Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 7: Analysis and Applications of PDEs in Biomathematics
Submit an article Journal homepage
1,730
Views
228
CrossRef citations to date
0
Altmetric
Original Articles

Lyapunov functional and global asymptotic stability for an infection-age model

P. Magal Department of Mathematics, University of Le Havre, 25 rue Philippe Lebon, 76058 Le Havre Cedex, France
,
C.C. McCluskey Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, CanadaCorrespondence[email protected]
&
G.F. Webb Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA
Pages 1109-1140 | Received 05 Mar 2009, Accepted 04 Jul 2009, Published online: 12 Feb 2010

Citations (228)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (18)

Cyrille Kenne, Pascal Zongo & René Dorville. (2022) A mathematical model for tilapia lake virus transmission with waning immunity. Journal of Biological Dynamics 16:1, pages 98-116.
Read now
Abdennasser Chekroun & Toshikazu Kuniya. (2020) An infection age-space structured SIR epidemic model with Neumann boundary condition. Applicable Analysis 99:11, pages 1972-1985.
Read now
Maia Martcheva & Hisashi Inaba. (2020) A Lyapunov–Schmidt method for detecting backward bifurcation in age-structured population models. Journal of Biological Dynamics 14:1, pages 543-565.
Read now
Xia Wang, Yuming Chen, Maia Martcheva & Libin Rong. (2020) Asymptotic analysis of a vector-borne disease model with the age of infection. Journal of Biological Dynamics 14:1, pages 332-367.
Read now
Rui Xu, Junyuan Yang, Xiaohong Tian & Jiazhe Lin. (2019) Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection. Journal of Biological Dynamics 13:1, pages 675-705.
Read now
J. Wang, M. Guo & T. Kuniya. (2018) Mathematical analysis for a multi-group SEIR epidemic model with age-dependent relapse. Applicable Analysis 97:10, pages 1751-1770.
Read now
Jinliang Wang, Di Wu & Hongquan Sun. (2018) Analysis of an SVIC model with age-dependent infection and asymptomatic carriers. Applicable Analysis 97:9, pages 1467-1495.
Read now
Junyuan Yang & Yuming Chen. (2018) Theoretical and numerical results for an age-structured SIVS model with a general nonlinear incidence rate. Journal of Biological Dynamics 12:1, pages 789-816.
Read now
Rui Xu. (2018) Global dynamics of an epidemiological model with age of infection and disease relapse. Journal of Biological Dynamics 12:1, pages 118-145.
Read now
Toshikazu Kuniya & Jinliang Wang. (2017) Lyapunov functions and global stability for a spatially diffusive SIR epidemic model. Applicable Analysis 96:11, pages 1935-1960.
Read now
Jinliang Wang, Jiying Lang & Yuming Chen. (2017) Global threshold dynamics of an SVIR model with age-dependent infection and relapse. Journal of Biological Dynamics 11:sup2, pages 427-454.
Read now
Leonid Shaikhet & Andrei Korobeinikov. (2016) Stability of a stochastic model for HIV-1 dynamics within a host. Applicable Analysis 95:6, pages 1228-1238.
Read now
Yan-Xia Dang, Xue-Zhi Li & Maia Martcheva. (2016) Competitive exclusion in a multi-strain immuno-epidemiological influenza model with environmental transmission. Journal of Biological Dynamics 10:1, pages 416-456.
Read now
Junyuan Yang, Maia Martcheva & Yuming Chen. (2016) Imitation dynamics of vaccine decision-making behaviours based on the game theory. Journal of Biological Dynamics 10:1, pages 31-58.
Read now
Jinliang Wang, Ran Zhang & Toshikazu Kuniya. (2015) The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes. Journal of Biological Dynamics 9:1, pages 73-101.
Read now
Li-Ming Cai, Maia Martcheva & Xue-Zhi Li. (2013) Competitive exclusion in a vector–host epidemic model with distributed delay†. Journal of Biological Dynamics 7:sup1, pages 47-67.
Read now
Constantinos I. Siettos & Lucia Russo. (2013) Mathematical modeling of infectious disease dynamics. Virulence 4:4, pages 295-306.
Read now
D. Breda, O. Diekmann, W. F. de Graaf, A. Pugliese & R. Vermiglio. (2012) On the formulation of epidemic models (an appraisal of Kermack and McKendrick). Journal of Biological Dynamics 6:sup2, pages 103-117.
Read now

Articles from other publishers (210)

Juping Zhang, Linlin Wang & Zhen Jin. (2024) Global stability for age-infection-structured human immunodeficiency virus model with heterogeneous transmission. Infectious Disease Modelling 9:2, pages 437-457.
Crossref
Abderrazak NABTi. (2024) Dynamical analysis of an age-structured SEIR model with relapse. Zeitschrift für angewandte Mathematik und Physik 75:3.
Crossref
Renhu Wang & Xuezhong Wang. (2023) Spatial dynamics of a reaction–diffusion SIS epidemic model with mass-action-type nonlinearity. International Journal of Biomathematics 17:04.
Crossref
Shuanglin Jing, Ling Xue, Hao Wang & Zhihang Peng. (2024) Global analysis of an age-structured tuberculosis model with an application to Jiangsu, China. Journal of Mathematical Biology 88:5.
Crossref
Peng Wu & Zhaosheng Feng. (2024) Global dynamics of a space-age structured covid-19 model coupling within-host infection and between-host transmission. Communications in Nonlinear Science and Numerical Simulation 131, pages 107801.
Crossref
Yi Chen, Lianwen Wang & Jinhui Zhang. (2024) Global asymptotic stability of an age-structured tuberculosis model: An analytical method to determine kernel coefficients in Lyapunov functional. Chaos, Solitons & Fractals 181, pages 114649.
