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The field theoretical ABC of epidemic dynamics

TL;DR: In this article, a review of mathematical models of infectious disease diffusion by simultaneously investigating the underlying microscopic dynamics in terms of percolation models, effective description via compartmental models and the employment of temporal symmetries is presented.
Abstract: Infectious diseases are a threat for human health with tremendous impact on our society at large. The recent COVID-19 pandemic, caused by the SARS-CoV-2, is the latest example of a highly infectious disease ravaging the world, since late 2019. It is therefore imperative to develop efficient mathematical models, able to substantially curb the damages of a pandemic by unveiling disease spreading dynamics and symmetries. This will help inform (non)-pharmaceutical prevention strategies. For the reasons above we wrote this report that goes at the heart of mathematical modelling of infectious disease diffusion by simultaneously investigating the underlying microscopic dynamics in terms of percolation models, effective description via compartmental models and the employment of temporal symmetries naturally encoded in the mathematical language of critical phenomena. Our report reviews these approaches and determines their common denominators, relevant for theoretical epidemiology and its link to important concepts in theoretical physics. We show that the different frameworks exhibit common features such as criticality and self-similarity under time rescaling. These features are naturally encoded within the unifying field theoretical approach. The latter leads to an efficient description of the time evolution of the disease via a framework in which (near) time-dilation invariance is explicitly realised. As important test of the relevance of symmetries we show how to mathematically account for observed phenomena such as multi-wave dynamics. The models presented here are of immediate relevance for different realms of scientific enquiry from medical applications to the understanding of human behaviour. Our review offers novel perspectives on how to model, capture, organise and understand epidemiological data and disease dynamics for modelling real-world phenomena.
Citations
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Posted ContentDOI
21 Jul 2021-medRxiv
TL;DR: In this article, a machine learning algorithm yielding a temporal clustering of the available dataset was designed to identify and define emerging persistent variants that are in agreement with known evidences and to highlight emerging variants of epidemiological interest as branching events that occur over time.
Abstract: Never before such a vast amount of data, including genome sequencing, has been collected for any viral pandemic than for the current case of COVID-19. This offers the possibility to trace the virus evolution and to assess the role mutations play in its spread within the population, in real time. To this end, we focused on the Spike protein for its central role in mediating viral outbreak and replication in host cells. Employing the Levenshtein distance on the Spike protein sequences, we designed a machine learning algorithm yielding a temporal clustering of the available dataset. From this, we were able to identify and define emerging persistent variants that are in agreement with known evidences. Our novel algorithm allowed us to define persistent variants as chains that remain stable over time and to highlight emerging variants of epidemiological interest as branching events that occur over time. Hence, we determined the relationship and temporal connection between variants of interest and the ensuing passage to dominance of the current variants of concern. Remarkably, the analysis and the relevant tools introduced in our work serve as an early warning for the emergence of new persistent variants once the associated cluster reaches 1% of the time-binned sequence data. We validated our approach and its effectiveness on the onset of the Alpha variant of concern. We further predict that the recently identified lineage AY.4.2 (`Delta plus`) is causing a new emerging variant. Comparing our findings with the epidemiological data we demonstrated that each new wave is dominated by a new emerging variant, thus confirming the hypothesis of the existence of a strong correlation between the birth of variants and the pandemic multi-wave temporal pattern. The above allows us to introduce the epidemiology of variants that we described via the Mutation epidemiological Renormalisation Group (MeRG) framework.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors explore the impact of lockdown strategies on the evolution of an epidemic and show that repeated lockdowns have a beneficial effect, reducing the final size of the infection, and that they represent a possible support strategy to vaccination policies.
Abstract: While vaccination is the optimal response to an epidemic, recent events have obliged us to explore new strategies for containing worldwide epidemics, like lockdown strategies, where the contacts among the population are strongly reduced in order to slow down the propagation of the infection. By analyzing a classical epidemic model, we explore the impact of lockdown strategies on the evolution of an epidemic. We show that repeated lockdowns have a beneficial effect, reducing the final size of the infection, and that they represent a possible support strategy to vaccination policies.

5 citations

Posted Content
TL;DR: In this paper, the authors propose a physical theory underlying the temporal evolution of competing virus variants that relies on the existence of (quasi) fixed points capturing the large time scale invariance of the dynamics.
Abstract: We propose a physical theory underlying the temporal evolution of competing virus variants that relies on the existence of (quasi) fixed points capturing the large time scale invariance of the dynamics. To motivate our result we first modify the time-honoured compartmental models of the SIR type to account for the existence of competing variants and then show how their evolution can be naturally re-phrased in terms of flow equations ending at quasi fixed points. As the natural next step we employ (near) scale invariance to organise the time evolution of the competing variants within the effective description of the epidemic Renormalization Group framework. We test the resulting theory against the time evolution of COVID-19 virus variants that validate the theory empirically.

