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Academic literature on the topic 'SIR Models'

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Published: 23 September 2022
Last updated: 20 April 2024

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Journal articles on the topic "SIR Models"

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Kaddar, Abdelilah, Abdelhadi Abta, and Hamad Talibi Alaoui. "A comparison of delayed SIR and SEIR epidemic models." Nonlinear Analysis: Modelling and Control 16, no. 2 (April 25, 2011): 181–90. http://dx.doi.org/10.15388/na.16.2.14104.

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In epidemiological research literatures, a latent or incubation period can be medelled by incorporating it as a delay effect (delayed SIR models), or by introducing an exposed class (SEIR models). In this paper we propose a comparison of a delayed SIR model and its corresponding SEIR model in terms of local stability. Also some numerical simulations are given to illustrate the theoretical results.
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Kuznetsov, Yu A., and C. Piccardi. "Bifurcation analysis of periodic SEIR and SIR epidemic models." Journal of Mathematical Biology 32, no. 2 (January 1994): 109–21. http://dx.doi.org/10.1007/bf00163027.

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Ciallella, Alessandro, Mario Pulvirenti, and Sergio Simonella. "Inhomogeneities in Boltzmann–SIR models." Mathematics and Mechanics of Complex Systems 9, no. 3 (December 31, 2021): 273–92. http://dx.doi.org/10.2140/memocs.2021.9.273.

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Bartoszek, Krzysztof, Wojciech Bartoszek, and Michał Krzemiński. "Simple SIR models with Markovian control." Japanese Journal of Statistics and Data Science 4, no. 1 (February 16, 2021): 731–62. http://dx.doi.org/10.1007/s42081-021-00107-1.

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AbstractWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving Markov chain. We formulate some questions and conjectures of a purely theoretical nature.
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Kloeden, P. E., and C. Pötzsche. "Nonautonomous bifurcation scenarios in SIR models." Mathematical Methods in the Applied Sciences 38, no. 16 (April 6, 2015): 3495–518. http://dx.doi.org/10.1002/mma.3433.

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Zaman, Gul, and Il Hyo Jung. "Stability techniques in SIR epidemic models." PAMM 7, no. 1 (December 2007): 2030063–64. http://dx.doi.org/10.1002/pamm.200701147.

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Shigemoto, Kazuyasu. "Various Logistic Curves in SIS and SIR Models." European Journal of Mathematics and Statistics 4, no. 1 (January 5, 2023): 1–6. http://dx.doi.org/10.24018/ejmath.2023.4.1.185.

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In our previous paper, the logistic curve of the removed number was derived from SIR and SEIR models in the case of the small basic reproduction number. In this paper, we derive various logistic curves of the removed, unsusceptible and infectious numbers respectively from SIS and SIR models in the case of small and large basic reproduction numbers.
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Guan, Li, Dong Li, Ke Wang, and Kun Zhao. "On a class of nonlocal SIR models." Journal of Mathematical Biology 78, no. 6 (January 2, 2019): 1581–604. http://dx.doi.org/10.1007/s00285-018-1320-0.

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Ucakan, Yasin, Seda Gulen, and Kevser Koklu. "Analysing of Tuberculosis in Turkey through SIR, SEIR and BSEIR Mathematical Models." Mathematical and Computer Modelling of Dynamical Systems 27, no. 1 (January 2, 2021): 179–202. http://dx.doi.org/10.1080/13873954.2021.1881560.

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Avram, Florin, Rim Adenane, and David I. Ketcheson. "A Review of Matrix SIR Arino Epidemic Models." Mathematics 9, no. 13 (June 28, 2021): 1513. http://dx.doi.org/10.3390/math9131513.

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Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies.
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Dissertations / Theses on the topic "SIR Models"

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Abdelsheed, Ismail Gad Ameen. "Fractional calculus: numerical methods and SIR models." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3422267.

