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Articles de revues sur le sujet « NONLINEAR INCIDENCE RATES »

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Auteur : Grafiati

Publié le 11 septembre 2023

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1

Liu, Wei-min, Herbert W. Hethcote et Simon A. Levin. « Dynamical behavior of epidemiological models with nonlinear incidence rates ». Journal of Mathematical Biology 25, n^o 4 (septembre 1987) : 359–80. http://dx.doi.org/10.1007/bf00277162.

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2

Hui, Jing, et Lansun Chen. « Impulsive vaccination of sir epidemic models with nonlinear incidence rates ». Discrete & ; Continuous Dynamical Systems - B 4, n^o 3 (2004) : 595–605. http://dx.doi.org/10.3934/dcdsb.2004.4.595.

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3

Mukherjee, D., J. Chattopadhyay et P. K. Tapaswi. « Global stability results of epidemiological models with nonlinear incidence rates ». Mathematical and Computer Modelling 18, n^o 2 (juillet 1993) : 89–92. http://dx.doi.org/10.1016/0895-7177(93)90009-n.

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4

Ponciano, José M., et Marcos A. Capistrán. « First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics ». PLoS Computational Biology 7, n^o 2 (17 février 2011) : e1001079. http://dx.doi.org/10.1371/journal.pcbi.1001079.

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5

Sachs, Dominik, Aleh Tsyvinski et Nicolas Werquin. « Nonlinear Tax Incidence and Optimal Taxation in General Equilibrium ». Econometrica 88, n^o 2 (2020) : 469–93. http://dx.doi.org/10.3982/ecta14681.

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We study the incidence of nonlinear labor income taxes in an economy with a continuum of endogenous wages. We derive in closed form the effects of reforming nonlinearly an arbitrary tax system, by showing that this problem can be formalized as an integral equation. Our tax incidence formulas are valid both when the underlying assignment of skills to tasks is fixed or endogenous. We show qualitatively and quantitatively that contrary to conventional wisdom, if the tax system is initially suboptimal and progressive, the general‐equilibrium “trickle‐down” forces may raise the benefits of increasing the marginal tax rates on high incomes. We finally derive a parsimonious characterization of optimal taxes.

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6

Rohith, G., et K. B. Devika. « Dynamics and control of COVID-19 pandemic with nonlinear incidence rates ». Nonlinear Dynamics 101, n^o 3 (25 juin 2020) : 2013–26. http://dx.doi.org/10.1007/s11071-020-05774-5.

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7

Liu, Yicheng, Yimin Du et Jianhong Wu. « Backward/Hopf bifurcations in SIS models with delayed nonlinear incidence rates ». Frontiers of Mathematics in China 3, n^o 4 (23 octobre 2008) : 535–53. http://dx.doi.org/10.1007/s11464-008-0040-y.

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8

Li, Li, Gui-Quan Sun et Zhen Jin. « Bifurcation and chaos in an epidemic model with nonlinear incidence rates ». Applied Mathematics and Computation 216, n^o 4 (avril 2010) : 1226–34. http://dx.doi.org/10.1016/j.amc.2010.02.014.

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9

Yuan, Zhaohui, et Lin Wang. « Global stability of epidemiological models with group mixing and nonlinear incidence rates ». Nonlinear Analysis : Real World Applications 11, n^o 2 (avril 2010) : 995–1004. http://dx.doi.org/10.1016/j.nonrwa.2009.01.040.

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10

Lu, Zhonghua, Xianning Liu et Lansun Chen. « Hopf bifurcation of nonlinear incidence rates SIR epidemiological models with stage structure ». Communications in Nonlinear Science and Numerical Simulation 6, n^o 4 (décembre 2001) : 205–9. http://dx.doi.org/10.1016/s1007-5704(01)90015-2.

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11

Wang, Yi, et Jinde Cao. « Global stability of general cholera models with nonlinear incidence and removal rates ». Journal of the Franklin Institute 352, n^o 6 (juin 2015) : 2464–85. http://dx.doi.org/10.1016/j.jfranklin.2015.03.030.

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12

Sun, Chengjun, Yiping Lin et Shoupeng Tang. « Global stability for an special SEIR epidemic model with nonlinear incidence rates ». Chaos, Solitons & ; Fractals 33, n^o 1 (juillet 2007) : 290–97. http://dx.doi.org/10.1016/j.chaos.2005.12.028.

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13

Upadhyay, Ranjit Kumar, Ashok Kumar Pal, Sangeeta Kumari et Parimita Roy. « Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates ». Nonlinear Dynamics 96, n^o 4 (4 avril 2019) : 2351–68. http://dx.doi.org/10.1007/s11071-019-04926-6.

