Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process
Infectious disease transmission, mainly affected by media coverage and stochastic perturbations, has imposed great social financial burden on the community in the past few decades and even threatened public health. However, there are few studies devoted to the theoretical dynamics of epidemic models...
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| Published in | Mathematics and computers in simulation Vol. 196; pp. 15 - 44 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.06.2022
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Infectious disease transmission, mainly affected by media coverage and stochastic perturbations, has imposed great social financial burden on the community in the past few decades and even threatened public health. However, there are few studies devoted to the theoretical dynamics of epidemic models with media coverage and biologically reasonable stochastic effect yet. In this sense, this paper mainly formulates and studies a stochastic epidemic model with media coverage and two mean-reverting Ornstein–Uhlenbeck processes. We first illustrate the biological implication and mathematically reasonable assumption of introducing the Ornstein–Uhlenbeck process as stochastic effect. It is theoretically proved that the solution to the stochastic model is unique and global, as well as the existence of an ergodic stationary distribution. After that, by solving the corresponding Fokker–Planck equation and using our developed algebraic equation theory, it is derived that the above global solution around the endemic equilibrium follows a unique probability density function. For completeness, the sufficient criteria for extinction exponentially of the model are established. Finally, several numerical simulations are provided to verify our theoretical results. Besides, the impact of stochastic noises and media coverage on epidemic transmission is studied by comparison with the previous results of a deterministic model. |
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| AbstractList | Infectious disease transmission, mainly affected by media coverage and stochastic perturbations, has imposed great social financial burden on the community in the past few decades and even threatened public health. However, there are few studies devoted to the theoretical dynamics of epidemic models with media coverage and biologically reasonable stochastic effect yet. In this sense, this paper mainly formulates and studies a stochastic epidemic model with media coverage and two mean-reverting Ornstein–Uhlenbeck processes. We first illustrate the biological implication and mathematically reasonable assumption of introducing the Ornstein–Uhlenbeck process as stochastic effect. It is theoretically proved that the solution to the stochastic model is unique and global, as well as the existence of an ergodic stationary distribution. After that, by solving the corresponding Fokker–Planck equation and using our developed algebraic equation theory, it is derived that the above global solution around the endemic equilibrium follows a unique probability density function. For completeness, the sufficient criteria for extinction exponentially of the model are established. Finally, several numerical simulations are provided to verify our theoretical results. Besides, the impact of stochastic noises and media coverage on epidemic transmission is studied by comparison with the previous results of a deterministic model. |
| Author | Zhou, Baoquan Jiang, Daqing Han, Bingtao Hayat, Tasawar |