Crossref
Hongying Shu, Hai-Yang Jin, Xiang-Sheng Wang & Jianhong Wu. (2024) Viral infection dynamics with immune chemokines and CTL mobility modulated by the infected cell density. Journal of Mathematical Biology 88:4.
Crossref
Xinxin Cheng, Yi Wang & Gang Huang. (2024) Dynamical analysis of an age-structured cholera transmission model on complex networks. Journal of Mathematical Analysis and Applications 531:2, pages 127833.
Crossref
Mostafa Adimy, Abdennasser Chekroun, Charlotte Dugourd-Camus & Hanene Meghelli. (2023) Global Asymptotic Stability of a Hybrid Differential–Difference System Describing SIR and SIS Epidemic Models with a Protection Phase and a Nonlinear Force of Infection. Qualitative Theory of Dynamical Systems 23:1.
Crossref
Dandan Sun, Zhidong Teng, Kai Wang & Tailei Zhang. (2024) Stability and Hopf bifurcation for age-structured SVIR epidemic model with different compartment ages and two delays effects. Journal of the Franklin Institute 361:2, pages 867-898.
Crossref
Dongxue Yan & Yu Cao. (2023) Rich dynamics of a delayed SIRS epidemic model with two-age structure and logistic growth. Advances in Continuous and Discrete Models 2023:1.
Crossref
Jin Yang, Zhuo Chen, Yuanshun Tan, Zijian Liu & Robert A. Cheke. (2023) Threshold dynamics of an age-structured infectious disease model with limited medical resources. Mathematics and Computers in Simulation 214, pages 114-132.
Crossref
Zhaohai Ma & Pierre Magal. (2023) Global asymptotic stability for Gurtin-MacCamy’s population dynamics model. Proceedings of the American Mathematical Society.
Crossref
Jianquan Li, Yijun Lou, Peijun Zhang & Yao Chen. (2023) An analytical approach to determining the coefficients in Lyapunov direct method: With application to an age-structured epidemiological model. Communications in Nonlinear Science and Numerical Simulation 126, pages 107419.
Crossref
Riya Das, Dhiraj Kumar Das & Tapan Kumar Kar. (2023) Qualitative analysis of TB transmission dynamics considering both the age since latency and relapse. Mathematics and Computers in Simulation.
Crossref
Salih Djilali, Soufiane Bentout, Tarik Mohamed Touaoula & Abdon Atangana. (2023) Threshold dynamics for an age‐structured heroin epidemic model with distributed delays. Mathematical Methods in the Applied Sciences 46:13, pages 13595-13619.
Crossref
Jinliang Wang, Ran Zhang & Yue Gao. (2021) Global Threshold Dynamics of an Infection Age-Space Structured HIV Infection Model with Neumann Boundary Condition. Journal of Dynamics and Differential Equations 35:3, pages 2279-2311.
Crossref
Yanshu Wang & Hailiang Zhang. (2023) Dynamical Analysis of an Age-Structured SVEIR Model with Imperfect Vaccine. Mathematics 11:16, pages 3526.
Crossref
Ismail Shah, Eiman, Hussam Alrabaiah, Burhanettin Ozdemir & Ateeq ur Rehman Irshad. (2023) Using advanced analysis together with fractional order derivative to investigate a smoking tobacco cancer model. Results in Physics 51, pages 106700.
Crossref
Jiawei Huo, Qiang Huo & Rong Yuan. (2023) Threshold Dynamics for Infection Age-Structured Epidemic Models with Spatial Diffusion and Degenerate Diffusion. Journal of Dynamics and Differential Equations.
Crossref
Jinxian Li, Hairong Yan & Zhen Jin. (2023) SIR dynamics with infection age in complex heterogeneous networks. Communications in Nonlinear Science and Numerical Simulation 121, pages 107183.
Crossref
Fatima Zohra Hathout, Tarik Mohammed Touaoula & Salih Djilali. (2023) Efficiency of Protection in the Presence of Immigration Process for an Age-Structured Epidemiological Model. Acta Applicandae Mathematicae 185:1.
Crossref
Soufiane Bentout, Salih Djilali, Toshikazu Kuniya & Jinliang Wang. (2023) Mathematical analysis of a vaccination epidemic model with nonlocal diffusion. Mathematical Methods in the Applied Sciences 46:9, pages 10970-10994.
Crossref
Xiaogang Liu, Yuming Chen, Xiaomin Li & Jianquan Li. (2023) Global stability of latency-age/stage-structured epidemic models with differential infectivity. Journal of Mathematical Biology 86:5.
Crossref
Salih Djilali, Yuming Chen & Soufiane Bentout. (2022) Asymptotic analysis of SIR epidemic model with nonlocal diffusion and generalized nonlinear incidence functional. Mathematical Methods in the Applied Sciences 46:5, pages 6279-6301.
Crossref
Shuxing Cao, Zhijie Chen & Zhanwen Yang. (2023) Numerical representations of global epidemic threshold for nonlinear infection-age SIR models. Mathematics and Computers in Simulation 204, pages 115-132.
Crossref
Bian Wang, Xiaohong Tian, Rui Xu & Chenwei Song. (2022) Threshold dynamics and optimal control of a dengue epidemic model with time delay and saturated incidence. Journal of Applied Mathematics and Computing 69:1, pages 871-893.
Crossref
Dongxue Yan, Mengqi Zhang & Jiashan Tang. (2023) The Global Dynamics of an Age-Structured Hand-Foot-Mouth Disease Model with Saturation Incidence and Time Delay. Discrete Dynamics in Nature and Society 2023, pages 1-21.
Crossref
Toshikazu Kuniya & Hisashi Inaba. (2023) Hopf bifurcation in a chronological age-structured SIR epidemic model with age-dependent infectivity. Mathematical Biosciences and Engineering 20:7, pages 13036-13060.