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14

Liu, Wei-min, Simon A. Levin et Yoh Iwasa. « Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models ». Journal of Mathematical Biology 23, n^o 2 (février 1986) : 187–204. http://dx.doi.org/10.1007/bf00276956.

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15

Alshammari, Fehaid Salem, et Muhammad Altaf Khan. « Dynamic behaviors of a modified SIR model with nonlinear incidence and recovery rates ». Alexandria Engineering Journal 60, n^o 3 (juin 2021) : 2997–3005. http://dx.doi.org/10.1016/j.aej.2021.01.023.

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16

Chowell, Gerardo, Lisa Sattenspiel, Shweta Bansal et Cécile Viboud. « Early sub-exponential epidemic growth : Simple models, nonlinear incidence rates, and additional mechanisms ». Physics of Life Reviews 18 (septembre 2016) : 114–17. http://dx.doi.org/10.1016/j.plrev.2016.08.016.

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17

Wang, Feng, Shan Wang et Youhua Peng. « Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations ». Discrete Dynamics in Nature and Society 2020 (5 mai 2020) : 1–12. http://dx.doi.org/10.1155/2020/9367879.

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In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results.

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18

Lee, Kwang Sung, et Daewook Kim. « Global dynamics of a pine wilt disease transmission model with nonlinear incidence rates ». Applied Mathematical Modelling 37, n^o 6 (mars 2013) : 4561–69. http://dx.doi.org/10.1016/j.apm.2012.09.042.

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19

Sun, Ruoyan, et Junping Shi. « Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates ». Applied Mathematics and Computation 218, n^o 2 (septembre 2011) : 280–86. http://dx.doi.org/10.1016/j.amc.2011.05.056.

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20

Kumar, Abhishek, et Nilam. « Mathematical analysis of a delayed epidemic model with nonlinear incidence and treatment rates ». Journal of Engineering Mathematics 115, n^o 1 (7 mars 2019) : 1–20. http://dx.doi.org/10.1007/s10665-019-09989-3.

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21

Halder, Manisha, et Dr D. S. Sharma. « A Mathematical Analysis of Dynamical Behaviour of Epidemiological Models with Nonlinear Incidence Rates ». International Journal of Scientific Research in Modern Science and Technology 2, n^o 5 (31 mai 2023) : 33–40. http://dx.doi.org/10.59828/ijsrmst.v2i5.86.

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An updated model of an epidemic is discussed, one in which incidence has plateaued but treatment has not been fully implemented. All equilibrium points are checked for existence. In this research, we examine how shifts from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) paradigm manifest in epidemiological models. These models hypothesize that the irresistible power is a nonlinear capability of the populace thickness of contaminated individuals. At last, this model might be utilized to research the elements of infection spread, provided that the two phenomena follow consistent patterns.

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22

Zhao, Xiangming, et Jianping Shi. « Dynamic behavior of a stochastic SIR model with nonlinear incidence and recovery rates ». AIMS Mathematics 8, n^o 10 (2023) : 25037–59. http://dx.doi.org/10.3934/math.20231278.

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<abstract><p>The spread of infectious diseases are inevitably affected by natural and social factors, and their evolution presents oscillations and other uncertainties. Therefore, it is of practical significance to consider stochastic noise interference in the studies of infectious disease models. In this paper, a stochastic SIR model with nonlinear incidence and recovery rate is studied. First, a unique global positive solution for any initial value of the system is proved. Second, we provide the sufficient conditions for disease extinction or persistence, and the influence of threshold $ \tilde{R_{0}} $ of the stochastic SIR model on disease state transition is analyzed. Additionally, we prove that the system has a stationary distribution under some given parameter conditions by building an appropriate stochastic Lyapunov function as well as using the equivalent condition of the Hasminskii theorem. Finally, the correctness of these theoretical results are validated by numerical simulations.</p></abstract>

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23

Li, Jun Hong, Ning Cui et Hong Kai Sun. « Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate ». Advanced Materials Research 479-481 (février 2012) : 1495–98. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.1495.

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An SIRS epidemic model with nonlinear incidence rate is studied. It is assumed that susceptible and infectious individuals have constant immigration rates. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the analytical results.

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24

Torku, Thomas, Abdul Khaliq et Fathalla Rihan. « SEINN : A deep learning algorithm for the stochastic epidemic model ». Mathematical Biosciences and Engineering 20, n^o 9 (2023) : 16330–61. http://dx.doi.org/10.3934/mbe.2023729.