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Fractional calculus is ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. The idea of generalizing differential operators to a non-integer order, in particular to the order 1/2, first appears in the correspondence of Leibniz with L’Hopital (1695), Johann Bernoulli (1695), and John Wallis (1697) as a mere question or maybe even play of thoughts. In the following three hundred years a lot of mathematicians contributed to the fractional calculus: Laplace (1812), Lacroix (1812), Fourier (1822), Abel (1823-1826), Liouville (1832-1837), Riemann (1847), Grunwald (1867-1872), Letnikov (1868-1872), Sonin (1869), Laurent (1884), Heaviside (1892-1912), Weyl (1917), Davis (1936), Erde`lyi (1939-1965), Gelfand and Shilov (1959-1964), Dzherbashian (1966), Caputo (1969), and many others. Yet, it is only after the First Conference on Fractional Calculus and its applications that the fractional calculus becomes one of the most intensively developing areas of mathematical analysis. Recently, many mathematicians and applied researchers have tried to model real processes using the fractional calculus. This is because of the fact that the realistic modeling of a physical phenomenon does not depend only on the instant time, but also on the history of the previous time which can be successfully achieved by using fractional calculus. In other words, the nature of the definition of the fractional derivatives have provided an excellent instrument for the modeling of memory and hereditary properties of various materials and processes.
Il calcolo frazionario e` ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. L’ idea di generalizzare operatori differenziali ad un ordine non intero, in particolare di ordine 1/2, compare per la prima volta in una corrispondenza di Leibniz con L’Hopital (1695), Johann Bernoulli (1695), e John Wallis (1697), come una semplice domanda o forse un gioco di pensieri. Nei successive trecento anni molti matematici hanno contribuito al calcolo frazionario: Laplace (1812), Lacroix (1812), di Fourier (1822), Abel (1823-1826), Liouville (1832-1837), Riemann (1847), Grunwald (1867-1872), Letnikov (1868-1872), Sonin (1869), Laurent (1884), Heaviside (1892-1912), Weyl (1917), Davis (1936), Erde`lyi (1939-1965), Gelfand e Shilov (1959-1964), Dzherbashian (1966), Caputo (1969), e molti altri. Eppure, è solo dopo la prima conferenza sul calcolo frazionario e le sue applicazioni che questo tema diventa una delle le aree più intensamente studiate dell’analisi matematica. Recentemente, molti matematici e ingegneri hanno cercato di modellare i processi reali utilizzando il calcolo frazionario. Questo a causa del fatto che spesso, la modellazione realistica di un fenomeno fisico non è locale nel tempo, ma dipende anche dalla storia, e questo comportamento può essere ben rappresentato attraverso modelli basati sul calcolo frazionario. In altre parole, la definizione dei derivata frazionaria fornisce un eccellente strumento per la modellazione della memoria e delle proprietà ereditarie di vari materiali e processi.
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Almeida, Priscila Roque de. "Modelos epidêmicos SIR, contínuos e discretos, e estratégias de vacinação." Universidade Federal de Viçosa, 2014. http://locus.ufv.br/handle/123456789/4933.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The main Objective Of this Work is to study and discretize the epidemic SIR model (Susceptible-Infected-Recovered) developed by Kermack and MCKendrick in 1927 [11], between its Consider the simple models With Vital dynamics and Constant and Vaccination strategies pulses, as a method Of epidemic ControL The study of the stability of Continuous-time models With pulse Vaccination is done by means of the Floquet theory. Already the rnethod Of ñnite difference appro- Ximation is used to forward discretize Continuous systems and the analysis On the stability of the new systems found is displayed The theoretical results are Conñrmed by numerical simulations.
O Objetivo principal desde trabalho é estudar e discretizar os modelos epidêmi- COS SIR (Suscetíveis-Infectados-Recuperados) desenvolvidos por MCKendrick e Kermack em 1927, [11], entre eles Consideramos os modelos simples Com dinâmica Vital e Com estratégias de Vacinação Constante e em pulsos, Como método de Con- trole epidêmico. O estudo da estabilidade dos modelos em tempo Contínuos Com Vacinação em pulsos é feito por meio, da Teoria de Floquet. Já 0 rnétodo de aproximação de diferenças ñnitas para frente é utilizado para discretizar os siste- mas Contínuos e é apresentada a análise sobre a estabilidade dos novos sistemas encontrados. Os resultados teóricos são Conñrmados por simulações numéricas.
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Estrada, López Mario Andrés 1989. "Teoremas limiares para o modelo SIR estocástico de epidemia." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307035.