Crossref
. (2023) Stability and Hopf bifurcation in an age-structured SIR epidemic model with relapse. Discrete and Continuous Dynamical Systems - B 28:3, pages 1643-1672.
Crossref
Huizi Yang, Zhanwen Yang & Shengqiang Liu. (2023) Numerical threshold of linearly implicit Euler method for nonlinear infection-age SIR models. Discrete and Continuous Dynamical Systems - B 28:1, pages 70.
Crossref
Xin Jiang & Ran Zhang. (2023) Global dynamics on a class of age-infection structured cholera model with immigration. Electronic Journal of Qualitative Theory of Differential Equations:6, pages 1-26.
Crossref
Charles Roberto Telles & Archisman Roy. 2023. Pervasive Computing and Social Networking. Pervasive Computing and Social Networking 685 696 .
Ruili Fan & Stefan A.H. Geritz. (2022) Modelling and optimising healthcare interventions in a model with explicit within- and between-host dynamics. Journal of Theoretical Biology 554, pages 111276.
Crossref
Peng Wu, Zhaosheng Feng & Xuebing Zhang. (2022) Global dynamics of an age–space structured HIV/AIDS model with viral load-dependent infection and conversion rates. Journal of Computational and Applied Mathematics 412, pages 114309.
Crossref
Siwaphorn Kanchanarat, Settapat Chinviriyasit & Wirawan Chinviriyasit. (2022) Mathematical Assessment of the Impact of the Imperfect Vaccination on Diphtheria Transmission Dynamics. Symmetry 14:10, pages 2000.
Crossref
Yuqiong Lan, Yanqiu Li & Dongmei Zheng. (2022) Global dynamics of an age-dependent multiscale hepatitis C virus model. Journal of Mathematical Biology 85:3.
Crossref
Chao Liu, Peng Chen, Qiyu Jia & Lora Cheung. (2022) Effects of Media Coverage on Global Stability Analysis and Optimal Control of an Age-Structured Epidemic Model with Multi-Staged Progression. Mathematics 10:15, pages 2712.
Crossref
Haifeng Wang & Xiaohong Tian. (2022) Asymptotic Properties and Stability Switch of a Delayed-Within-Host-Dengue Infection Model with Mitosis and Immune Response. International Journal of Bifurcation and Chaos 32:08.
Crossref
Ferdinand Pfab, Roger M. Nisbet & Cheryl J. Briggs. (2022) A time-since-infection model for populations with two pathogens. Theoretical Population Biology 144, pages 1-12.
Crossref
Xiao-mei Feng, Li-li Liu & Feng-qin Zhang. (2022) Dynamical Behavior of SEIR-SVS Epidemic Models with Nonlinear Incidence and Vaccination. Acta Mathematicae Applicatae Sinica, English Series 38:2, pages 282-303.
Crossref
Cruz Vargas‐De‐León. (2021) Global stability of nonhomogeneous coexisting equilibrium state for the multispecies Lotka–Volterra mutualism models with diffusion. Mathematical Methods in the Applied Sciences 45:4, pages 2123-2131.
Crossref
V. Skakauskas. (2022) The Kermack-McKendrick epidemic model with variable infectivity modified. Journal of Mathematical Analysis and Applications 507:2, pages 125817.
Crossref
Cyrille Kenne, Gisèle Mophou, René Dorville & Pascal Zongo. (2022) A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity. Mathematics 10:4, pages 670.
Crossref
Jingjing Lu, Qiaoling Chen, Zhidong Teng & Tingting Zheng. (2021) Dynamical analysis of an age‐structured SIRE epidemic model with two routes of infection in environment. Studies in Applied Mathematics 148:2, pages 461-497.
Crossref
Fatima Zohra Hathout, Tarik Mohammed Touaoula & Salih Djilali. (2022) Mathematical analysis of a triple age dependent epidemiological model with including a protection strategy. Discrete and Continuous Dynamical Systems - B 27:12, pages 7409.
Crossref
Zhong-Kai Guo, Hai-Feng Huo & Hong Xiang. (2022) Analysis of an age-structured model for HIV-TB co-infection. Discrete & Continuous Dynamical Systems - B 27:1, pages 199.
Crossref
Dandan Sun, Yingke Li, Zhidong Teng, Tailei Zhang & Jingjing Lu. (2021) Dynamical properties in an SVEIR epidemic model with age‐dependent vaccination, latency, infection, and relapse. Mathematical Methods in the Applied Sciences 44:17, pages 12810-12834.
Crossref
Xin Jiang. (2021) Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates. Mathematics 9:23, pages 2993.
Crossref
Xue-Zhi Li, Shasha Gao, Yi-Ke Fu & Maia Martcheva. (2021) Modeling and Research on an Immuno-Epidemiological Coupled System with Coinfection. Bulletin of Mathematical Biology 83:11.
Crossref
Vijay Pal Bajiya, Jai Prakash Tripathi, Vipul Kakkar, Jinshan Wang & Guiquan Sun. (2021) Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age. Chinese Annals of Mathematics, Series B 42:6, pages 833-860.
Crossref
Yunfei Lv, Yongzhen Pei & Rong Yuan. (2021) On a periodic age-structured mosquito population model with spatial structure. Nonlinear Analysis: Real World Applications 61, pages 103337.
Crossref
Toshikazu Kuniya. (2021) Structure of epidemic models: toward further applications in economics. The Japanese Economic Review 72:4, pages 581-607.
Crossref
Lili Liu, Jian Zhang, Ran Zhang & Hongquan Sun. (2021) Hopf Bifurcation of an Age-Structured Epidemic Model with Quarantine and Temporary Immunity Effects. International Journal of Bifurcation and Chaos 31:12, pages 2150183.
