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Автор: Grafiati

Опубліковано: 23 вересня 2022

Оновлено: 20 квітня 2024

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1

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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Анотація:

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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2

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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3

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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4

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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Анотація:

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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5

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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6

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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7

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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Анотація:

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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8

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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9

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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10

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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Анотація:

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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11

Okabe, Yutaka, and Akira Shudo. "Microscopic Numerical Simulations of Epidemic Models on Networks." Mathematics 9, no. 9 (April 22, 2021): 932. http://dx.doi.org/10.3390/math9090932.

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Анотація:

Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential equations. We perform microscopic numerical simulations for corresponding epidemic models on networks. Comparing a random network and a scale-free network for the spread of the infection, we emphasize the role of hubs in a scale-free network. We also present a simple derivation of the exact solution of the SIR model.

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12

Prathom, Kiattisak, and Asama Jampeepan. "Direct numerical solutions of the SIR and SEIR models via the Dirichlet series approach." PLOS ONE 18, no. 6 (June 30, 2023): e0287556. http://dx.doi.org/10.1371/journal.pone.0287556.

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Compartment models are implemented to understand the dynamic of a system. To analyze the models, a numerical tool is required. This manuscript presents an alternative numerical tool for the SIR and SEIR models. The same idea could be applied to other compartment models. The result starts with transforming the SIR model to an equivalent differential equation. The Dirichlet series satisfying the differential equation leads to an alternative numerical method to obtain the model’s solutions. The derived Dirichlet solution not only matches the numerical solution obtained by the fourth-order Runge-Kutta method (RK-4), but it also carries the long-run behavior of the system. The SIR solutions obtained by the RK-4 method, an approximated analytical solution, and the Dirichlet series approximants are graphically compared. The Dirichlet series approximants order 15 and the RK-4 method are almost perfectly matched with the mean square error less than 2 × 10−5. A specific Dirichlet series is considered in the case of the SEIR model. The process to obtain a numerical solution is done in the similar way. The graphical comparisons of the solutions achieved by the Dirichlet series approximants order 20 and the RK-4 method show that both methods produce almost the same solution. The mean square errors of the Dirichlet series approximants order 20 in this case are less than 1.2 × 10−4.

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13

Goenka, Aditya, Lin Liu, and Manh-Hung Nguyen. "SIR economic epidemiological models with disease induced mortality." Journal of Mathematical Economics 93 (March 2021): 102476. http://dx.doi.org/10.1016/j.jmateco.2021.102476.

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14

González-Ramírez, L. Rocío, Osvaldo Osuna, and Geiser Villavicencio-Pulido. "Oscillations in seasonal SIR models with saturated treatment." Revista Integración 34, no. 2 (July 1, 2016): 125–31. http://dx.doi.org/10.18273/revint.v34n2-2016001.

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15

d'Onofrio, Alberto, and Piero Manfredi. "Behavioral SIR models with incidence-based social-distancing." Chaos, Solitons & Fractals 159 (June 2022): 112072. http://dx.doi.org/10.1016/j.chaos.2022.112072.

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16

Harir, Atimad, Hassan El Harfi, Said Melliani, and L. Saadia Chadli. "Fuzzy Solutions of the SIR Models using VIM." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 30, no. 01 (February 2022): 43–61. http://dx.doi.org/10.1142/s0218488522500039.

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Анотація:

The aim of this paper first presents a new solution to the SIR model with fuzzy initial value, elementary properties of this new solution are given. We study the application of variational iteration method in finding the approximate solution of SIR model with fuzzy initial value. The presented method have been applied in a direct way without linearization, disretization or perturbation. Result obtained by this method and fuzzy initial value shows that both are in excellent agreement which indicates their affectiveness and reliability.

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17

Clancy, Damian. "SIR epidemic models with general infectious period distribution." Statistics & Probability Letters 85 (February 2014): 1–5. http://dx.doi.org/10.1016/j.spl.2013.10.017.

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18

Bolzoni, Luca, Elena Bonacini, Cinzia Soresina, and Maria Groppi. "Time-optimal control strategies in SIR epidemic models." Mathematical Biosciences 292 (October 2017): 86–96. http://dx.doi.org/10.1016/j.mbs.2017.07.011.

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19

Paeng, Seong-Hun, and Jonggul Lee. "Continuous and discrete SIR-models with spatial distributions." Journal of Mathematical Biology 74, no. 7 (October 28, 2016): 1709–27. http://dx.doi.org/10.1007/s00285-016-1071-8.

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20

Centrone, Francesca, and Ernesto Salinelli. "LYAPUNOV FUNCTIONS IN SIR MODELS WITH VACCINATING BEHAVIOUR." Far East Journal of Mathematical Sciences (FJMS) 125, no. 2 (August 20, 2020): 139–50. http://dx.doi.org/10.17654/ms125020139.