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<abstract><p>Stochastic modeling predicts various outcomes from stochasticity in the data, parameters and dynamical system. Stochastic models are deemed more appropriate than deterministic models accounting in terms of essential and practical information about a system. The objective of the current investigation is to address the issue above through the development of a novel deep neural network referred to as a stochastic epidemiology-informed neural network. This network learns knowledge about the parameters and dynamics of a stochastic epidemic vaccine model. Our analysis centers on examining the nonlinear incidence rate of the model from the perspective of the combined effects of vaccination and stochasticity. Based on empirical evidence, stochastic models offer a more comprehensive understanding than deterministic models, mainly when we use error metrics. The findings of our study indicate that a decrease in randomness and an increase in vaccination rates are associated with a better prediction of nonlinear incidence rates. Adopting a nonlinear incidence rate enables a more comprehensive representation of the complexities of transmitting diseases. The computational analysis of the proposed method, focusing on sensitivity analysis and overfitting analysis, shows that the proposed method is efficient. Our research aims to guide policymakers on the effects of stochasticity in epidemic models, thereby aiding the development of effective vaccination and mitigation policies. Several case studies have been conducted on nonlinear incidence rates using data from Tennessee, USA.</p></abstract>

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25

Chinyoka, Mirirai, Tinashe B. Gashirai et Steady Mushayabasa. « On the Dynamics of a Fractional-Order Ebola Epidemic Model with Nonlinear Incidence Rates ». Discrete Dynamics in Nature and Society 2021 (3 décembre 2021) : 1–12. http://dx.doi.org/10.1155/2021/2125061.

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We propose a new fractional-order model to investigate the transmission and spread of Ebola virus disease. The proposed model incorporates relevant biological factors that characterize Ebola transmission during an outbreak. In particular, we have assumed that susceptible individuals are capable of contracting the infection from a deceased Ebola patient due to traditional beliefs and customs practiced in many African countries where frequent outbreaks of the disease are recorded. We conducted both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Model parameters were estimated based on the 2014-2015 Ebola outbreak in Sierra Leone. In addition, numerical simulation results are presented to demonstrate the analytical findings.

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26

Han, Ping, Zhengbo Chang et Xinzhu Meng. « Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates ». Complexity 2020 (8 mai 2020) : 1–17. http://dx.doi.org/10.1155/2020/8596371.

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This paper considers a stochastic SIR epidemic system affected by mixed nonlinear incidence rates. Using Markov semigroup theory and the Fokker–Planck equation, we explore the asymptotic dynamics of the stochastic system. We first investigate the existence of a positive solution and its uniqueness. Furthermore, we prove that the stochastic system has an asymptotically stable stationary distribution. In addition, the sufficient conditions for disease extinction are also obtained, which imply that the white noise can suppress and control the spread of infectious diseases. Finally, in order to illustrate the analytical results, we give some numerical simulations.

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27

Muroya, Yoshiaki, Yoichi Enatsu et Yukihiko Nakata. « Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays ». Nonlinear Analysis : Real World Applications 12, n^o 4 (août 2011) : 1897–910. http://dx.doi.org/10.1016/j.nonrwa.2010.12.002.

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28

Elaiw, A. M., et N. H. AlShamrani. « Dynamics of viral infection models with antibodies and general nonlinear incidence and neutralize rates ». International Journal of Dynamics and Control 4, n^o 3 (27 mai 2015) : 303–17. http://dx.doi.org/10.1007/s40435-015-0181-2.

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29

Soufiane, Bentout, et Tarik Mohammed Touaoula. « Global analysis of an infection age model with a class of nonlinear incidence rates ». Journal of Mathematical Analysis and Applications 434, n^o 2 (février 2016) : 1211–39. http://dx.doi.org/10.1016/j.jmaa.2015.09.066.

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30

Chen, Hao, et Jitao Sun. « Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates ». Applied Mathematics and Computation 218, n^o 8 (décembre 2011) : 4391–400. http://dx.doi.org/10.1016/j.amc.2011.10.015.

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31

Enatsu, Yoichi, Eleonora Messina, Yoshiaki Muroya, Yukihiko Nakata, Elvira Russo et Antonia Vecchio. « Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates ». Applied Mathematics and Computation 218, n^o 9 (janvier 2012) : 5327–36. http://dx.doi.org/10.1016/j.amc.2011.11.016.

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32

El Koufi, Amine, Jihad Adnani, Abdelkrim Bennar et Noura Yousfi. « Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate ». International Journal of Differential Equations 2019 (21 août 2019) : 1–9. http://dx.doi.org/10.1155/2019/9275051.