Crossref
Suxia Zhang, Yanna Liu & Hui Cao. (2021) Bifurcation analysis of an age‐structured epidemic model with two staged‐progressions. Mathematical Methods in the Applied Sciences 44:14, pages 11482-11497.
Crossref
Huaixing Li & Jiaoyan Wang. (2021) Global Dynamics of an SEIR Model with the Age of Infection and Vaccination. Mathematics 9:18, pages 2195.
Crossref
Sheng-Fu Wang, Lin Hu & Lin-Fei Nie. (2021) Global dynamics and optimal control of an age-structure Malaria transmission model with vaccination and relapse. Chaos, Solitons & Fractals 150, pages 111216.
Crossref
Cyrille Kenne, René Dorville, Gisèle Mophou & Pascal Zongo. (2021) An Age-Structured Model for Tilapia Lake Virus Transmission in Freshwater with Vertical and Horizontal Transmission. Bulletin of Mathematical Biology 83:8.
Crossref
Teddy Lazebnik, Svetlana Bunimovich-Mendrazitsky & Leonid Shaikhet. (2021) Novel Method to Analytically Obtain the Asymptotic Stable Equilibria States of Extended SIR-Type Epidemiological Models. Symmetry 13:7, pages 1120.
Crossref
Soufiane Bentout, Salih Djilali, Sunil Kumar & Tarik Mohammed Touaoula. (2021) Threshold dynamics of difference equations for SEIR model with nonlinear incidence function and infinite delay. The European Physical Journal Plus 136:5.
Crossref
Chunmei Shi. (2021) The convergence and stability of full discretization scheme for stochastic age-structured population models. Applied Mathematics and Computation 396, pages 125867.
Crossref
Sanhong Liu & Ran Zhang. (2020) On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids. Bulletin of the Malaysian Mathematical Sciences Society 44:3, pages 1345-1370.
Crossref
Soufiane Bentout, Salih Djilali & Abdenasser Chekroun. (2021) Global threshold dynamics of an age structured alcoholism model. International Journal of Biomathematics 14:03.
Crossref
Jin-Fu Chen, Yi-Mu Du, Hui Dong & C P Sun. (2021) Hierarchical coarse-grained approach to the duration-dependent spreading dynamics on complex networks. Journal of Physics: Complexity 2:2, pages 02LT01.
Crossref
Soufiane Bentout, Abdessamad Tridane, Salih Djilali & Tarik Mohammed Touaoula. (2021) Age-Structured Modeling of COVID-19 Epidemic in the USA, UAE and Algeria. Alexandria Engineering Journal 60:1, pages 401-411.
Crossref
Soufiane Bentout, Yuming Chen & Salih Djilali. (2020) Global Dynamics of an SEIR Model with Two Age Structures and a Nonlinear Incidence. Acta Applicandae Mathematicae 171:1.
Crossref
Kento Okuwa, Hisashi Inaba & Toshikazu Kuniya. (2021) An age-structured epidemic model with boosting and waning of immune status. Mathematical Biosciences and Engineering 18:5, pages 5707-5736.
Crossref
Zakya Sari, Tarik Mohammed Touaoula & Bedreddine Ainseba. (2021) Mathematical analysis of an age structured epidemic model with a quarantine class. Mathematical Modelling of Natural Phenomena 16, pages 57.
Crossref
Mboya Ba, Ramsès Djidjou-Demasse, Mountaga Lam & Jean-Jules Tewa. (2021) Optimal intervention strategies of staged progression HIV infections through an age-structured model with probabilities of ART drop out. Mathematical Modelling of Natural Phenomena 16, pages 30.
Crossref
Necibe Tuncer & Sunil Giri. (2021) Dynamics of a Vector-Borne model with direct transmission and age of infection. Mathematical Modelling of Natural Phenomena 16, pages 28.
Crossref
Menggen Chen & Moshu Xu. 2021. Computing and Data Science. Computing and Data Science 185 192 .
Dongxue Yan, Hui Cao & Suxia Zhang. (2020) Global dynamics for a TB transmission model with age-structure and delay. International Journal of Biomathematics 13:07, pages 2050055.
Crossref
Abdennasser Chekroun & Toshikazu Kuniya. (2020) Global threshold dynamics of an infection age-structured SIR epidemic model with diffusion under the Dirichlet boundary condition. Journal of Differential Equations 269:8, pages 117-148.
Crossref
Jingjing Lu, Zhidong Teng & Yingke Li. (2020) An age-structured model for coupling within-host and between-host dynamics in environmentally-driven infectious diseases. Chaos, Solitons & Fractals 139, pages 110024.
Crossref
Liming Cai, Zhaoqing Li, Chayu Yang & Jin Wang. (2020) Global analysis of an environmental disease transmission model linking within-host and between-host dynamics. Applied Mathematical Modelling 86, pages 404-423.
Crossref
Zijian Liu, Chunfang Guo, Jin Yang & Hong Li. (2020) Steady States Analysis of a Nonlinear Age-Structured Tumor Cell Population Model with Quiescence and Bidirectional Transition. Acta Applicandae Mathematicae 169:1, pages 455-474.
Crossref
Chunyang Qin, Xia Wang & Libin Rong. (2020) An Age-Structured Model of HIV Latent Infection with Two Transmission Routes: Analysis and Optimal Control. Complexity 2020, pages 1-22.
Crossref
Suxia Zhang, Fei Li & Xiaxia Xu. (2020) Dynamics of an infection-age model with staged-progression. Journal of Physics: Conference Series 1592:1, pages 012069.
Crossref
Liming Cai, Gaoxu Fan, Chayu Yang & Jin Wang. (2020) Modeling and analyzing cholera transmission dynamics with vaccination age. Journal of the Franklin Institute 357:12, pages 8008-8034.