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Orientador: Élcio Lebensztayn
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Este trabalho tem como objetivo estudar o modelo SIR (suscetível-infectado-removido) de epidemia nas versões determinística e estocástica. Nosso objetivo é encontrar limitantes para a probabilidade de que o tamanho da epidemia não sobrepasse certa proporção do número inicial de suscetíveis. Iniciamos apresentando as definições e a dinâmica do processo de epidemia determinístico. Obtemos um valor limiar para o número inicial de suscetíveis para que a epidemia exploda ou não. Consideramos o modelo de epidemia estocástico SIR assumindo que não há período latente, isto é, que um infectado pode transmitir a infecção ao instante de ser contagiado. O modelo é considerado com uma configuração inicial de suscetíveis e infectados e é feita especial ênfases no estudo da variável aleatória ''tamanho da epidemia'', que é definida como a diferença entre o número de suscetíveis ao começar e ao terminar a propagação da doença. Como na parte determinística, obtemos teoremas limiares para o modelo de epidemia estocástico. Os métodos usados para encontrar os limitantes são os de análise da cadeia de Markov imersa e de comparação estocástica
Abstract: This work has as objective to study the SIR (susceptible-infected-removed) epidemic model in the deterministic and stochastic version. Our objective is to find bounds for the probability that the size of the epidemic does not exceed certain proportion of the initial number of susceptible individuals. We begin presenting the definitions and the dynamics for the deterministic model for a general epidemic. We obtain a threshold value for the initial number of susceptible individuals for the epidemic to build up or not. As fundamental part of this work, we consider a stochastic epidemic SIR model assuming there is no latent period, that is, one infected can transmit the infection at the moment of being infected. The model is considered with an initial configuration of susceptible and infected individuals and the study is focused on the random variable ''size of the epidemic'', which is defined as the difference between the number of susceptible individuals at the start and at the end of the propagation of the epidemic. As in the deterministic part, we obtain a threshold theorem for the stochastic epidemic. The methods used to prove the theorem are analysis of the embedded chain and the stochastic comparison
Mestrado
Estatistica
Mestre em Estatística
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Medlock, Jan P. "The effect of stochastic migration on an SIR model for the transmission of HIV." Thesis, Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/30547.

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Ozanne, Marie Veronica. "Bayesian compartmental models for zoonotic visceral leishmaniasis in the Americas." Diss., University of Iowa, 2019. https://ir.uiowa.edu/etd/6825.

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Visceral leishmaniasis (VL) is a serious neglected tropical disease that is endemic in 98 countries and presents a significant public health risk. The epidemiology of VL is complex. In the Americas, it is a zoonotic disease that is caused by a parasite and transmitted among humans and dogs through the bite of an infected sand fly vector. The infection also can be transmitted vertically from mother to child during pregnancy. Infected individuals can be classified as asymptomatic or symptomatic; both classes can transmit infection. In part due to its complexity, VL transmission dynamics are not fully understood. Stochastic compartmental epidemic models are a powerful set of tools that can be used to study these transmission dynamics. Past compartmental models for VL have been developed in a deterministic framework to accommodate complexity while remaining computationally tractable. In this work, we propose stochastic compartmental models for VL, which are simpler than their deterministic counterparts, but also have several advantages. Notably, this framework allows us to: (1) define a probability of infection transmission between two individuals, (2) obtain both parameter estimates and corresponding uncertainty measures, and (3) employ formal model comparisons. In this dissertation, we develop both population level and individual level Bayesian compartmental models to study both vector and vertical VL transmission dynamics. As part of this model development, we introduce a compartmental model that allows for two infectious classes. We also derive source specific reproductive numbers to quantify the contributions of different species and infectious classes to maintaining infection in a population. Finally, we propose a formal model comparison method for Bayesian models with high-dimensional discrete parameter spaces. These models, reproductive numbers, and model comparison method are explored in the context of simulations and real VL data from Brazil and the United States.
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Terefe, Yibeltal Adane. "Bifurcation analysis and nonstandard finite difference schemes for Kermack and McKendrick type epidemiological models." Diss., University of Pretoria, 2012. http://hdl.handle.net/2263/24917.

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The classical SIR and SIS epidemiological models are extended by considering the number of adequate contacts per infective in unit time as a function of the total population in such a way that this number grows less rapidly as the total population increases. A diffusion term is added to the SIS model and this leads to a reaction–diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the SIR and SIS models, with the disease–free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, for both models, the endemic equilibrium is locally asymptotically stable and traveling wave solutions are found for the SIS diffusion model. Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous SIR and SIS models are presented. In particular, for the SIS model, a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided. On the other hand the SIS model is extended to a Volterra integral equation, for which the existence of multiple endemic equilibria is proved. This fact is confirmed by numerical simulations.
Dissertation (MSc)--University of Pretoria, 2012.
Mathematics and Applied Mathematics
unrestricted
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Tosun, Kursad. "QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC MODELS IN MATHEMATICAL EPIDEMIOLOGY." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/dissertations/732.