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We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.

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33

Li, Junhong, et Ning Cui. « Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment ». Scientific World Journal 2013 (2013) : 1–5. http://dx.doi.org/10.1155/2013/209256.

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This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.

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34

Zhang, Ling, Jingmei Pang et Jinliang Wang. « Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates ». Abstract and Applied Analysis 2013 (2013) : 1–11. http://dx.doi.org/10.1155/2013/354287.

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We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production numberR0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.

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35

Lv, Wei, Xue-Ying Liu, Xin-Jian Xu et Jie Lou. « Vaccination of a multi-group model of zoonotic diseases with direct and indirect transmission ». International Journal of Biomathematics 12, n^o 06 (août 2019) : 1950068. http://dx.doi.org/10.1142/s1793524519500682.

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Vaccination plays an important role in preventing or reducing the spread of zoonotic diseases. In this paper, we develop a susceptible-vaccinated-exposed-infectious-pathogen multi-group epidemic model of zoonotic diseases incorporating nonlinear direct and indirect incidence rates, nonlinear pathogen shedding rates, and common environmental contamination. Under certain assumptions, we first obtained the basic reproduction number of the model. Then, we utilized the comparison principle and global Lyapunov function method to prove global stability of dynamical equilibria. Finally, we analyzed optimal vaccination strategy. All the theoretical predictions were verified by numerical simulations.

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36

Ozair, Muhammad. « Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission ». Journal of Applied Mathematics 2014 (2014) : 1–9. http://dx.doi.org/10.1155/2014/204241.

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The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable wheneverR0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.

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37

STRUCHINER, CLAUDIO J., ROBERT C. BRUNET, M. ELIZABETH HALLORAN, EDUARDO MASSAD et RAYMUNDO S. AZEVEDO-NETO. « ON THE USE OF STATE-SPACE MODELS FOR THE EVALUATION OF HEALTH INTERVENTIONS ». Journal of Biological Systems 03, n^o 03 (septembre 1995) : 851–65. http://dx.doi.org/10.1142/s0218339095000770.

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Health intervention programs, such as vaccination, can be evaluated by comparing incidence rates of infection between unprotected and protected individuals in a population. Incidence rate ratios are usually estimated by following up on time a control and treated groups in order to collect information on person-time and cases in each group, or using the Cox model. This approach can be expensive and time consuming. An alternative approach is to use prevalence data to reconstitute past incidence. Current-status data are readily available or easily gathered and can be used to estimate incidence rates. This can only be achieved, however, under certain assumptions of time homogeneity and irreversibility of the outcome of interest. We discuss a simple transmission model appropriate to evaluate health interventions that confer long term protection and expand on previous statistical procedures to estimate the relevant parameters. Nonlinear nonormal state-space models allow for the estimation of incidence rates of infection which vary with age under age-dependent differential mortality.

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38

Jin, Li, Yunxian Dai, Yu Xiao et Yiping Lin. « RANK-ONE CHAOS IN A DELAYED SIR EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TREATMENT RATES ». Journal of Applied Analysis & ; Computation 11, n^o 4 (2021) : 1779–801. http://dx.doi.org/10.11948/20200190.

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39

Wang, Jinliang, et Xianning Liu. « Modeling diseases with latency and nonlinear incidence rates : global dynamics of a multi-group model ». Mathematical Methods in the Applied Sciences 39, n^o 8 (26 août 2015) : 1964–76. http://dx.doi.org/10.1002/mma.3613.

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40

Zhang, Hong, Juan Xia et Paul Georgescu. « Multigroup deterministic and stochasticSEIRIepidemic models with nonlinear incidence rates and distributed delays : A stability analysis ». Mathematical Methods in the Applied Sciences 40, n^o 18 (13 juin 2017) : 6254–75. http://dx.doi.org/10.1002/mma.4453.

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41

El Koufi, Amine. « Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process ». Complexity 2022 (22 avril 2022) : 1–13. http://dx.doi.org/10.1155/2022/8093696.

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In this work, we study a stochastic SIS epidemic model with Lévy jumps and nonlinear incidence rates. Firstly, we present our proposed model and its parameters. We establish sufficient conditions for the extinction and persistence of the disease in the population using some stochastic analysis background. We illustrate our theoretical results by numerical simulations. We conclude that the white noise and Lévy jump influence the transmission of the epidemic.

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42

Wang, Lei, Zhidong Teng, Tingting Tang et Zhiming Li. « Threshold Dynamics in Stochastic SIRS Epidemic Models with Nonlinear Incidence and Vaccination ». Computational and Mathematical Methods in Medicine 2017 (2017) : 1–20. http://dx.doi.org/10.1155/2017/7294761.