Crossref
Shengfu Wang & Lin-Fei Nie. (2020) Global Dynamics for a Vector-Borne Disease Model with Class-Age-Dependent Vaccination, Latency and General Incidence Rate. Qualitative Theory of Dynamical Systems 19:2.
Crossref
Xi-Chao Duan, I Hyo Jung, Xue-Zhi Li & Maia Martcheva. (2020) Dynamics and optimal control of an age-structured SIRVS epidemic model. Mathematical Methods in the Applied Sciences 43:7, pages 4239-4256.
Crossref
W. S. Hart, P. K. Maini, C. A. Yates & R. N. Thompson. (2020) A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics: influenza A as a case study. Journal of The Royal Society Interface 17:166, pages 20200230.
Crossref
Xiangming Zhang & Zhihua Liu. (2019) Hopf Bifurcation for a Susceptible-Infective Model with Infection-Age Structure. Journal of Nonlinear Science 30:1, pages 317-367.
Crossref
Soufiane Bentout, Abdennasser Chekroun & Toshikazu Kuniya. (2020) Parameter estimation and prediction for coronavirus disease outbreak 2019 (COVID-19) in Algeria. AIMS Public Health 7:2, pages 306-318.
Crossref
Antoine Perasso & Quentin Richard. (2020) Asymptotic Behavior of Age-Structured and Delayed Lotka--Volterra Models. SIAM Journal on Mathematical Analysis 52:5, pages 4284-4313.
Crossref
Quentin Richard. (2020) Global stability in a competitive infection-age structured model. Mathematical Modelling of Natural Phenomena 15, pages 54.
Crossref
Simran K. Sandhu, Andrew Yu. Morozov & József Z. Farkas. (2019) Modelling evolution of virulence in populations with a distributed parasite load. Journal of Mathematical Biology 80:1-2, pages 111-141.
Crossref
Yan-Xia Dang, Juan Wang, Xue-Zhi Li & Mini Ghosh. 2020. Mathematical Analysis and Applications in Modeling. Mathematical Analysis and Applications in Modeling 403 447 .
Xue-Zhi Li, Junyuan Yang & Maia MartchevaXue-Zhi Li, Junyuan Yang & Maia Martcheva. 2020. Age Structured Epidemic Modeling. Age Structured Epidemic Modeling 301 359 .
Xue-Zhi Li, Junyuan Yang & Maia MartchevaXue-Zhi Li, Junyuan Yang & Maia Martcheva. 2020. Age Structured Epidemic Modeling. Age Structured Epidemic Modeling 211 257 .
Xue-Zhi Li, Junyuan Yang & Maia MartchevaXue-Zhi Li, Junyuan Yang & Maia Martcheva. 2020. Age Structured Epidemic Modeling. Age Structured Epidemic Modeling 153 209 .
Xue-Zhi Li, Junyuan Yang & Maia MartchevaXue-Zhi Li, Junyuan Yang & Maia Martcheva. 2020. Age Structured Epidemic Modeling. Age Structured Epidemic Modeling 105 151 .
RUI XU, NING BAI & XIAOHONG TIAN. (2019) GLOBAL DYNAMICS OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH AGE-DEPENDENT LATENCY AND ACTIVE INFECTION. Journal of Biological Systems 27:04, pages 503-530.
Crossref
Pierre Magal, Ousmane Seydi & Feng-Bin Wang. (2019) Monotone abstract non-densely defined Cauchy problems applied to age structured population dynamic models. Journal of Mathematical Analysis and Applications 479:1, pages 450-481.
Crossref
Dongxue Yan & Hui Cao. (2019) The global dynamics for an age-structured tuberculosis transmission model with the exponential progression rate. Applied Mathematical Modelling 75, pages 769-786.
Crossref
Yu Yang, Jinling Zhou & Cheng-Hsiung Hsu. (2019) Threshold dynamics of a diffusive SIRI model with nonlinear incidence rate. Journal of Mathematical Analysis and Applications 478:2, pages 874-896.
Crossref
Hai-Feng Huo, Peng Yang & Hong Xiang. (2019) Dynamics for an SIRS epidemic model with infection age and relapse on a scale-free network. Journal of the Franklin Institute 356:13, pages 7411-7443.
Crossref
Xia Wang, Yuming Chen & Xinyu Song. (2019) Global dynamics of a cholera model with age structures and multiple transmission modes. International Journal of Biomathematics 12:05, pages 1950051.
Crossref
Jianhua Pang, Jing Chen, Zijian Liu, Ping Bi & Shigui Ruan. (2018) Local and Global Stabilities of a Viral Dynamics Model with Infection-Age and Immune Response. Journal of Dynamics and Differential Equations 31:2, pages 793-813.
Crossref
Kosaku Kitagawa, Toshikazu Kuniya, Shinji Nakaoka, Yusuke Asai, Koichi Watashi & Shingo Iwami. (2019) Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection. Bulletin of Mathematical Biology 81:5, pages 1427-1441.
Crossref
Michael T. Meehan, Daniel G. Cocks, Johannes Müller & Emma S. McBryde. (2019) Global stability properties of a class of renewal epidemic models. Journal of Mathematical Biology 78:6, pages 1713-1725.
Crossref
Xamxinur Abdurahman, Zhidong Teng & Ling Zhang. (2019) Global dynamics in a heroin epidemic model with different conscious stages and two distributed delays. International Journal of Biomathematics 12:03, pages 1950038.
Crossref
Mingwang Shen, Yanni Xiao, Libin Rong & Lauren Ancel Meyers. (2019) Conflict and accord of optimal treatment strategies for HIV infection within and between hosts. Mathematical Biosciences 309, pages 107-117.
Crossref
Tsuyoshi Kajiwara, Toru Sasaki & Yoji Otani. (2018) Global stability of an age-structured model for pathogen–immune interaction. Journal of Applied Mathematics and Computing 59:1-2, pages 631-660.