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We introduce random fluctuations on contact and recovery rates in three basic deterministic models in mathematical epidemiology and obtain stochastic counterparts. This paper addresses qualitative and quantitative analysis of stochastic SIS model with disease deaths and demographic effects, and stochastic SIR models with/without disease deaths and demographic effects. We prove the global existence of a unique strong solution and discuss stochastic asymptotic stability of disease free and endemic equilibria. We also investigate numerical properties of these models and prove the convergence of the Balanced Implicit Method approximation to the analytic solution. We simulate the models with fairly realistic parameters to visualize our conclusions.
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Graf, Brolund Alice. "Compartmental Models in Social Dynamics." Thesis, Uppsala universitet, Avdelningen för systemteknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-448163.

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The dynamics of many aspects of social behaviour, such as spread of fads and fashion, collective action, group decision-making, homophily and disagreement, have been captured by mathematical models. The power of these models is that they can provide novel insight into the emergent dynamics of groups, e.g. 'epidemics' of memes, tipping points for collective action, wisdom of crowds and leadership by small numbers of individuals, segregation and polarisation. A current weakness in the scientific models is their sheer number. 'New' models are continually 'discovered' by physicists, engineers and mathematicians. The models are analysed mathematically, but very seldom provide predictions that can be tested empirically. In this work, we provide a framework of simple models, based on Lotka's original idea of using chemical reactions to describe social interactions. We show how to formulate models for social epidemics, social recovery, cycles, collective action, group decision-making, segregation and polarisation, which we argue encompass the majority of social dynamics models. We present an open-access tool, written in Python, for specifying social interactions, studying them in terms of mass action, and creating spatial simulations of model dynamics. We argue that the models in this article provide a baseline of empirically testable predictions arising from social dynamics, and that before creating new and more complicated versions of the same idea, researchers should explain how their model differs substantially from our baseline models.
Matematiska modeller kan hjälpa oss att förstå många typer av sociala fenomen, som ryktesspridning, spridning av memes, gruppbeslut, segregation och radikalisering. Det finns idag otaliga modeller för sociala beteenden hos människor och djur, och fler presenteras kontinuerligt. Det stora antalet modeller försvårar navigering inom forskningsfältet, och många av modellerna är dessutom komplicerade och svåra att verifiera genom experiment. I detta arbete föreslås ett ramverk av grundläggande modeller, som var och en modellerar en aspekt av socialt beteende; det gäller sociala epidemier, cykler, gemensamt handlande, gruppbeslut, segregation och polarisering. Vi menar att dessa modeller utgör majoriteten av de verifierbara aspekter av socialt beteende som studeras, och att de bör behandlas som en utgångspunkt när en ny modell ska introduceras. Vilka av mekanismerna från utgångspunkten finns representerade i modellen? Skiljer den sig ens nämnvärt från utgångspunkten? Genom att ha en god förståelse för grundmodellerna, och genom att förklara på vilket sätt en ny modell skiljer sig från dem, kan forskare undvika att presentera modeller som i praktiken är mer komplicerade varianter av sådana som redan finns. I detta arbete visar vi hur dessa grundläggande modeller kan formuleras och studeras. Modellerna bygger på enkla regler om vad som händer när individer i en befolkning möter varandra. Till exempel, om en person som har vetskap om ett rykte träffar någon som inte har det, kan ryktet spridas vidare. Därför har antaganden om vilka personer som kan träffa varandra stor påverkan på de resultat som modellerna ger. I detta arbete studeras varje modell med två olika metoder: i den ena har alla personer i befolkningen samma sannolikhet att träffa varandra, i den andra representeras befolkningen av ett rutnät, där varje plats motsvarar en individ. I den senare har alltså varje person ett begränsat antal grannar att interagera med. Vilken av dessa två metoder man väljer har stor betydelse för vilka beteenden modellerna förutspår. Som ett komplement till detta arbete presenteras ett verktyg i form av ett Python-program som utför analysen av modellerna. Detta kan användas för att undersöka grundmodellerna som presenteras i detta arbete, men också för att formulera och analysera nya modeller på samma sätt. På det viset kan nya modeller enkelt jämföras mot grundmodellerna. Verktyget är användbart både som introduktion för de som är nya inom social dynamik, men också för de forskare som som vill ta fram nya modeller och föra forskningsfältet vidare.
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Bourdin, Félicien. "Modélisation macroscopique de mouvements de foule à deux types, modèles SIR condensés." Thesis, université Paris-Saclay, 2022. http://www.theses.fr/2022UPASM013.