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21

Bichara, Derdei, Yun Kang, Carlos Castillo-Chavez, Richard Horan, and Charles Perrings. "SIS and SIR Epidemic Models Under Virtual Dispersal." Bulletin of Mathematical Biology 77, no. 11 (October 21, 2015): 2004–34. http://dx.doi.org/10.1007/s11538-015-0113-5.

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22

O’Regan, Suzanne M., Thomas C. Kelly, Andrei Korobeinikov, Michael J. A. O’Callaghan, and Alexei V. Pokrovskii. "Lyapunov functions for SIR and SIRS epidemic models." Applied Mathematics Letters 23, no. 4 (April 2010): 446–48. http://dx.doi.org/10.1016/j.aml.2009.11.014.

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23

Du, Nguyen, Alexandru Hening, Nhu Nguyen, and George Yin. "Hybrid stochastic epidemic sir models with hidden states." Nonlinear Analysis: Hybrid Systems 49 (August 2023): 101368. http://dx.doi.org/10.1016/j.nahs.2023.101368.

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24

Korobeinikov, Andrei. "Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages." Bulletin of Mathematical Biology 71, no. 1 (September 4, 2008): 75–83. http://dx.doi.org/10.1007/s11538-008-9352-z.

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25

Huang, Gang, Yasuhiro Takeuchi, Wanbiao Ma, and Daijun Wei. "Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate." Bulletin of Mathematical Biology 72, no. 5 (January 21, 2010): 1192–207. http://dx.doi.org/10.1007/s11538-009-9487-6.

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26

Rempała, Grzegorz A. "Equivalence of mass action and Poisson network SIR epidemic models." BIOMATH 12, no. 2 (December 15, 2023): 2311237. http://dx.doi.org/10.55630/j.biomath.2023.11.237.

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Анотація:

This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a century ago by Kermack and McKendrick. We demonstrate that the decline pattern in susceptibles is identical for both models. This equivalence carries practical implications: the susceptibles decay curve, often referred to as the epidemic or incidence curve, is frequently used in empirical studies to forecast epidemic dynamics. Although the curves for susceptibles align perfectly, those for infections do differ. Yet, the infection curves tend to converge and become almost indistinguishable in high-degree networks. In summary, our analysis suggests that under many practical scenarios, it's acceptable to use the classical SIR model as a close approximation to the Poisson SIR network model.

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27

Hussain, Sajid, Zafar Iqbal, Muhammad Mansoor, and Rashid Ahmed. "Bivariate and Multivariate Data Cloning through Non Linear Regression Models." Scientific Inquiry and Review 7, no. 3 (August 28, 2023): 1–21. http://dx.doi.org/10.32350/sir.73.01.

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Анотація:

Nonlinear regression analysis holds significant popularity in mathematical, engineering, and social science domains. Disciplines like financial matters, biology, and natural chemistry have broadly utilized nonlinear regression models (NLRMs). Cloned datasets have their own importance in such areas which provide the same fit of bivariate and multivariate nonlinear regression models for the actual datasets. This article presents a sequence of cloned datasets that give exactly the same fit of bivariate and multivariate nonlinear regression models.

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28

Shi, Jiaxin, and Dongwei Huang. "Calculation Method and Application of Basic Regeneration Number for a Class of Stochastic Systems." WSEAS TRANSACTIONS ON SYSTEMS 21 (October 11, 2022): 193–98. http://dx.doi.org/10.37394/23202.2022.21.21.

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Анотація:

Considering the influence of random noise on SIR, SEIR and SEIAR infectious disease models, we establish SIR, SEIR and SEIAR models with random disturbance, and deduce the calculation formula of the basic regeneration number of the random infectious disease model in the sense of mean value by using Itô formula. The effectiveness of the basic regeneration number calculation method is verified by numerical simulation of the system evolution process.

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29

Wu, Fanli. "SIR Model Adjustment for Covid Spread in China." Highlights in Science, Engineering and Technology 72 (December 15, 2023): 610–15. http://dx.doi.org/10.54097/tn9ztz26.

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One of the ways to reduce the harm caused by COVID-19 pandemic is developing policies that balance the health and economy of society. These policies rely on large amount epidemic data. Traditional epidemiological SIR models become the basis for COVID-19 models to replicate and predict the epidemic's trend. This study seeks to find out which model is more suitable for countries under strict control policies. Through the collection and analysis of information on the epidemic in China, this study concluded that there are two pieces of data are suitable for this study. In this study, the two parts of data are calculated and combined with other studies to obtain the parameter values for different models. The SIR and SEIR models in this study yielded interesting results. Simulations of the SIR model under mass lockdown policies produced reliable data forecasts for infection days. The SEIR model has a relatively accurate prediction of the trend of the proportion of infections population. However, other models based on COVID-19 characteristics do not produce as much information as compared to the above two models.