Crossref
Ran Zhang, Dan Li & Shengqiang Liu. (2019) GLOBAL ANALYSIS OF AN AGE-STRUCTURED SEIR MODEL WITH IMMIGRATION OF POPULATION AND NONLINEAR INCIDENCE RATE. Journal of Applied Analysis & Computation 9:4, pages 1470-1492.
Crossref
Liming Cai, Jinliang Liu, Gaoxu Fan & Huidong Chen. (2019) GLOBAL DYNAMICS OF A CHOLERA MODEL WITH AGE-OF-IMMUNITY STRUCTURE AND REINFECTION. Journal of Applied Analysis & Computation 9:5, pages 1731-1749.
Crossref
Abdennasser Chekroun & Toshikazu Kuniya. (2019) An infection age-space-structured SIR epidemic model with Dirichlet boundary condition. Mathematical Modelling of Natural Phenomena 14:5, pages 505.
Crossref
Yuji Li, Rui Xu & Jiazhe Lin. (2018) Global dynamics for a class of infection-age model with nonlinear incidence. Nonlinear Analysis: Modelling and Control 24:1, pages 47-72.
Crossref
Yuji Li, Rui Xu & Jiazhe Lin. (2018) The stability analysis of an epidemic model with saturating incidence and age-structure in the exposed and infectious classes. Advances in Difference Equations 2018:1.
Crossref
Xiaoyan Wang, Junyuan Yang & Fei Xu. (2018) Analysis and control of an age-structured HIV-1 epidemic model with different transmission mechanisms. Advances in Difference Equations 2018:1.
Crossref
Zhipeng Qiu, Michael Y. Li & Zhongwei Shen. (2018) Global dynamics of an infinite dimensional epidemic model with nonlocal state structures. Journal of Differential Equations 265:10, pages 5262-5296.
Crossref
Suxia Zhang & Hongbin Guo. (2018) Global analysis of age-structured multi-stage epidemic models for infectious diseases. Applied Mathematics and Computation 337, pages 214-233.
Crossref
Junyuan Yang & Xiaoyan Wang. (2018) Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility. Complexity 2018, pages 1-15.
Crossref
Ghaus ur Rahman, Ravi P. Agarwal, Lili Liu & Asaf Khan. (2018) Threshold dynamics and optimal control of an age-structured giving up smoking model. Nonlinear Analysis: Real World Applications 43, pages 96-120.
Crossref
Mohamed Nor Frioui, Sofiane El-hadi Miri & Tarik Mohamed Touaoula. (2017) Unified Lyapunov functional for an age-structured virus model with very general nonlinear infection response. Journal of Applied Mathematics and Computing 58:1-2, pages 47-73.
Crossref
Junyuan Yang & Fei Xu. (2018) Global stability of two SIS epidemic mean-field models on complex networks: Lyapunov functional approach. Journal of the Franklin Institute 355:14, pages 6763-6779.
Crossref
Xia Wang, Yuming Chen & Shengqiang Liu. (2017) Global dynamics of a vector-borne disease model with infection ages and general incidence rates. Computational and Applied Mathematics 37:4, pages 4055-4080.
Crossref
Shanshan Chen, Michael Small, Yizhou Tao & Xinchu Fu. (2018) Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks. Bulletin of Mathematical Biology 80:8, pages 2049-2087.
Crossref
Xia Wang, Ying Zhang & Xinyu Song. (2018) An age-structured epidemic model with waning immunity and general nonlinear incidence rate. International Journal of Biomathematics 11:05, pages 1850069.
Crossref
Chuncheng Wang, Dejun Fan, Ling Xia & Xiaoyu Yi. (2018) Global stability for a multi-group SVIR model with age of vaccination. International Journal of Biomathematics 11:05, pages 1850068.
Crossref
Khalid Hattaf & Yu Yang. (2018) Global dynamics of an age-structured viral infection model with general incidence function and absorption. International Journal of Biomathematics 11:05, pages 1850065.
Crossref
Gergely Röst, Toshikazu Kuniya, Seyed M. Moghadas & Jianhong Wu. (2018) Global dynamics of an epidemiological model with age-of-infection dependent treatment rate. Ricerche di Matematica 67:1, pages 125-140.
Crossref
Xia Wang, Yuming Chen & Shengqiang Liu. (2018) Dynamics of an age‐structured host‐vector model for malaria transmission. Mathematical Methods in the Applied Sciences 41:5, pages 1966-1987.
Crossref
Chang-Yuan Cheng, Yueping Dong & Yasuhiro Takeuchi. (2018) An age-structured virus model with two routes of infection in heterogeneous environments. Nonlinear Analysis: Real World Applications 39, pages 464-491.
Crossref
Franciane Azevedo, Marcos Amaku, Francisco Antonio Bezerra Coutinho, Luis Fernandez Lopez & Eduardo Massad. (2018) The effect of the infection within the individual host on its propagation in the population. Infectious Disease Modelling 3, pages 345-361.
Crossref
Pierre Magal & Shigui RuanPierre Magal & Shigui Ruan. 2018. Theory and Applications of Abstract Semilinear Cauchy Problems. Theory and Applications of Abstract Semilinear Cauchy Problems 357 449 .
Rui Xu, Xiaohong Tian & Fengqin Zhang. (2017) Global dynamics of a tuberculosis transmission model with age of infection and incomplete treatment. Advances in Difference Equations 2017:1.
Crossref
Yingke Li, Zhidong Teng, Cheng Hu & Qing Ge. (2017) Global stability of an epidemic model with age-dependent vaccination, latent and relapse. Chaos, Solitons & Fractals 105, pages 195-207.
Crossref
Yannick Tchaptchie Kouakep. (2017) Perturbation of a globally stable equilibrium: application on an age-structured model. São Paulo Journal of Mathematical Sciences 11:2, pages 430-455.