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In this paper, the dynamical behaviors for a stochastic SIRS epidemic model with nonlinear incidence and vaccination are investigated. In the models, the disease transmission coefficient and the removal rates are all affected by noise. Some new basic properties of the models are found. Applying these properties, we establish a series of new threshold conditions on the stochastically exponential extinction, stochastic persistence, and permanence in the mean of the disease with probability one for the models. Furthermore, we obtain a sufficient condition on the existence of unique stationary distribution for the model. Finally, a series of numerical examples are introduced to illustrate our main theoretical results and some conjectures are further proposed.

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43

Yang, Junyuan, Xiaoxia Li et Fengqin Zhang. « Global dynamics of a heroin epidemic model with age structure and nonlinear incidence ». International Journal of Biomathematics 09, n^o 03 (25 février 2016) : 1650033. http://dx.doi.org/10.1142/s1793524516500339.

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A heroin model with nonlinear incidence rate and age structure is investigated. The basic reproduction number is determined whether or not a heroin epidemic breaks out. By employing the Lyapunov functionals, the drug-free equilibrium is globally asymptotically stable if [Formula: see text]; while the drug spread equilibrium is also globally asymptotically stable if [Formula: see text]. Our results imply that improving detected rates and drawing up the efficient prevention play more important role than increasing the treatment for drug users.

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44

Zhang, Hong, Juan Xia et Paul Georgescu. « Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay ». Nonlinear Analysis : Modelling and Control 2017, n^o 1 (27 décembre 2016) : 64–83. http://dx.doi.org/10.15388/na.2017.1.5.

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45

Khan, Ihsan Ullah, Muhammad Qasim, Amine El Koufi et Hafiz Ullah. « The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates ». Mathematical Problems in Engineering 2022 (20 septembre 2022) : 1–10. http://dx.doi.org/10.1155/2022/6962160.

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In the present paper, the SIR model with nonlinear recovery and Monod type equation as incidence rates is proposed and analyzed. The expression for basic reproduction number is obtained which plays a main role in the stability of disease-free and endemic equilibria. The nonstandard finite difference (NSFD) scheme is constructed for the model and the denominator function is chosen such that the suggested scheme ensures solutions boundedness. It is shown that the NSFD scheme does not depend on the step size and gives better results in all respects. To prove the local stability of disease-free equilibrium point, the Jacobean method is used; however, Schur–Cohn conditions are applied to discuss the local stability of the endemic equilibrium point for the discrete NSFD scheme. The Enatsu criterion and Lyapunov function are employed to prove the global stability of disease-free and endemic equilibria. Numerical simulations are also presented to discuss the advantages of NSFD scheme as well as to strengthen the theoretical results. Numerical simulations specify that the NSFD scheme preserves the important properties of the continuous model. Consequently, they can produce estimates which are entirely according to the solutions of the model.

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46

Enatsu, Yoichi, Yukihiko Nakata, Yoshiaki Muroya, Giuseppe Izzo et Antonia Vecchio. « Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates ». Journal of Difference Equations and Applications 18, n^o 7 (juillet 2012) : 1163–81. http://dx.doi.org/10.1080/10236198.2011.555405.

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47

Li, Gui-Hua, et Yong-Xin Zhang. « Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates ». PLOS ONE 12, n^o 4 (20 avril 2017) : e0175789. http://dx.doi.org/10.1371/journal.pone.0175789.

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48

Enatsu, Yoichi, Yukihiko Nakata et Yoshiaki Muroya. « Global stability of sirs epidemic models with a class of nonlinear incidence rates and distributed delays ». Acta Mathematica Scientia 32, n^o 3 (mai 2012) : 851–65. http://dx.doi.org/10.1016/s0252-9602(12)60066-6.

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49

Enatsu, Yoichi, Eleonora Messina, Yukihiko Nakata, Yoshiaki Muroya, Elvira Russo et Antonia Vecchio. « Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates ». Journal of Applied Mathematics and Computing 39, n^o 1-2 (11 septembre 2011) : 15–34. http://dx.doi.org/10.1007/s12190-011-0507-y.

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50

Sun, Guiquan, Zhen Jin, Quan-Xing Liu et Li Li. « Pattern formation in a spatialS–Imodel with non-linear incidence rates ». Journal of Statistical Mechanics : Theory and Experiment 2007, n^o 11 (27 novembre 2007) : P11011. http://dx.doi.org/10.1088/1742-5468/2007/11/p11011.

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