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On étudie dans cette thèse la modélisation macroscopique des mouvements de foule dans le cas d'une population divisée en plusieurs types ayant des comportements différents, ainsi que le développement de modèles d'épidémiologie dits ``SIR'' permettant l'analyse de la propagation d'une maladie infectieuse dans une école. Ces deux problématiques ont été étudiées séparément~: au sujet initial (les mouvements de foule) s'est superposé le problème de modélisation d'épidémie en milieu scolaire suite à une sollicitation de MODCOV19, une plateforme créée par le CNRS et l'INSMI pour centraliser et coordonner les projets de modélisation autour de l'épidémie de COVID-19. Cette thèse est donc composée de deux parties indépendantes. On analyse d'une part la convergence de différents schémas numériques découlant d'approches différentes de l'équation de mouvement de foule à deux types - flot gradient, catching-up, volumes finis. On étudie également l'homogénéisation de modèles microscopiques de particules vers le problème macroscopique. On s'intéresse enfin au problème inverse d'identification des paramètres des modèles étant donnée l'observation d'un mouvement de foule. D'autre part, on développe un type de modèle SIR dit ``condensé'', où les quantités épidémiologiques sont définies à l'échelle de groupes d'individus. On analyse formellement la qualité du processus de condensation lorsque l'on a accès à l'ensemble des interactions dans la population, et on présente l'implémentation effective réalisée en collaboration avec MODCOV19
We study in this thesis the macroscopic modelling of crowd motion in the case of a population divided in several types that may have different behaviours, as well as the development of SIR models in order to analyse the spread of an infectious disease in a school. These two issues were studied separetely. As the original topic of this thesis was crowd motion, we answered to a proposition of MODCOV19 - a platform created by CNRS and INSMI to centralize and coordinate modeling projects on the COVID-19 outbreak - to design epidemiological models adapted to school media. This work is thus composed of two independent parts. On the one hand we analyse the convergence of several numerical schemes that stem from different standpoints on the macroscopic crowd motion equation - optimal transport, gradient flow, finite volumes. We study as well the homogenization of microscopic models of particles towards the macroscopic model. We eventually investigate the inverse problem of identifying of the parameters of a model, being observed the motion of a crowd. On the other hand, we develop a class of ``condensed'' SIR models, where the epidemiological quantities are defined at the scale of groups of individuals. We formally analyse the quality of the condensation process when a full description of the interaction within the population is available. We then detail the implementation carried out in collaboration with MODCOV19
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Bouzalmat, Ibrahim. "Modélisation probabiliste de la dynamique de transmission de la fièvre typhoïde à Mayotte avec étude de risques épidémiques." Electronic Thesis or Diss., Université de Montpellier (2022-....), 2023. http://www.theses.fr/2023UMONS064.

