TY - JOUR AU - Jin, Z. AU - Haque, M. AU - Liu, Q. PY - 2008 DA - 2008// TI - Pulse vaccination in the periodic infection rate SIR epidemic model JO - Int. J. Biomath. VL - 4 UR - https://doi.org/10.1142/S1793524508000370 DO - 10.1142/S1793524508000370 ID - Jin2008 ER - TY - JOUR AU - Huo, H. AU - Ma, Z. PY - 2010 DA - 2010// TI - Dynamics of a delayed epidemic model with non-monotonic incidence rate JO - Commun. Nonlinear Sci. Numer. Simul. VL - 15 UR - https://doi.org/10.1016/j.cnsns.2009.04.018 DO - 10.1016/j.cnsns.2009.04.018 ID - Huo2010 ER - TY - JOUR AU - Driessche, P. AU - Watmough, J. PY - 2000 DA - 2000// TI - A simple SIS epidemic model with a backward bifurcation JO - J. Math. Biol. VL - 40 UR - https://doi.org/10.1007/s002850000032 DO - 10.1007/s002850000032 ID - Driessche2000 ER - TY - JOUR AU - Kermack, W. AU - McKendric, A. PY - 1927 DA - 1927// TI - A contribution to the mathematical theory of epidemics JO - Proc. R. Soc. Ser. A VL - 115 ID - Kermack1927 ER - TY - JOUR AU - Cai, Y. AU - Kang, Y. AU - Banerjee, M. AU - Wang, W. PY - 2016 DA - 2016// TI - A stochastic epidemic model incorporating media coverage JO - Commun. Math. Sci. VL - 14 UR - https://doi.org/10.4310/CMS.2016.v14.n4.a1 DO - 10.4310/CMS.2016.v14.n4.a1 ID - Cai2016 ER - TY - JOUR AU - Zhao, D. AU - Sun, J. AU - Tan, Y. AU - Wu, J. AU - Dou, Y. PY - 2018 DA - 2018// TI - An extended SEIR model considering homepage effect for the information propagation of online social networks JO - Physica A VL - 512 UR - https://doi.org/10.1016/j.physa.2018.08.006 DO - 10.1016/j.physa.2018.08.006 ID - Zhao2018 ER - TY - JOUR AU - Fan, X. AU - Wang, Z. PY - 2013 DA - 2013// TI - Stability analysis of an SEIR epidemic model with stochastic perturbation and numerical simulation JO - Int. J. Nonlinear Sci. Numer. Simul. VL - 14 UR - https://doi.org/10.1515/ijnsns-2012-0054 DO - 10.1515/ijnsns-2012-0054 ID - Fan2013 ER - TY - JOUR AU - Britton, T. AU - Ouedraogo, D. PY - 2018 DA - 2018// TI - SEIRS epidemics with disease fatalities in growing populations JO - Math. Biosci. VL - 296 UR - https://doi.org/10.1016/j.mbs.2017.11.006 DO - 10.1016/j.mbs.2017.11.006 ID - Britton2018 ER - TY - JOUR AU - Wang, X. AU - Peng, H. AU - Shi, B. AU - Jiang, D. AU - Zhang, S. PY - 2019 DA - 2019// TI - Optimal vaccination strategy of a constrained time-varying SEIR epidemic model JO - Commun. Nonlinear Sci. Numer. Simul. VL - 67 UR - https://doi.org/10.1016/j.cnsns.2018.07.003 DO - 10.1016/j.cnsns.2018.07.003 ID - Wang2019 ER - TY - JOUR AU - Li, X. AU - Gupur, G. AU - Zhu, G. PY - 2015 DA - 2015// TI - Threshold and stability results for an age-structured SEIR epidemic model JO - Comput. Math. Appl. VL - 42 ID - Li2015 ER - TY - JOUR AU - Khan, A. AU - Zaman, G. PY - 2018 DA - 2018// TI - Global analysis of an age-structured SEIR endemic model JO - Chaos Solitons Fractals VL - 108 UR - https://doi.org/10.1016/j.chaos.2018.01.037 DO - 10.1016/j.chaos.2018.01.037 ID - Khan2018 ER - TY - JOUR AU - Liu, Q. AU - Jiang, D. AU - Hayat, T. AU - Alsaedi, A. PY - 2018 DA - 2018// TI - Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence JO - Physica A VL - 512 UR - https://doi.org/10.1016/j.physa.2018.08.054 DO - 10.1016/j.physa.2018.08.054 ID - Liu2018 ER - TY - JOUR AU - Wang, L. AU - Liu, Z. AU - Zhang, X. PY - 2016 DA - 2016// TI - Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence JO - Appl. Math. Comput. VL - 284 ID - Wang2016 ER - TY - JOUR AU - Liu, Q. AU - Jiang, D. AU - Hayat, T. AU - Ahmad, B. PY - 2017 DA - 2017// TI - Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence JO - Physica A VL - 476 UR - https://doi.org/10.1016/j.physa.2017.02.028 DO - 10.1016/j.physa.2017.02.028 ID - Liu2017 ER - TY - JOUR AU - Wei, F. AU - Xue, R. PY - 2020 DA - 2020// TI - Stability and extinction of SEIR epidemic models with generalized nonlinear incidence JO - Math. Comput. Simul. VL - 170 UR - https://doi.org/10.1016/j.matcom.2018.09.029 DO - 10.1016/j.matcom.2018.09.029 ID - Wei2020 ER - TY - JOUR AU - Wei, F. AU - Lin, Q. PY - 2018 DA - 2018// TI - Dynamical behavior for a stochastic epidemic model with nonlinear incidence JO - Acta Math. Sinica (Chin. Ser.) VL - 61 ID - Wei2018 ER - TY - JOUR AU - Khan, M. AU - Khan, Y. AU - Islam, S. PY - 2018 DA - 2018// TI - Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment JO - Physica A VL - 493 UR - https://doi.org/10.1016/j.physa.2017.10.038 DO - 10.1016/j.physa.2017.10.038 ID - Khan2018 ER - TY - JOUR AU - Liu, J. AU - Wei, F. PY - 2016 DA - 2016// TI - Dynamics of stochastic SEIS epidemic model with varying population size JO - Physica A VL - 464 UR - https://doi.org/10.1016/j.physa.2016.06.120 DO - 10.1016/j.physa.2016.06.120 ID - Liu2016 ER - TY - JOUR AU - Cao, B. AU - Shan, M. AU - Zhang, Q. AU - Wang, W. PY - 2017 DA - 2017// TI - A stochastic SIS epidemic model with vaccination JO - Physica A VL - 486 UR - https://doi.org/10.1016/j.physa.2017.05.083 DO - 10.1016/j.physa.2017.05.083 ID - Cao2017 ER - TY - JOUR AU - Liu, Q. AU - Chen, Q. AU - Jiang, D. PY - 2016 DA - 2016// TI - The threshold of a stochastic delayed SIR epidemic model with temporary immunity JO - Physica A VL - 450 UR - https://doi.org/10.1016/j.physa.2015.12.056 DO - 10.1016/j.physa.2015.12.056 ID - Liu2016 ER - TY - JOUR AU - Gray, A. AU - Greenhalgh, D. AU - Hu, L. AU - Mao, X. AU - Pan, J. PY - 2011 DA - 2011// TI - A stochastic differential equation SIS epidemic model JO - SIAM J. Appl. Math. VL - 71 UR - https://doi.org/10.1137/10081856X DO - 10.1137/10081856X ID - Gray2011 ER - TY - JOUR AU - Liu, J. AU - Chen, L. AU - Wei, F. PY - 2018 DA - 2018// TI - The persistence and extinction of a stochastic SIS epidemic model with logistic growth JO - Adv. Differ. Equ. VL - 2018 UR - https://doi.org/10.1186/s13662-018-1528-8 DO - 10.1186/s13662-018-1528-8 ID - Liu2018 ER - TY - JOUR AU - Agaba, G. AU - Kyrychko, Y. AU - Blyuss, K. PY - 2017 DA - 2017// TI - Dynamics of vaccination in a time-delayed epidemic model with awareness JO - Math. Biosci. VL - 294 UR - https://doi.org/10.1016/j.mbs.2017.09.007 DO - 10.1016/j.mbs.2017.09.007 ID - Agaba2017 ER - TY - JOUR AU - Chen, L. AU - Wei, F. PY - 2017 DA - 2017// TI - Persistence and distribution of a stochastic susceptible–infected–recovered epidemic model with varying population size JO - Physica A VL - 483 UR - https://doi.org/10.1016/j.physa.2017.04.114 DO - 10.1016/j.physa.2017.04.114 ID - Chen2017 ER - TY - JOUR AU - Stolerman, L. AU - Coombs, D. AU - Boatto, S. PY - 2015 DA - 2015// TI - SIR-network model and its application to dengue fever JO - SIAM J. Appl. Math. VL - 75 UR - https://doi.org/10.1137/140996148 DO - 10.1137/140996148 ID - Stolerman2015 ER - TY - JOUR AU - Hethcote, H. AU - Driessche, P. PY - 1991 DA - 1991// TI - Some epidemiological models with nonlinear incidence JO - J. Math. Biol. VL - 29 UR - https://doi.org/10.1007/BF00160539 DO - 10.1007/BF00160539 ID - Hethcote1991 ER - TY - JOUR AU - Hui, J. AU - Chen, L. PY - 2004 DA - 2004// TI - Impulsive vaccination of SIR epidemic models with nonlinear incidence rates JO - Discrete Contin. Dyn. Syst., Ser. B VL - 4 ID - Hui2004 ER - TY - BOOK AU - Anderson, R. AU - May, R. PY - 1990 DA - 1990// TI - Infectious Diseases of Humans: Dynamics and Control PB - Oxford University Press CY - Oxford ID - Anderson1990 ER - TY - JOUR AU - May, R. AU - Anderson, R. PY - 1978 DA - 1978// TI - Regulation and stability of host-parasite population interactions II: destabilizing process JO - J. Anim. Ecol. VL - 47 UR - https://doi.org/10.2307/3933 DO - 10.2307/3933 ID - May1978 ER - TY - JOUR AU - Wei, F. AU - Chen, F. PY - 2016 DA - 2016// TI - Asymptotic behaviors of a stochastic SIRS epidemic model with saturated incidence JO - J. Syst. Sci. Math. Sci. VL - 36 ID - Wei2016 ER - TY - JOUR AU - Gan, S. AU - Wei, F. PY - 2018 DA - 2018// TI - Study on a susceptible–infected–vaccinated model with delay and proportional vaccination JO - Int. J. Biomath. VL - 11 UR - https://doi.org/10.1142/S1793524518501024 DO - 10.1142/S1793524518501024 ID - Gan2018 ER - TY - JOUR AU - Lu, R. AU - Wei, F. PY - 2019 DA - 2019// TI - Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate JO - Physica A VL - 513 UR - https://doi.org/10.1016/j.physa.2018.09.016 DO - 10.1016/j.physa.2018.09.016 ID - Lu2019 ER - TY - JOUR AU - Zhao, Y. AU - Wei, F. PY - 2017 DA - 2017// TI - Impact of random perturbations with state-dependent on an epidemic model JO - J. Northeast Norm. Univ., Nat. Sci. Ed. VL - 49 ID - Zhao2017 ER - TY - JOUR AU - Driessche, P. AU - Watmough, J. PY - 2002 DA - 2002// TI - Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission JO - Math. Biosci. VL - 180 UR - https://doi.org/10.1016/S0025-5564(02)00108-6 DO - 10.1016/S0025-5564(02)00108-6 ID - Driessche2002 ER - TY - JOUR AU - Diekmann, O. AU - Heesterbeek, J. A. P. PY - 1990 DA - 1990// TI - On the definition and the computation of the basic reproduction ratio R0$R_{0}$ in models for infectious diseases in heterogeneous populations JO - J. Math. Biol. VL - 28 UR - https://doi.org/10.1007/BF00178324 DO - 10.1007/BF00178324 ID - Diekmann1990 ER - TY - JOUR AU - Driessche, P. AU - Watmough, J. PY - 2000 DA - 2000// TI - A simple SIS epidemic model with a backward bifurcation JO - J. Math. Biol. VL - 40 UR - https://doi.org/10.1007/s002850000032 DO - 10.1007/s002850000032 ID - Driessche2000 ER - TY - BOOK AU - Mao, X. R. PY - 2007 DA - 2007// TI - Stochastic Differential Equations and Applications PB - Horwood CY - Chichester ID - Mao2007 ER - TY - JOUR AU - Zhao, Y. AU - Jiang, D. PY - 2013 DA - 2013// TI - Dynamics of stochastically perturbed SIS epidemic model with vaccination JO - Abstr. Appl. Anal. VL - 2013 ID - Zhao2013 ER - TY - JOUR AU - Zhao, Y. AU - Jiang, D. PY - 2014 DA - 2014// TI - The threshold of a stochastic SIS epidemic model with vaccination JO - Appl. Math. Comput. VL - 243 ID - Zhao2014 ER - TY - BOOK AU - Hasminskij, R. PY - 1980 DA - 1980// TI - Stochastic Stability of Differential Equations PB - Noordhoff CY - Alphen aan den Rijn UR - https://doi.org/10.1007/978-94-009-9121-7 DO - 10.1007/978-94-009-9121-7 ID - Hasminskij1980 ER - TY - JOUR AU - Higham, D. J. PY - 2001 DA - 2001// TI - An algorithmic introduction to numerical simulation of stochastic differential equations JO - SIAM Rev. VL - 43 UR - https://doi.org/10.1137/S0036144500378302 DO - 10.1137/S0036144500378302 ID - Higham2001 ER -