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30

Wang, Jinliang, Xianning Liu, Toshikazu Kuniya, and Jingmei Pang. "Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility." Discrete & Continuous Dynamical Systems - B 22, no. 7 (2017): 2795–812. http://dx.doi.org/10.3934/dcdsb.2017151.

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31

Liu, Zhenjie. "Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates." Nonlinear Analysis: Real World Applications 14, no. 3 (June 2013): 1286–99. http://dx.doi.org/10.1016/j.nonrwa.2012.09.016.

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32

Yuan, Chengjun, Daqing Jiang, Donal O’Regan, and Ravi P. Agarwal. "Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation." Communications in Nonlinear Science and Numerical Simulation 17, no. 6 (June 2012): 2501–16. http://dx.doi.org/10.1016/j.cnsns.2011.07.025.

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33

Liu, Junli, Baoyang Peng, and Tailei Zhang. "Effect of discretization on dynamical behavior of SEIR and SIR models with nonlinear incidence." Applied Mathematics Letters 39 (January 2015): 60–66. http://dx.doi.org/10.1016/j.aml.2014.08.012.

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34

Waters, Edward Kyle, Harvinder Sidhu, and Geoff Mercer. "Spatial heterogeneity in simple deterministic SIR models assessed ecologically." ANZIAM Journal 54 (April 9, 2013): 23. http://dx.doi.org/10.21914/anziamj.v54i0.5871.

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35

Moharir, P. S. "Stein estimation for SIR-predictable models of earthquake occurrence." Journal of Earth System Science 102, no. 2 (June 1993): 367–81. http://dx.doi.org/10.1007/bf02861509.

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36

Koss, Lorelei. "SIR Models: Differential Equations that Support the Common Good." CODEE Journal 12, no. 1 (2019): 61–71. http://dx.doi.org/10.5642/codee.201912.01.06.

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37

Zhao, Wencai, Tongqian Zhang, Zhengbo Chang, Xinzhu Meng, and Yulin Liu. "Dynamical Analysis of SIR Epidemic Models with Distributed Delay." Journal of Applied Mathematics 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/154387.

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Анотація:

SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction numberRis got. In order to study the important role of vaccination to prevent diseases, the model with distributed delay under impulsive vaccination is formulated. And the sufficient conditions of globally asymptotic stability of “infection-free” periodic solution and the permanence of the model are obtained by using Floquet’s theorem, small-amplitude perturbation skills, and comparison theorem. Lastly, numerical simulation is presented to illustrate our main conclusions that vaccination has significant effects on the dynamical behaviors of the model. The results can provide effective tactic basis for the practical infectious disease prevention.

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38

Gathy, Maude, and Claude Lefèvre. "From damage models to SIR epidemics and cascading failures." Advances in Applied Probability 41, no. 1 (March 2009): 247–69. http://dx.doi.org/10.1239/aap/1240319584.

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Анотація:

This paper is concerned with a nonstationary Markovian chain of cascading damage that constitutes an iterated version of a classical damage model. The main problem under study is to determine the exact distribution of the total outcome of this process when the cascade of damages finally stops. Two different applications are discussed, namely the final size for a wide class of SIR (susceptible → infective → removed) epidemic models and the total number of failures for a system of components in reliability. The starting point of our analysis is the recent work of Lefèvre (2007) on a first-crossing problem for the cumulated partial sums of independent parametric distributions, possibly nonstationary but stable by convolution. A key mathematical tool is provided by a nonstandard family of remarkable polynomials, called the generalised Abel–Gontcharoff polynomials. Somewhat surprisingly, the approach followed will allow us to relax some model assumptions usually made in epidemic theory and reliability. To close, approximation by a branching process is also investigated to a certain extent.

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39

Gathy, Maude, and Claude Lefèvre. "From damage models to SIR epidemics and cascading failures." Advances in Applied Probability 41, no. 01 (March 2009): 247–69. http://dx.doi.org/10.1017/s0001867800003219.

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Анотація:

This paper is concerned with a nonstationary Markovian chain of cascading damage that constitutes an iterated version of a classical damage model. The main problem under study is to determine the exact distribution of the total outcome of this process when the cascade of damages finally stops. Two different applications are discussed, namely the final size for a wide class of SIR (susceptible → infective → removed) epidemic models and the total number of failures for a system of components in reliability. The starting point of our analysis is the recent work of Lefèvre (2007) on a first-crossing problem for the cumulated partial sums of independent parametric distributions, possibly nonstationary but stable by convolution. A key mathematical tool is provided by a nonstandard family of remarkable polynomials, called the generalised Abel–Gontcharoff polynomials. Somewhat surprisingly, the approach followed will allow us to relax some model assumptions usually made in epidemic theory and reliability. To close, approximation by a branching process is also investigated to a certain extent.

