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Journal articles on the topic 'NONLINEAR INCIDENCE RATES'

Author: Grafiati

Published: 11 September 2023

Last updated: 31 July 2025

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1

Liu, Wei-min, Herbert W. Hethcote, and Simon A. Levin. "Dynamical behavior of epidemiological models with nonlinear incidence rates." Journal of Mathematical Biology 25, no. 4 (1987): 359–80. http://dx.doi.org/10.1007/bf00277162.

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2

Hui, Jing, and Lansun Chen. "Impulsive vaccination of sir epidemic models with nonlinear incidence rates." Discrete & Continuous Dynamical Systems - B 4, no. 3 (2004): 595–605. http://dx.doi.org/10.3934/dcdsb.2004.4.595.

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3

Mukherjee, D., J. Chattopadhyay, and P. K. Tapaswi. "Global stability results of epidemiological models with nonlinear incidence rates." Mathematical and Computer Modelling 18, no. 2 (1993): 89–92. http://dx.doi.org/10.1016/0895-7177(93)90009-n.

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4

Ponciano, José M., and Marcos A. Capistrán. "First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics." PLoS Computational Biology 7, no. 2 (2011): e1001079. http://dx.doi.org/10.1371/journal.pcbi.1001079.

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5

Sachs, Dominik, Aleh Tsyvinski, and Nicolas Werquin. "Nonlinear Tax Incidence and Optimal Taxation in General Equilibrium." Econometrica 88, no. 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 increasi

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6

Rohith, G., and K. B. Devika. "Dynamics and control of COVID-19 pandemic with nonlinear incidence rates." Nonlinear Dynamics 101, no. 3 (2020): 2013–26. http://dx.doi.org/10.1007/s11071-020-05774-5.

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7

Liu, Yicheng, Yimin Du, and Jianhong Wu. "Backward/Hopf bifurcations in SIS models with delayed nonlinear incidence rates." Frontiers of Mathematics in China 3, no. 4 (2008): 535–53. http://dx.doi.org/10.1007/s11464-008-0040-y.

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8

Li, Li, Gui-Quan Sun, and Zhen Jin. "Bifurcation and chaos in an epidemic model with nonlinear incidence rates." Applied Mathematics and Computation 216, no. 4 (2010): 1226–34. http://dx.doi.org/10.1016/j.amc.2010.02.014.

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9

Yuan, Zhaohui, and Lin Wang. "Global stability of epidemiological models with group mixing and nonlinear incidence rates." Nonlinear Analysis: Real World Applications 11, no. 2 (2010): 995–1004. http://dx.doi.org/10.1016/j.nonrwa.2009.01.040.

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10

Lu, Zhonghua, Xianning Liu, and Lansun Chen. "Hopf bifurcation of nonlinear incidence rates SIR epidemiological models with stage structure." Communications in Nonlinear Science and Numerical Simulation 6, no. 4 (2001): 205–9. http://dx.doi.org/10.1016/s1007-5704(01)90015-2.

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11

Wang, Yi, and Jinde Cao. "Global stability of general cholera models with nonlinear incidence and removal rates." Journal of the Franklin Institute 352, no. 6 (2015): 2464–85. http://dx.doi.org/10.1016/j.jfranklin.2015.03.030.

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12

Sun, Chengjun, Yiping Lin, and Shoupeng Tang. "Global stability for an special SEIR epidemic model with nonlinear incidence rates." Chaos, Solitons & Fractals 33, no. 1 (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, and Parimita Roy. "Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates." Nonlinear Dynamics 96, no. 4 (2019): 2351–68. http://dx.doi.org/10.1007/s11071-019-04926-6.

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14

Liu, Wei-min, Simon A. Levin, and Yoh Iwasa. "Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models." Journal of Mathematical Biology 23, no. 2 (1986): 187–204. http://dx.doi.org/10.1007/bf00276956.