Crossref
Salih Djilali, Tarik Mohammed Touaoula & Sofiane El-Hadi Miri. (2017) A Heroin Epidemic Model: Very General Non Linear Incidence, Treat-Age, and Global Stability. Acta Applicandae Mathematicae 152:1, pages 171-194.
Crossref
Liming Cai, Necibe Tuncer & Maia Martcheva. (2017) How does within‐host dynamics affect population‐level dynamics? Insights from an immuno‐epidemiological model of malaria. Mathematical Methods in the Applied Sciences 40:18, pages 6424-6450.
Crossref
Wen-Jing Feng, Li-Ming Cai & Kaihui Liu. (2017) Dynamics of a dengue epidemic model with class-age structure. International Journal of Biomathematics 10:08, pages 1750109.
Crossref
Bin Cao, Hai-Feng Huo & Hong Xiang. (2017) Global stability of an age-structure epidemic model with imperfect vaccination and relapse. Physica A: Statistical Mechanics and its Applications 486, pages 638-655.
Crossref
Xi-Chao Duan, Jun-Feng Yin & Xue-Zhi Li. (2017) Global Hopf bifurcation of an SIRS epidemic model with age-dependent recovery. Chaos, Solitons & Fractals 104, pages 613-624.
Crossref
ZHIPING WANG & RUI XU. (2017) GLOBAL DYNAMICS OF AN SVIR EPIDEMIOLOGICAL MODEL WITH INFECTION AGE AND NONLINEAR INCIDENCE. Journal of Biological Systems 25:03, pages 419-440.
Crossref
Xia Wang & Sanyi Tang. (2017) A multiscale model on hospital infections coupling macro and micro dynamics. Communications in Nonlinear Science and Numerical Simulation 50, pages 256-270.
Crossref
Junyuan Yang, Zhen Jin, Lin Wang & Fei Xu. (2017) A note on an age-of-infection SVIR model with nonlinear incidence. International Journal of Biomathematics 10:05, pages 1750064.
Crossref
Jinhu Xu, Yan Geng & Yicang Zhou. (2017) Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy. Applied Mathematics and Computation 305, pages 62-83.
Crossref
M. I. Betti, L. M. Wahl & M. Zamir. (2017) Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure. Bulletin of Mathematical Biology 79:7, pages 1586-1611.
Crossref
Junyuan Yang, Yuming Chen & Toshikazu Kuniya. (2017) Threshold dynamics of an age-structured epidemic model with relapse and nonlinear incidence. IMA Journal of Applied Mathematics 82:3, pages 629-655.
Crossref
Shanjing Ren. (2017) Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse. Mathematical Biosciences and Engineering 14:5/6, pages 1337-1360.
Crossref
Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li & Maia Martcheva. (2017) Global dynamics of a vector-host epidemic model with age of infection. Mathematical Biosciences and Engineering 14:5/6, pages 1159-1186.
Crossref
Yanxia Dang, Zhipeng Qiu & Xuezhi Li. (2017) Competitive exclusion in an infection-age structured vector-host epidemic model. Mathematical Biosciences and Engineering 14:4, pages 901-931.
Crossref
Jean-Baptiste Burie, Arnaud Ducrot & Abdoul Aziz Mbengue. (2017) Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants. Discrete & Continuous Dynamical Systems - B 22:7, pages 2879-2905.
Crossref
Jinliang Wang, Xianning Liu, Toshikazu Kuniya & Jingmei Pang. (2017) Global stability for multi-group SIR and SEIR epidemic models with age-dependent susceptibility. Discrete & Continuous Dynamical Systems - B 22:7, pages 2795-2812.
Crossref
Xia Wang, Yijun Lou & Xinyu Song. (2016) Age‐Structured Within‐Host HIV Dynamics with Multiple Target Cells. Studies in Applied Mathematics 138:1, pages 43-76.
Crossref
Hisashi InabaHisashi Inaba. 2017. Age-Structured Population Dynamics in Demography and Epidemiology. Age-Structured Population Dynamics in Demography and Epidemiology 379 442 .
Hisashi InabaHisashi Inaba. 2017. Age-Structured Population Dynamics in Demography and Epidemiology. Age-Structured Population Dynamics in Demography and Epidemiology 287 331 .
Hisashi InabaHisashi Inaba. 2017. Age-Structured Population Dynamics in Demography and Epidemiology. Age-Structured Population Dynamics in Demography and Epidemiology 219 286 .
Abba Mahamane Oumarou & Yannick Tchaptchie Kouakep. (2016) Vertical transmission and reproduction rate: modeling a common strategy for two related diseases. SpringerPlus 5:1.
Crossref
Toshikazu Kuniya, Jinliang Wang & Hisashi Inaba. (2016) A multi-group SIR epidemic model with age structure. Discrete and Continuous Dynamical Systems - Series B 21:10, pages 3515-3550.
Crossref
Junyuan Yang, Yuming Chen & Fei Xu. (2016) Effect of infection age on an SIS epidemic model on complex networks. Journal of Mathematical Biology 73:5, pages 1227-1249.
Crossref
Yuming Chen, Shaofen Zou & Junyuan Yang. (2016) Global analysis of an SIR epidemic model with infection age and saturated incidence. Nonlinear Analysis: Real World Applications 30, pages 16-31.
Crossref
Arnaud Ducrot. (2016) Spatial propagation for a two component reaction–diffusion system arising in population dynamics. Journal of Differential Equations 260:12, pages 8316-8357.
Crossref
Béatrice Laroche & Antoine Perasso. (2015) Threshold behaviour of a SI epidemiological model with two structuring variables. Journal of Evolution Equations 16:2, pages 293-315.
Crossref
Cruz Vargas‐De‐León. (2015) Global stability properties of age‐dependent epidemic models with varying rates of recurrence. Mathematical Methods in the Applied Sciences 39:8, pages 2057-2064.