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Ce manuscrit de thèse vise à étudier la transmission de la fièvre typhoïde à Mayotte en utilisant des approches de modélisation mathématique. Nous introduisons tout d'abord le contexte de notre étude, les problématiques associées et les objectifs de la thèse. Un état de l'art sur la modélisation mathématique de la transmission de la fièvre typhoïde est présenté, mettant en évidence la spécificité de notre approche. Nous proposons un modèle initial en deux versions, déterministe et stochastique, pour décrire la dynamique de transmission de la maladie à Mayotte. Nous explorons le comportement du modèle à travers des simulations numériques dans différents scénarios, en mettant en évidence les facteurs clés de la transmission. Cependant, en raison des limitations du jeu de données disponibles, nous proposons un modèle stochastique simplifié et une méthode d'estimation paramétrique. Cette approche nous permet d'ajuster le modèle aux données disponibles et d'estimer les caractéristiques clés de la transmission de la fièvre typhoïde à Mayotte. En enrichissant notre modèle, nous introduisons de nouvelles extensions. Nous incluons un compartiment pour les individus exposés, prenant en compte la durée d'incubation de la maladie. Les propriétés théoriques de ce modèle sont étudiées et illustrées par des simulations numériques. De plus, nous proposons une méthodologie d'estimation des paramètres adaptée à ce nouveau modèle, et des simulations numériques ont été réalisées pour évaluer la performance de notre approche d'estimation. Nous examinons ensuite l'impact de la pluviométrie sur la transmission de la fièvre typhoïde à Mayotte, en utilisant des données publiques de précipitations. Nous identifions une saisonnalité de la pluie et estimons les paramètres du modèle sous différents régimes. Les résultats soulignent l'importance de cette variable météorologique dans la propagation de l'épidémie.Ce manuscrit ouvre des perspectives de recherche, telles que l'extension du modèle à d'autres maladies infectieuses présentes à Mayotte et sa généralisation à d'autres territoires. Ces travaux contribueront à une meilleure compréhension et gestion des maladies infectieuses à Mayotte et dans d'autres régions similaires
The aim of this thesis manuscript is to study the transmission of typhoid fever in Mayotte using mathematical modelling approaches. We first introduce the context of our study, the associated issues, and the objectives of the thesis. A state-of-the-art review on mathematical modeling of typhoid fever transmission is presented, highlighting the specificity of our approach. We propose an initial model in two versions, deterministic and stochastic, to describe the transmission dynamics of the disease in Mayotte. We explore the behavior of the model through numerical simulations in different scenarios, highlighting key factors of transmission. However, due to the limitations of the available dataset, we propose a simplified stochastic model and a parametric estimation method. This approach enables us to fit the model to the available data and to estimate the key characteristics of typhoid fever transmission in Mayotte. In enriching our model, we are introducing new extensions. We include a compartment for individuals exposed, taking into account the incubation period of the disease. The theoretical properties of this model are studied and illustrated by numerical simulations. In addition, we propose a parameter estimation methodology adapted to this new model, and numerical simulations have been carried out to evaluate the performance of our estimation approach. We then examine the impact of rainfall on the transmission of typhoid fever in Mayotte, using publicly available precipitation data. We identify rainfall seasonality and estimate model parameters under different regimes. The results highlight the importance of this meteorological variable in the spread of the epidemic.This manuscript opens up research perspectives, such as the extension of the model to other infectious diseases present in Mayotte and its generalisation to other territories. This work will contribute to a better understanding and management of infectious diseases in Mayotte and other similar regions
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Books on the topic "SIR Models"

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Kingman, J. F. C. (John Frank Charles), ed. Probability and mathematical genetics: [papers in honour of Sir John Kingman]. Cambridge, UK: Cambridge University Press, 2010.

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Cathedral, Canterbury, and Sir John Soane's Museum, eds. The petrified music of architecture: Sir Herbert Oakley's collection of cathedral models, Canterbury Cathedral. London: Sir John Soane's Museum, 2011.

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Intercambio sin ser conocido: Austausch unbekannterweise. Saarbrücken: Saarländisches Künstlerhaus, 2000.

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Hellwig, Marcus. SIR - Modell durch eine neue Dichte unterstützt. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-36476-2.

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Hellwig, Marcus. Das probabilistische SIR-Modell (PSIR) im Pandemieprozess. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-39596-4.

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Montesinos, Gustavo. Un general sin modelo. Cuenca, Ecuador: Núcleo del Azuay de la Casa de la Cultura Ecuatoriana, 2004.

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Inmigración: ¿integración sin modelo? Madrid: Alianza, 2013.

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Kazar, Baris M., and Mete Celik. Spatial AutoRegression (SAR) Model. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4614-1842-9.

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Hellwig, Marcus. The Probabilistic SIR Model (PSIR) in the Pandemic Process. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-31190-1.

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An assessment of contemporary models of forgiveness. New York: P. Lang, 2010.

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Book chapters on the topic "SIR Models"

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Kiss, István Z., Joel C. Miller, and Péter L. Simon. "Hierarchies of SIR models." In Interdisciplinary Applied Mathematics, 255–72. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50806-1_7.

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Milgroom, Michael G. "Epidemiology and SIR Models." In Biology of Infectious Disease, 253–68. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-38941-2_16.

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Marques, Joao Alexandre Lobo, Francisco Nauber Bernardo Gois, José Xavier-Neto, and Simon James Fong. "Epidemiology Compartmental Models—SIR, SEIR, and SEIR with Intervention." In Predictive Models for Decision Support in the COVID-19 Crisis, 15–39. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61913-8_2.