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15

Torku, Thomas, Abdul Khaliq, and Fathalla Rihan. "SEINN: A deep learning algorithm for the stochastic epidemic model." Mathematical Biosciences and Engineering 20, no. 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 center

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16

Li, Jun Hong, Ning Cui, and Hong Kai Sun. "Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate." Advanced Materials Research 479-481 (February 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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17

Alshammari, Fehaid Salem, and Muhammad Altaf Khan. "Dynamic behaviors of a modified SIR model with nonlinear incidence and recovery rates." Alexandria Engineering Journal 60, no. 3 (2021): 2997–3005. http://dx.doi.org/10.1016/j.aej.2021.01.023.

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18

Halder, Manisha, and 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, no. 5 (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

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19

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

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20

Wang, Feng, Shan Wang, and Youhua Peng. "Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations." Discrete Dynamics in Nature and Society 2020 (May 5, 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 illustr

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21

Lee, Kwang Sung, and Daewook Kim. "Global dynamics of a pine wilt disease transmission model with nonlinear incidence rates." Applied Mathematical Modelling 37, no. 6 (2013): 4561–69. http://dx.doi.org/10.1016/j.apm.2012.09.042.

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22

Sun, Ruoyan, and Junping Shi. "Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates." Applied Mathematics and Computation 218, no. 2 (2011): 280–86. http://dx.doi.org/10.1016/j.amc.2011.05.056.

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23

Kumar, Abhishek, and Nilam. "Mathematical analysis of a delayed epidemic model with nonlinear incidence and treatment rates." Journal of Engineering Mathematics 115, no. 1 (2019): 1–20. http://dx.doi.org/10.1007/s10665-019-09989-3.

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24

Zhao, Xiangming, and Jianping Shi. "Dynamic behavior of a stochastic SIR model with nonlinear incidence and recovery rates." AIMS Mathematics 8, no. 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 thr

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25

El Koufi, Amine, Jihad Adnani, Abdelkrim Bennar, and Noura Yousfi. "Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate." International Journal of Differential Equations 2019 (August 21, 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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26

Chinyoka, Mirirai, Tinashe B. Gashirai, and Steady Mushayabasa. "On the Dynamics of a Fractional-Order Ebola Epidemic Model with Nonlinear Incidence Rates." Discrete Dynamics in Nature and Society 2021 (December 3, 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 r

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27

Han, Ping, Zhengbo Chang, and Xinzhu Meng. "Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates." Complexity 2020 (May 8, 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 il

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28

Muroya, Yoshiaki, Yoichi Enatsu, and Yukihiko Nakata. "Monotone iterative techniques to SIRS epidemic models with nonlinear incidence rates and distributed delays." Nonlinear Analysis: Real World Applications 12, no. 4 (2011): 1897–910. http://dx.doi.org/10.1016/j.nonrwa.2010.12.002.

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29

Elaiw, A. M., and N. H. AlShamrani. "Dynamics of viral infection models with antibodies and general nonlinear incidence and neutralize rates." International Journal of Dynamics and Control 4, no. 3 (2015): 303–17. http://dx.doi.org/10.1007/s40435-015-0181-2.

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30

Soufiane, Bentout, and Tarik Mohammed Touaoula. "Global analysis of an infection age model with a class of nonlinear incidence rates." Journal of Mathematical Analysis and Applications 434, no. 2 (2016): 1211–39. http://dx.doi.org/10.1016/j.jmaa.2015.09.066.

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31

Chen, Hao, and Jitao Sun. "Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates." Applied Mathematics and Computation 218, no. 8 (2011): 4391–400. http://dx.doi.org/10.1016/j.amc.2011.10.015.

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32

Enatsu, Yoichi, Eleonora Messina, Yoshiaki Muroya, Yukihiko Nakata, Elvira Russo, and Antonia Vecchio. "Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates." Applied Mathematics and Computation 218, no. 9 (2012): 5327–36. http://dx.doi.org/10.1016/j.amc.2011.11.016.

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33

Saidi, Nabil, and Atika Radid. "Dynamics of a fractional order SEIRS epidemic model with vaccination and nonlinear incidence rates." Scientific African 29 (September 2025): e02825. https://doi.org/10.1016/j.sciaf.2025.e02825.