3 citations

Posted Content
TL;DR: In this paper, the temporal variability of the Spike protein sequence has been used to identify, classify and track emerging virus variants, which can be used as an early warning system for the emergence of new persistent variants that may pose a threat of triggering a new wave of COVID-19.
Abstract: Applying a ML approach to the temporal variability of the Spike protein sequence enables us to identify, classify and track emerging virus variants. Our analysis is unbiased, in the sense that it does not require any prior knowledge of the variant characteristics, and our results are validated by other informed methods that define variants based on the complete genome. Furthermore, correlating persistent variants of our approach to epidemiological data, we discover that each new wave of the COVID-19 pandemic is driven and dominated by a new emerging variant. Our results are therefore indispensable for further studies on the evolution of SARS-CoV-2 and the prediction of evolutionary patterns that determine current and future mutations of the Spike proteins, as well as their diversification and persistence during the viral spread. Moreover, our ML algorithm works as an efficient early warning system for the emergence of new persistent variants that may pose a threat of triggering a new wave of COVID-19. Capable of a timely identification of potential new epidemiological threats when the variant only represents 1% of the new sequences, our ML strategy is a crucial tool for decision makers to define short and long term strategies to curb future outbreaks. The same methodology can be applied to other viral diseases, influenza included, if sufficient sequencing data is available.
Posted ContentDOI
TL;DR: In this article, the authors study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease.
Abstract: We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19 across Europe. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-19 . We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing different versions of HPs in this model, we are capable of providing quantitative estimates on the effectiveness of the underlying measures as a function of the fraction of the population that is vaccinated and the vaccination rate. We apply our models to the latest COVID-19 wave in several European countries, notably Germany and Austria, which validate our theoretical findings.
References
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Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
Abstract: (1) One of the most striking features in the study of epidemics is the difficulty of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population. It was with a view to obtaining more insight regarding the effects of the various factors which govern the spread of contagious epidemics that the present investigation was undertaken. Reference may here be made to the work of Ross and Hudson (1915-17) in which the same problem is attacked. The problem is here carried to a further stage, and it is considered from a point of view which is in one sense more general. The problem may be summarised as follows: One (or more) infected person is introduced into a community of individuals, more or less susceptible to the disease in question. The disease spreads from the affected to the unaffected by contact infection. Each infected person runs through the course of his sickness, and finally is removed from the number of those who are sick, by recovery or by death. The chances of recovery or death vary from day to day during the course of his illness. The chances that the affected may convey infection to the unaffected are likewise dependent upon the stage of the sickness. As the epidemic spreads, the number of unaffected members of the community becomes reduced. Since the course of an epidemic is short compared with the life of an individual, the population may be considered as remaining constant, except in as far as it is modified by deaths due to the epidemic disease itself. In the course of time the epidemic may come to an end. One of the most important probems in epidemiology is to ascertain whether this termination occurs only when no susceptible individuals are left, or whether the interplay of the various factors of infectivity, recovery and mortality, may result in termination, whilst many susceptible individuals are still present in the unaffected population. It is difficult to treat this problem in its most general aspect. In the present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

8,238 citations

Book
11 Jul 1991
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Abstract: Part 1 Microparasites: biology of host-microparasite associations the basic model - statics static aspects of eradication and control the basic model - dynamics dynamic aspects of eradication and control beyond the basic model - empirical evidence of inhomogeneous mixing age-related transmission rates genetic heterogeneity social heterogeneity and sexually transmitted diseases spatial and other kinds of heterogeneity endemic infections in developing countries indirectly transmitted microparasites. Part 2 Macroparasites: biology of host-macroparasite associations the basic model - statics the basic model - dynamics acquired immunity heterogeneity within the human community indirectly transmitted helminths experimental epidemiology parasites, genetic variability, and drug resistance the ecology and genetics of host-parasite associations.

7,675 citations

Journal ArticleDOI
Scott Kirkpatrick1
TL;DR: In this article, an extension of percolation theory to treat transport is described, and a general expression for the conductance of such networks is derived, which relates to the spin-stiffness coefficient of dilute ferromagnet.
Abstract: Extensions of percolation theory to treat transport are described. Resistor networks, from which resistors are removed at random, provide the natural generalization of the lattice models for which percolation thresholds and percolation probabilities have previously been considered. The normalized conductance, $G$, of such networks proves to be a sharply defined quantity with a characteristic concentration dependence near threshold which appears sensitive only to dimensionality. Numerical results are presented for several families of $3D$ and $2D$ network models. Except close to threshold, the models based on bond percolation are accurately described by a simple effective medium theory, which can also treat continuous media or situations less drastic than the percolation models, for example, materials in which local conductivity has a continuous distribution of values. The present calculations provide the first quantitative test of this theory. A "Green's function" derivation of the effective medium theory, which makes contact with similar treatments of disordered alloys, is presented. Finally, a general expression for the conductance of a percolation model is obtained which relates $G$ to the spin-stiffness coefficient, $D$, of an appropriately defined model dilute ferromagnet. We use this relationship to argue that the "percolation channels" through which the current flows above threshold must be regarded as three dimensional.

4,342 citations

Book
28 Oct 2007
TL;DR: Mathematical modeling of infectious dis-eases has progressed dramatically over the past 3 decades and continues to be a valuable tool at the nexus of mathematics, epidemiol-ogy, and infectious diseases research.
Abstract: By Matthew James Keelingand Pejman RohaniPrinceton, NJ: Princeton University Press,2008.408 pp., Illustrated. $65.00 (hardcover).Mathematical modeling of infectious dis-eases has progressed dramatically over thepast 3 decades and continues to flourishat the nexus of mathematics, epidemiol-ogy, and infectious diseases research. Nowrecognized as a valuable tool, mathemat-ical models are being integrated into thepublic health decision-making processmore than ever before. However, despiterapid advancements in this area, a formaltraining program for mathematical mod-eling is lacking, and there are very fewbooks suitable for a broad readership. Tosupport this bridging science, a commonlanguage that is understood in all con-tributing disciplines is required.

3,467 citations