| Author_xml | – sequence: 1 givenname: Baoquan surname: Zhou fullname: Zhou, Baoquan organization: College of Science, China University of Petroleum (East China), Qingdao 266580, PR China – sequence: 2 givenname: Daqing surname: Jiang fullname: Jiang, Daqing email: daqingjiang2010@hotmail.com organization: College of Science, China University of Petroleum (East China), Qingdao 266580, PR China – sequence: 3 givenname: Bingtao surname: Han fullname: Han, Bingtao organization: College of Science, China University of Petroleum (East China), Qingdao 266580, PR China – sequence: 4 givenname: Tasawar surname: Hayat fullname: Hayat, Tasawar organization: Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia |
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| Cites_doi | 10.1098/rsif.2020.0174 10.1016/j.physa.2017.04.173 10.1007/s11538-007-9196-y 10.1016/j.apm.2014.03.037 10.1016/S0022-0396(02)00089-X 10.1016/j.chaos.2020.109865 10.1137/S0036144500378302 10.1016/j.mbs.2011.01.005 10.1016/0025-5564(76)90132-2 10.1016/j.chaos.2020.110601 10.1007/s10884-016-9532-8 10.1016/j.physa.2019.121759 10.1016/j.jde.2015.08.024 10.1016/j.chaos.2020.109643 10.1007/s11009-019-09697-6 10.1016/j.jde.2018.09.026 10.1155/2014/680743 10.1016/j.physa.2018.06.099 10.1007/s00038-020-01426-y 10.1137/120896463 10.1016/j.physa.2018.09.124 10.3934/dcdsb.2018250 10.1080/17486700701425870 10.1016/j.jmaa.2014.08.019 10.1016/j.matcom.2021.05.009 10.1016/j.nonrwa.2004.10.001 10.1016/j.jde.2020.04.046 10.1007/s10440-018-0196-8 10.1017/jpr.2015.18 10.1016/j.cnsns.2008.06.024 10.1016/j.jmaa.2015.07.025 10.1080/17442508008833146 10.1098/rspa.1927.0118 10.1016/S0304-4149(01)00126-0 10.2307/1427522 10.1155/2009/609306 10.1016/j.apm.2020.03.027 10.1016/j.cnsns.2019.05.001 10.1016/j.chaos.2019.01.025 10.1016/j.aml.2013.11.002 10.1007/s11538-015-0086-4 |
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| Keywords | Ergodic stationary distribution Density function Ornstein–Uhlenbeck process Fokker–Planck equation Extinction exponentially |
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| References | Lin, Jiang, Xia (b30) 2014; 236 Mao (b35) 1997 Li, Cui (b28) 2009; 14 Pang, Cui (b42) 2009 K. Qi, D. Jiang, T. Hayat, A. Alsaedi, Virus dynamics behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses, Math. Comput. Simulation Sahu, Dhar (b47) 2015; 421 Sun, Yang, Arino, Khan (b49) 2011; 230 Liu, Deng (b32) 2020; 364 Organization (b41) 2020 Ruan, Wang (b46) 2003; 188 Hethcote (b17) 1976; 28 Kermack, Kendrick (b23) 1927; 115 Organization (b40) 2011 Ma, Zhou, Li (b34) 2015 Zhang, Yuan (b59) 2021; 394 Oksendal (b39) 2000 Zhao, Jiang (b60) 2014; 34 Das, Khatuaa, Kar, Jana (b9) 2021; 404 Cai, Kang, Banerjee, Wang (b3) 2015; 259 Zhou, Jiang, Dai (b63) 2021; 143 Cai, Kang, Wang (b4) 2017; 305 Kyrychko, Blyuss (b27) 2005; 6 Qi, Jiang (b43) 2020; 85 Cai, Jiao, Gui, Liu, Wang (b2) 2018; 329 Yadava, Verma (b52) 2020; 140 . Zhang, Jiang, Liu, O’Regan (b57) 2016; 433 Meyn, Tweedie (b38) 1993; 25 Caraballo, Fatini, Khalifi (b5) 2020; 133 Zhou, Zhang, Jiang (b64) 2020; 137 Du, Dieu, Nhu (b11) 2019; 160 Zhao, Lin, Dai (b61) 2014; 2014 Jude, Dalexis, Kokou-Kpolou (b21) 2020; 65 Kutoyants (b26) 2003 Wang, Jiang, Hayat, Alsaedi, Ahmad (b51) 2019 Zhang, Jiang (b55) 2020; 22 Kar, Nandi, Jana, Mandal (b22) 2019; 120 Zhang, Jiang, Hayat, Ahmad (b56) 2017; 483 Ji, Jiang (b19) 2014; 38 Li, Liu, Cui (b29) 2019; 266 Lipster (b31) 1980; 3 Dieu (b10) 2018; 30 Rajasekar, Pitchaimani (b45) 2020; 377 Wang, Cai, Ding, Gui (b50) 2018; 509 Chen, Wua, Feng, Qian, Sun (b8) 2021; 390 Mao (b36) 2002; 97 Han, Jiang, Zhou (b14) 2020 Higham (b18) 2001; 43 Du, Yin (b12) 2016; 53 Liu, Wu, Zhu (b33) 2007; 8 Jia, Wang, Song, Li, Jusup, Wang (b20) 2020; 17 Yuan, Li (b53) 2009; 2009 