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34

Lv, Wei, Xue-Ying Liu, Xin-Jian Xu, and Jie Lou. "Vaccination of a multi-group model of zoonotic diseases with direct and indirect transmission." International Journal of Biomathematics 12, no. 06 (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 op

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35

STRUCHINER, CLAUDIO J., ROBERT C. BRUNET, M. ELIZABETH HALLORAN, EDUARDO MASSAD, and RAYMUNDO S. AZEVEDO-NETO. "ON THE USE OF STATE-SPACE MODELS FOR THE EVALUATION OF HEALTH INTERVENTIONS." Journal of Biological Systems 03, no. 03 (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 ra

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36

Li, Junhong, and 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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37

Zhang, Ling, Jingmei Pang, and 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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38

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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39

El Koufi, Amine. "Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process." Complexity 2022 (April 22, 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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40

Jin, Li, Yunxian Dai, Yu Xiao, and Yiping Lin. "RANK-ONE CHAOS IN A DELAYED SIR EPIDEMIC MODEL WITH NONLINEAR INCIDENCE AND TREATMENT RATES." Journal of Applied Analysis & Computation 11, no. 4 (2021): 1779–801. http://dx.doi.org/10.11948/20200190.

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41

Wang, Jinliang, and Xianning Liu. "Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model." Mathematical Methods in the Applied Sciences 39, no. 8 (2015): 1964–76. http://dx.doi.org/10.1002/mma.3613.

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42

Zhang, Hong, Juan Xia, and Paul Georgescu. "Multigroup deterministic and stochasticSEIRIepidemic models with nonlinear incidence rates and distributed delays: A stability analysis." Mathematical Methods in the Applied Sciences 40, no. 18 (2017): 6254–75. http://dx.doi.org/10.1002/mma.4453.

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43

Singh, Manoj Kumar, Anjali., Brajesh K. Singh, and Carlo Cattani. "Impact of general incidence function on three-strain SEIAR model." Mathematical Biosciences and Engineering 20, no. 11 (2023): 19710–31. http://dx.doi.org/10.3934/mbe.2023873.

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<abstract><p>We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and recovered compartments. The model is well-posed and verified through existence, positivity and boundedness. Eight equilibria comprise a disease-free equilibria and seven endemic equilibrium points following the existence of thre

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44

Wang, Lei, Zhidong Teng, Tingting Tang, and 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 dis

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45

Yang, Junyuan, Xiaoxia Li, and Fengqin Zhang. "Global dynamics of a heroin epidemic model with age structure and nonlinear incidence." International Journal of Biomathematics 09, no. 03 (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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46

Lahrouz, Aadil. "Dynamics of a delayed epidemic model with varying immunity period and nonlinear transmission." International Journal of Biomathematics 08, no. 02 (2015): 1550027. http://dx.doi.org/10.1142/s1793524515500278.

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An epidemic model with a class of nonlinear incidence rates and distributed delay is analyzed. The nonlinear incidence is used to describe the saturated or the psychological effect of certain serious epidemics on the community when the number of infectives is getting larger. The distributed delay is derived to describe the dynamics of infectious diseases with varying immunity. Lyapunov functionals are used to show that the disease-free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one. Moreover, it is shown that the disease is p

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47

Zhang, Hong, Juan Xia, and Paul Georgescu. "Stability analyses of deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delay." Nonlinear Analysis: Modelling and Control 2017, no. 1 (2016): 64–83. http://dx.doi.org/10.15388/na.2017.1.5.

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48

Khan, Ihsan Ullah, Muhammad Qasim, Amine El Koufi, and Hafiz Ullah. "The Stability Analysis and Transmission Dynamics of the SIR Model with Nonlinear Recovery and Incidence Rates." Mathematical Problems in Engineering 2022 (September 20, 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 eq

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49

Enatsu, Yoichi, Yukihiko Nakata, Yoshiaki Muroya, Giuseppe Izzo, and 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, no. 7 (2012): 1163–81. http://dx.doi.org/10.1080/10236198.2011.555405.

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50

Li, Gui-Hua, and Yong-Xin Zhang. "Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates." PLOS ONE 12, no. 4 (2017): e0175789. http://dx.doi.org/10.1371/journal.pone.0175789.

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