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Mickens, Ronald E. "SIR Models for Disease Spread." In Mathematical Modelling with Differential Equations, 161–80. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003178972-8.

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Andersson, Håkan, and Tom Britton. "The standard SIR epidemic model." In Stochastic Epidemic Models and Their Statistical Analysis, 11–18. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1158-7_2.

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Hincapié P., Doracelly, Juan Ospina G., Anthony Uyi Afuwape, and Ruben D. Gómez A. "Epidemic Thresholds in SIR and SIIR Models Applying an Algorithmic Method." In Lecture Notes in Computer Science, 119–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-89746-0_12.

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da Costa, Walley, Líliam Medeiros, and Sandra Sandri. "A Fuzzy Cellular Automata for SIR Compartmental Models." In Fuzzy Logic and Applications, 234–47. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03200-9_24.

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Britton, Tom, and Etienne Pardoux. "Chapter 4 Inference for Continuous Time SIR models." In Lecture Notes in Mathematics, 417–46. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-30900-8_15.

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Milazzo, Paolo. "Analysis of COVID-19 Data with PRISM: Parameter Estimation and SIR Modelling." In From Data to Models and Back, 123–33. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70650-0_8.

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Hollman, Arthur. "War injuries used as research models · The triple response of the skin to injury, the H substance · Monograph on blood vessels of the human skin · Physiology and medicine · Third edition of The Mechanism · Nobel Prize for Einthoven · Death of Mackenzie · Controversy over dog experiments." In Sir Thomas Lewis, 109–24. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0927-3_8.

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Conference papers on the topic "SIR Models"

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Cherian, Jacob P., and Jubilant J. Kizhakkethottam. "A Technical Assessment of SIR, SIR-V and SEIR Epidemic Models." In 2023 IEEE International Conference on Recent Advances in Systems Science and Engineering (RASSE). IEEE, 2023. http://dx.doi.org/10.1109/rasse60029.2023.10363532.

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Ganti, Radha Krishna, and Martin Haenggi. "SIR asymptotics in general cellular network models." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282607.

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Alutto, Martina, Leonardo Cianfanelli, Giacomo Como, and Fabio Fagnani. "Multiple peaks in network SIR epidemic models." In 2022 IEEE 61st Conference on Decision and Control (CDC). IEEE, 2022. http://dx.doi.org/10.1109/cdc51059.2022.9992408.

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Buhrii, Khrystyna, and Yuriy Golovaty. "SIR Models on Complex Networks and Impact of Vaccination." In 2023 IEEE 13th International Conference on Electronics and Information Technologies (ELIT). IEEE, 2023. http://dx.doi.org/10.1109/elit61488.2023.10310758.

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Bicher, Martin, Gunter Schneckenreither, and Niki Popper. "Mean-Field based comparison of two age-dependent SIR models." In 2015 Winter Simulation Conference (WSC). IEEE, 2015. http://dx.doi.org/10.1109/wsc.2015.7408469.

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Hansson, Jonas, Alain Govaert, Richard Pates, Emma Tegling, and Kristian Soltesz. "Limitations of time-delayed case isolation in heterogeneous SIR models." In 2022 American Control Conference (ACC). IEEE, 2022. http://dx.doi.org/10.23919/acc53348.2022.9867465.

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Dunyak, Alex, and Peter E. Caines. "Large Scale Systems and SIR Models: A Featured Graphon Approach." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683048.

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Isabel, Laurencia, Kie Van Ivanky Saputra, and Helena Margaretha. "Predicting BPJS health insurance premiums using SIR-like participant models and frequency–severity model." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2022 (MATHTECH 2022): Navigating the Everchanging Norm with Mathematics and Technology. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0192491.

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Viskic, I., and R. Domer. "A Flexible, Syntax Independent Representation (SIR) for System Level Design Models." In 9th EUROMICRO Conference on Digital System Design (DSD'06). IEEE, 2006. http://dx.doi.org/10.1109/dsd.2006.6.

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Alutto, Martina, Giacomo Como, and Fabio Fagnani. "On SIR epidemic models with feedback-controlled interactions and network effects." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683007.

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Reports on the topic "SIR Models"

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Ellison, Glenn. Implications of Heterogeneous SIR Models for Analyses of COVID-19. Cambridge, MA: National Bureau of Economic Research, June 2020. http://dx.doi.org/10.3386/w27373.

