributed computing ,Feature (machine learning) ,Terminology - Abstract
An important feature of many real-world networks is the transient nature of some interactions. Thus far, our models have explicitly assumed that the network is static. That is, we assume that the rate of partner turnover is so slow that we can ignore its impact on epidemic dynamics.Over the past decade, there has been tremendous progress in modelling and analysing disease spread in non-static networks, i.e. networks whose structure changes due to endogenous or exogenous factors, or because of the disease dynamics unfolding on the network. The terminology used to describe such networks is not standardised. We summarise some common terminology and link it to the relation between the time scales of the dynamics on the network and the dynamics of the network. Ordered from static to networks that change quickly, we have
- Published
- 2017
41. Introduction to networks and diseases
- Author
-
Péter L. Simon, Istvan Z. Kiss, and Joel C. Miller
- Subjects
Mathematical model ,Order (exchange) ,Computer science ,Real systems ,Process (engineering) ,Management science ,0103 physical sciences ,010306 general physics ,All models are wrong ,01 natural sciences ,010305 fluids & plasmas - Abstract
Mathematical models are caricatures of real systems that aim to capture the fundamental mechanisms of some process in order to explain observations or predict outcomes. No model — no matter how complicated — is perfect, or in the words of George Box [46]: “All models are wrong; some models are useful”. A useful model can provide valuable insights which improve our understanding of a system, and ultimately informs our decision-making.
- Published
- 2017
42. Mean-field approximations for heterogeneous networks
- Author
-
István Z. Kiss, Joel C. Miller, and Péter L. Simon
- Published
- 2017
43. Propagation models on networks: bottom-up
- Author
-
Péter L. Simon, Istvan Z. Kiss, and Joel C. Miller
- Subjects
Closed system (control theory) ,Computer science ,Order (ring theory) ,Applied mathematics ,Node (circuits) ,State (functional analysis) ,Top-down and bottom-up design ,Representation (mathematics) - Abstract
In this chapter, we present a different approach to deriving exact models. In Chapter 2, we began with equations for every possible state of the system and then aggregated them into a simpler form. Here, we begin by deriving separate equations for the status of each node. These typically depend on the states of pairs of nodes, so we introduce equations for the pairs, which in turn depend on triples. We build up equations at each level. For a typical network, the number of equations we obtain is too large to be tractable. Consequently, we introduce “closures”, whereby terms corresponding to larger structures are represented in terms of smaller structures, in order to create a closed system of equations. In most cases, this representation involves an approximation, but in the case of SIR dynamics on trees or networks with cut-vertices, it is possible to reduce the number of equations considerably while keeping the model exact.
- Published
- 2017
44. Hierarchies of SIR models
- Author
-
Istvan Z. Kiss, Joel C. Miller, and Péter L. Simon
- Subjects
Computer science ,Mathematical economics - Abstract
This chapter focuses on the relationships between the continuous-time SIR models we have previously derived and identifying conditions under which they are appropriate. Unless otherwise noted, the models discussed in this chapter are SIR models. Each of these models involves some assumptions, and to understand their limitations, we need to understand whether the true spread “respects” these assumptions.
- Published
- 2017
45. Non-Markovian epidemics
- Author
-
Istvan Z. Kiss, Joel C. Miller, and Péter L. Simon
- Subjects
education.field_of_study ,Queueing theory ,Distribution (number theory) ,Population ,Markov process ,01 natural sciences ,010104 statistics & probability ,symbols.namesake ,Mixing (mathematics) ,Probability theory ,0103 physical sciences ,symbols ,Quantitative Biology::Populations and Evolution ,Statistical physics ,Limit (mathematics) ,0101 mathematics ,010306 general physics ,education ,Branching process ,Mathematics - Abstract
Early studies of non-Markovian epidemics focused on SIR dynamics on fully connected networks, or homogeneously mixing populations, with the infection process being Markovian but with the infectious period taken from a general distribution [8, 278, 292, 293]. These approaches use probability theory arguments and typically focus on characterising the distribution of final epidemic sizes for finite populations, or on the average size in the infinite population limit. Similarly, the quasi-stationary distribution in a stochastic SIS model, again in a fully connected network, has been the subject of many studies [66, 230, 231]. More recently, it has been shown that one can readily apply results from queueing [19] or branching process [233] theory, or use martingales [65] to cast the same questions within a different framework and obtain results more readily.
- Published
- 2017
46. Disease spread in networks with large-scale structure
- Author
-
Joel C. Miller, Péter L. Simon, and Istvan Z. Kiss
- Subjects
Degree correlation ,Theoretical computer science ,Scale (ratio) ,Process (engineering) ,Computer science ,Scale structure ,Closure (topology) ,Degree distribution ,Preferential attachment - Abstract
This book has developed analytic models of disease spread on networks. All of our tractable models require closure assumptions. The closure process assumes that we can explain the dynamics at the network scale by understanding the dynamics locally at the level of small units with random connections between these units.