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40

Pandey, Abhishek, Anuj Mubayi, and Jan Medlock. "Comparing vector–host and SIR models for dengue transmission." Mathematical Biosciences 246, no. 2 (December 2013): 252–59. http://dx.doi.org/10.1016/j.mbs.2013.10.007.

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41

Marinov, Tchavdar T., Rossitza S. Marinova, Joe Omojola, and Michael Jackson. "Inverse problem for coefficient identification in SIR epidemic models." Computers & Mathematics with Applications 67, no. 12 (July 2014): 2218–27. http://dx.doi.org/10.1016/j.camwa.2014.02.002.

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42

Zhuang, Lili, Noel Cressie, Laura Pomeroy, and Daniel Janies. "Multi-species SIR models from a dynamical Bayesian perspective." Theoretical Ecology 6, no. 4 (June 21, 2013): 457–73. http://dx.doi.org/10.1007/s12080-013-0180-x.

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43

WATERS, E. K., H. S. SIDHU, and G. N. MERCER. "SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY." ANZIAM Journal 54, no. 1-2 (October 2012): 23–36. http://dx.doi.org/10.1017/s1446181113000035.

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Анотація:

AbstractPatchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

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44

Temime, Laura, and Guy Thomas. "Estimation of Balanced Simultaneous Confidence Sets for SIR Models." Communications in Statistics - Simulation and Computation 35, no. 3 (September 2006): 803–12. http://dx.doi.org/10.1080/03610910600716621.

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45

Lefèvre, Claude, and Matthieu Simon. "SIR-Type Epidemic Models as Block-Structured Markov Processes." Methodology and Computing in Applied Probability 22, no. 2 (April 3, 2019): 433–53. http://dx.doi.org/10.1007/s11009-019-09710-y.

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46

Allen, Linda J. S. "Some discrete-time SI, SIR, and SIS epidemic models." Mathematical Biosciences 124, no. 1 (November 1994): 83–105. http://dx.doi.org/10.1016/0025-5564(94)90025-6.

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47

Awawdeh, Fadi, A. Adawi, and Z. Mustafa. "Solutions of the SIR models of epidemics using HAM." Chaos, Solitons & Fractals 42, no. 5 (December 2009): 3047–52. http://dx.doi.org/10.1016/j.chaos.2009.04.012.

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48

Siegel, D., and H. Kunze. "Monotonicity Properties of the SIS and SIR Epidemic Models." Journal of Mathematical Analysis and Applications 185, no. 1 (July 1994): 65–85. http://dx.doi.org/10.1006/jmaa.1994.1233.

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49

Knolle, Helmut, and Jairo Santanilla. "SIR epidemic models with spatial spread in bounded domains." Electronic Journal of Differential Equations, Special Issue 01 (March 18, 2022): 315–25. http://dx.doi.org/10.58997/ejde.sp.01.k2.

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Анотація:

The spread of an infectious disease which confers immunity after recovery from infection, can be described by a SIR model, i.e. a system of three differential equations for the dependent variables \(S\), \(I\), and \(R\), which are the numbers (densities) of susceptible, infectious and recovered (immune) individuals, respectively. The equations for \(S\) and \(I\) are typically nonlinear. In this article, we consider two spatio-temporal SIR models. The first model is similar to reaction-diffusion systems in chemistry. A simple birth-and-death process is incorporated, and it is assumed, that a fraction f of the newborns is vaccinated and is then immune for life. We show how the smallest eigenvalue of the eigenvalue problem associated with the linearized equation for I is related to the basic reproduction number \(\mathcal{R}_0\), a key concept in the mathematical theory of infectious diseases. Here it is defined by a variational principle. We show that the disease-free equilibrium is asymptotically stable if \(\mathcal{R}_0<1\), or if \(\mathcal{R}_0\ge 1\) and \(f>1-1/{\mathcal{R}_0}\), and unstable if \(\mathcal{R}_0>1\) and \(f<1-1/\mathcal{R}_0\). In the other model we assume that the population consists of sedentary individuals who leave their home only temporarily. Both models suggest that restriction of mobility may be counterproductive for the control of an epidemic outbreak. For more information see https://ejde.math.txstate.edu/special/01/k2/abstr.html

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El Chaal, Rachid, Said Bouchefra, and Moulay Othman Aboutafail. "Stochastic Dynamics and Extinction Time in SIR Epidemiological Models." Acadlore Transactions on Applied Mathematics and Statistics 1, no. 3 (December 31, 2023): 181–202. http://dx.doi.org/10.56578/atams010305.

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