Crossref
Jinliang Wang, Ran Zhang & Toshikazu Kuniya. (2016) The dynamics of an SVIR epidemiological model with infection age: Table 1.. IMA Journal of Applied Mathematics 81:2, pages 321-343.
Crossref
Suxia Zhang & Xiaxia Xu. (2016) A mathematical model for hepatitis B with infection-age structure. Discrete and Continuous Dynamical Systems - Series B 21:4, pages 1329-1346.
Crossref
Bentout Soufiane & Tarik Mohammed Touaoula. (2016) Global analysis of an infection age model with a class of nonlinear incidence rates. Journal of Mathematical Analysis and Applications 434:2, pages 1211-1239.
Crossref
Xichao Duan, Sanling Yuan & Kaifa Wang. (2016) Dynamics of a diffusive age-structured HBV model with saturating incidence. Mathematical Biosciences and Engineering 13:5, pages 935-968.
Crossref
Jinliang Wang, Ran Zhang & Toshikazu Kuniya. (2016) A note on dynamics of an age-of-infection cholera model. Mathematical Biosciences and Engineering 13:1, pages 227-247.
Crossref
C. Connell McCluskey. (2016) Global stability for an $SEI$ model of infectious disease with age structure and immigration of infecteds. Mathematical Biosciences and Engineering 13:2, pages 381-400.
Crossref
Jinhu Xu & Yicang Zhou. (2016) Global stability of a multi-group model with generalized nonlinear incidence and vaccination age. Discrete and Continuous Dynamical Systems - Series B 21:3, pages 977-996.
Crossref
Jinliang Wang, Ran Zhang & Toshikazu Kuniya. (2015) Global dynamics for a class of age-infection HIV models with nonlinear infection rate. Journal of Mathematical Analysis and Applications 432:1, pages 289-313.
Crossref
Bin Fang, Xuezhi Li, Maia Martcheva & Liming Cai. (2015) Global stability for a heroin model with age-dependent susceptibility. Journal of Systems Science and Complexity 28:6, pages 1243-1257.
Crossref
Junyuan Yang, Maia Martcheva & Lin Wang. (2015) Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence. Mathematical Biosciences 268, pages 1-8.
Crossref
Lili Liu, Jinliang Wang & Xianning Liu. (2015) Global stability of an SEIR epidemic model with age-dependent latency and relapse. Nonlinear Analysis: Real World Applications 24, pages 18-35.
Crossref
Bin Fang, Xue-Zhi Li, Maia Martcheva & Li-Ming Cai. (2015) Global asymptotic properties of a heroin epidemic model with treat-age. Applied Mathematics and Computation 263, pages 315-331.
Crossref
Liman Dai & Xingfu Zou. (2015) Analysis of a within-host age-structured model with mutations between two viral strains. Journal of Mathematical Analysis and Applications 426:2, pages 953-970.
Crossref
Mingwang Shen, Yanni Xiao & Libin Rong. (2015) Global stability of an infection-age structured HIV-1 model linking within-host and between-host dynamics. Mathematical Biosciences 263, pages 37-50.
Crossref
Cameron J. Browne. (2015) A multi-strain virus model with infected cell age structure: Application to HIV. Nonlinear Analysis: Real World Applications 22, pages 354-372.
Crossref
Yu Yang, Shigui Ruan & Dongmei Xiao. (2015) Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function. Mathematical Biosciences and Engineering 12:4, pages 859-877.
Crossref
Raúl Peralta, Cruz Vargas-De-León & Pedro Miramontes. (2015) Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age. Abstract and Applied Analysis 2015, pages 1-8.
Crossref
C. Connell McCluskey. (2015) Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations. SIAM Journal on Applied Dynamical Systems 14:1, pages 1-24.
Crossref
Gregory Roth & Sebastian J. Schreiber. (2013) Persistence in fluctuating environments for interacting structured populations. Journal of Mathematical Biology 69:5, pages 1267-1317.
Crossref
Cruz Vargas-De-León, Lourdes Esteva & Andrei Korobeinikov. (2014) Age-dependency in host-vector models: The global analysis. Applied Mathematics and Computation 243, pages 969-981.
Crossref
Xichao Duan, Sanling Yuan, Zhipeng Qiu & Junling Ma. (2014) Global stability of an SVEIR epidemic model with ages of vaccination and latency. Computers & Mathematics with Applications 68:3, pages 288-308.
Crossref
Xiao-Yan Wang, Yan-Ping Bai, Jun-Yuan Yang & Feng-Qin Zhang. (2014) Global stability of an epidemic model for HIV–TB co-infection with infection-age. International Journal of Biomathematics 07:04, pages 1450043.
Crossref
Yukihiko Nakata, Yoichi Enatsu, Hisashi Inaba, Toshikazu Kuniya, Yoshiaki Muroya & Yasuhiro Takeuchi. (2014) Stability of epidemic models with waning immunity. SUT Journal of Mathematics 50:2.
Crossref
Pierre Magal & Shigui Ruan. (2014) Susceptible-infectious-recovered models revisited: From the individual level to the population level. Mathematical Biosciences 250, pages 26-40.
Crossref
Danga Duplex Elvis Houpa, Tagne Eric Miamdjo & Tchaptchie Yannick Kouakep. (2014) A General Model for Hepatitis B Disease with Age-Dependent Susceptibility and Transmission Probabilities. Applied Mathematics 05:04, pages 707-722.
Crossref
Yuming Chen, Junyuan Yang & Fengqin Zhang. (2014) The global stability of an SIRS model with infection age. Mathematical Biosciences and Engineering 11:3, pages 449-469.
Crossref

Displaying 200 of 228 citing articles. Use the download link below to view the full list of citing articles.

Download full citations list

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.