- Published
- 2017
47. PDE limits for large networks
- Author
-
Péter L. Simon, Istvan Z. Kiss, and Joel C. Miller
- Subjects
Markov chain ,Master equation ,Ode ,Applied mathematics ,Probability distribution ,State space ,State (functional analysis) ,Expected value ,Random variable ,Mathematics - Abstract
In previous chapters, it was shown that dynamics on networks can be described by continuous-time Markov chains, where probabilities of states are determined by master equations. While limiting mean-field ODE models can provide a good approximation of the expected value of certain random variables, a PDE-based approach is needed if information on the probability distribution of these is desired. The aim of this chapter is to develop and study mathematical methods to estimate the accuracy of mean-field ODE and PDE approximations. This will be carried out for continuous-time Markov chains with state space {0, 1, …, N}, for which transition from state k is possible only to states k − 1 and k + 1. These processes are called birth–death or one-step processes.
- Published
- 2017
48. Mapping Out Emerging Network Structures in Dynamic Network Models Coupled with Epidemics
- Author
-
Istvan Z. Kiss, Joel C. Miller, Péter L. Simon, and Luc Berthouze
- Subjects
Structure (mathematical logic) ,Bifurcation theory ,Steady state (electronics) ,Dynamic network analysis ,Degree (graph theory) ,Node (networking) ,Econometrics ,Network structure ,Pairwise comparison ,Topology ,Mathematics - Abstract
We consider the susceptible – infected – susceptible (SIS) epidemic on a dynamic network model with addition and deletion of links depending on node status. We analyse the resulting pairwise model using classical bifurcation theory to map out the spectrum of all possible epidemic behaviours. However, the major focus of the chapter is on the evolution and possible equilibria of the resulting networks. Whereas most studies are driven by determining system-level outcomes, e.g., whether the epidemic dies out or becomes endemic, with little regard for the emerging network structure, here, we want to buck this trend by augmenting the system-level results with mapping out of the structure and properties of the resulting networks. We find that depending on parameter values the network can become disconnected and show bistable-like behaviour whereas the endemic steady state sees the emergence of networks with qualitatively different degree distributions. In particular, we observe de-phased oscillations of both prevalence and network degree during which there is role reversal between the level and nature of the connectivity of susceptible and infected nodes. We conclude with an attempt at describing what a potential bifurcation theory for networks would look like.
- Published
- 2017
49. Percolation-based approaches for disease modelling
- Author
-
Péter L. Simon, Istvan Z. Kiss, and Joel C. Miller
- Subjects
Disease modelling ,Percolation (cognitive psychology) ,Computer science ,Node (networking) ,Complete theory ,Topology ,humanities ,Giant component - Abstract
The methods introduced thus far are applicable to both SIS and SIR diseases. This chapter focuses primarily on SIR disease. Once a node u becomes infected with an SIR disease, no other node affects the timing of any other action of u. This permits simplifications leading to a more complete theory of SIR disease.
- Published
- 2017
50. Modeling disease spread in populations with birth, death, and concurrency
- Author
-
Anja C. Slim and Joel C. Miller
- Subjects
Computer science ,Distributed computing ,Concurrency ,Econometrics ,Human immunodeficiency virus (HIV) ,medicine ,Disease ,medicine.disease_cause - Abstract
The existence of sexual partnerships that overlap in time (concurrent relationships) is believed by some to be a significant contributing factor to the spread of HIV, although this is controversial. We derive an analytic model which allows us to investigate and compare disease spread in populations with and without concurrency. We can identify regions of parameter space in which its impact is negligible, and other regions in which it plays a major role. We also see that the impact of concurrency on the initial growth phase can be much larger than its impact on the equilibrium size. We see that the effect of concurrency saturates, which leads to the perhaps surprising conclusion that interventions targeting concurrency may be most effective in populations with low to moderate levels of concurrency.Author SummaryWe consider the spread of an infectious disease through a population modeled by a dynamic network with demographic turnover. We develop a stochastic model of the disease and derive governing equations that exactly predict the large population (deterministic) limit of the stochastic model. We use this to investigate the role of concurrency and find that interventions targeting concurrency may be most effective in populations with lower levels of concurrency.Our model is not intended to be an accurate representation of any single population. Rather it is intended to give general insights for intervention design and to provide a framework which can be further specialized to particular populations.This model is the first model to allow for analytic investigation of the impact of concurrent partnerships in a population exhibiting demographic turnover. Thus it will be useful for investigating the “concurrency hypothesis.”
- Published
- 2016
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