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Wallace, Sean, Scott Lux, Constandinos Mitsingas, Irene Andsager, and Tapan Patel. Performance testing and modeling of a transpired ventilation preheat solar wall : performance evaluation of facilities at Fort Drum, NY, and Kansas Air National Guard, Topeka, KS. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42000.

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This work performed measurement and verification of installed, operational solar wall systems at Fort Drum, NY, and Forbes Field, Air National Guard, Topeka, KS. Actual annual savings were compared estimated savings generated by a solar wall modeling tool (RETScreen). A comparison with the RETScreen modeling tool shows that the measured actively heated air provided by the solar wall provides 57% more heat than the RETScreen tool predicted, after accounting for boiler efficiency. The solar wall at Fort Drum yields a net savings of $851/yr, for a simple payback of 146 years and a SIR of 0.16. RETScreen models indicate that the solar wall system at Forbes Field, Kansas Air National Guard, Topeka, KS saves $9,350/yr, for a simple payback of 58.8 years and a SIR of 0.34. Although results showed that, due to low natural gas prices, the Fort Drum system was not economically viable, it was recommended that the system still be used to meet renewable energy and fossil fuel reduction goals. The current system becomes economical (SIR 1.00) at a natural gas rate of $16.00/MMBTU or $1.60 /therm.
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Dunn, Tim. Briefing on DUO2 SFR Models. Office of Scientific and Technical Information (OSTI), August 2015. http://dx.doi.org/10.2172/1554226.

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Acemoglu, Daron, Victor Chernozhukov, Iván Werning, and Michael Whinston. Optimal Targeted Lockdowns in a Multi-Group SIR Model. Cambridge, MA: National Bureau of Economic Research, May 2020. http://dx.doi.org/10.3386/w27102.

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Whinston, Michael D., Ivàn Werning, Victor Chernozhukov, and Daron Acemoglu. A Multi-Risk SIR Model with Optimally Targeted Lockdown. The IFS, May 2020. http://dx.doi.org/10.1920/wp.cem.2020.1420.

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Dudley, J. P., and S. V. Samsonov. SAR interferometry with the RADARSAT Constellation Mission. Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/329396.

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The RADARSAT Constellation Mission (RCM) is Canada's latest system of C-band Synthetic Aperture Radar (SAR) Earth observation satellites. The system of three satellites, spaced equally in a common orbit, allows for a rapid four-day repeat interval. The RCM has been designed with a selection of stripmap, spotlight, and ScanSAR beam modes which offer varied combinations of spatial resolution and coverage. Using Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques, the growing archive of SAR data gathered by RCM can be used for change detection and ground deformation monitoring for diverse applications in Canada and around the world. In partnership with the Canadian Space Agency (CSA), the Canada Centre for Mapping and Earth Observation (CCMEO) has developed an automated system for generating standard and advanced deformation products and change detection from SAR data acquired by RCM and RADARSAT-2 satellites using DInSAR processing methodology. Using this system, this paper investigates four key interferometric properties of the RCM system which were not available on the RADARSAT-1 or RADARSAT-2 missions: The impact of the high temporal resolution of the four-day repeat cycle of the RCM on temporal decorrelation trends is tested and fitted against simple temporal decay models. The effect of the normalization and the precision of the radiometric calibration on interferometric spatial coherence is investigated. The performance of the RCM ScanSAR mode for wide area interferometric analysis is tested. The performance of the novel RCM Compact-polarization (CP) mode for interferometric analysis is also investigated.
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Atkeson, Andrew, Karen Kopecky, and Tao Zha. Estimating and Forecasting Disease Scenarios for COVID-19 with an SIR Model. Cambridge, MA: National Bureau of Economic Research, June 2020. http://dx.doi.org/10.3386/w27335.

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Faillace, E. R., J. J. Cheng, and C. Yu. RESRAD benchmarking against six radiation exposure pathway models. Office of Scientific and Technical Information (OSTI), October 1994. http://dx.doi.org/10.2172/10194337.

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Carin, Lawrence. Efficient Electromagnetic Scattering Models for UWB SAR Calibration. Fort Belvoir, VA: Defense Technical Information Center, June 2000. http://dx.doi.org/10.21236/ada572039.

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Walker, David T. SAR Assimilation for Near-Shore Spectral Wave Models. Fort Belvoir, VA: Defense Technical Information Center, September 2003. http://dx.doi.org/10.21236/ada620256.

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