Zhang, Fan, Gao (b54) 2018; 514 Khasminskii (b24) 2011 Meng, Li, Gao (b37) 2018; 339 Han, Zhou, Jiang (b15) 2021; 405 Blower (b1) 2004; 11 Gardiner (b13) 1983 Shu, Wang, Watmough (b48) 2013; 73 Zhang, Xu, Lei, Qiao (b58) 2019; 77 He, Tang, Wang (b16) 2019; 532 Korobeinikov (b25) 2007; 69 Zu, Jiang (b66) 2018; 330 Zhu, Wang, Li, Guo, Wang (b65) 2019; 359 Chekroun, Kuniya (b7) 2020; 269 Caraballo, Fatini (b6) 2018; 23 Zhao, Yuan, Ma (b62) 2015; 77 Li (10.1016/j.matcom.2022.01.014_b28) 2009; 14 Organization (10.1016/j.matcom.2022.01.014_b41) 2020 Du (10.1016/j.matcom.2022.01.014_b11) 2019; 160 Blower (10.1016/j.matcom.2022.01.014_b1) 2004; 11 Du (10.1016/j.matcom.2022.01.014_b12) 2016; 53 Li (10.1016/j.matcom.2022.01.014_b29) 2019; 266 Qi (10.1016/j.matcom.2022.01.014_b43) 2020; 85 Kutoyants (10.1016/j.matcom.2022.01.014_b26) 2003 Han (10.1016/j.matcom.2022.01.014_b14) 2020 Kermack (10.1016/j.matcom.2022.01.014_b23) 1927; 115 Organization (10.1016/j.matcom.2022.01.014_b40) 2011 Dieu (10.1016/j.matcom.2022.01.014_b10) 2018; 30 Wang (10.1016/j.matcom.2022.01.014_b50) 2018; 509 Zhang (10.1016/j.matcom.2022.01.014_b56) 2017; 483 Sun (10.1016/j.matcom.2022.01.014_b49) 2011; 230 Caraballo (10.1016/j.matcom.2022.01.014_b6) 2018; 23 Oksendal (10.1016/j.matcom.2022.01.014_b39) 2000 Meyn (10.1016/j.matcom.2022.01.014_b38) 1993; 25 Chen (10.1016/j.matcom.2022.01.014_b8) 2021; 390 Cai (10.1016/j.matcom.2022.01.014_b4) 2017; 305 Zhang (10.1016/j.matcom.2022.01.014_b57) 2016; 433 He (10.1016/j.matcom.2022.01.014_b16) 2019; 532 Hethcote (10.1016/j.matcom.2022.01.014_b17) 1976; 28 Pang (10.1016/j.matcom.2022.01.014_b42) 2009 Zhang (10.1016/j.matcom.2022.01.014_b55) 2020; 22 Zhao (10.1016/j.matcom.2022.01.014_b61) 2014; 2014 Zhang (10.1016/j.matcom.2022.01.014_b54) 2018; 514 Khasminskii (10.1016/j.matcom.2022.01.014_b24) 2011 Higham (10.1016/j.matcom.2022.01.014_b18) 2001; 43 Mao (10.1016/j.matcom.2022.01.014_b36) 2002; 97 Korobeinikov (10.1016/j.matcom.2022.01.014_b25) 2007; 69 Sahu (10.1016/j.matcom.2022.01.014_b47) 2015; 421 Yuan (10.1016/j.matcom.2022.01.014_b53) 2009; 2009 10.1016/j.matcom.2022.01.014_b44 Cai (10.1016/j.matcom.2022.01.014_b3) 2015; 259 Ruan (10.1016/j.matcom.2022.01.014_b46) 2003; 188 Zhou (10.1016/j.matcom.2022.01.014_b63) 2021; 143 Liu (10.1016/j.matcom.2022.01.014_b33) 2007; 8 Zhang (10.1016/j.matcom.2022.01.014_b58) 2019; 77 Zhang (10.1016/j.matcom.2022.01.014_b59) 2021; 394 Ji (10.1016/j.matcom.2022.01.014_b19) 2014; 38 Cai (10.1016/j.matcom.2022.01.014_b2) 2018; 329 Meng (10.1016/j.matcom.2022.01.014_b37) 2018; 339 Yadava (10.1016/j.matcom.2022.01.014_b52) 2020; 140 Chekroun (10.1016/j.matcom.2022.01.014_b7) 2020; 269 Lin (10.1016/j.matcom.2022.01.014_b30) 2014; 236 Zhao (10.1016/j.matcom.2022.01.014_b60) 2014; 34 Jude (10.1016/j.matcom.2022.01.014_b21) 2020; 65 Rajasekar (10.1016/j.matcom.2022.01.014_b45) 2020; 377 Zu (10.1016/j.matcom.2022.01.014_b66) 2018; 330 Ma (10.1016/j.matcom.2022.01.014_b34) 2015 Gardiner (10.1016/j.matcom.2022.01.014_b13) 1983 Caraballo (10.1016/j.matcom.2022.01.014_b5) 2020; 133 Zhou (10.1016/j.matcom.2022.01.014_b64) 2020; 137 Shu (10.1016/j.matcom.2022.01.014_b48) 2013; 73 Jia (10.1016/j.matcom.2022.01.014_b20) 2020; 17 Wang (10.1016/j.matcom.2022.01.014_b51) 2019 Liu (10.1016/j.matcom.2022.01.014_b32) 2020; 364 Kyrychko (10.1016/j.matcom.2022.01.014_b27) 2005; 6 Lipster (10.1016/j.matcom.2022.01.014_b31) 1980; 3 Han (10.1016/j.matcom.2022.01.014_b15) 2021; 405 Mao (10.1016/j.matcom.2022.01.014_b35) 1997 Kar (10.1016/j.matcom.2022.01.014_b22) 2019; 120 Das (10.1016/j.matcom.2022.01.014_b9) 2021; 404 Zhu (10.1016/j.matcom.2022.01.014_b65) 2019; 359 Zhao (10.1016/j.matcom.2022.01.014_b62) 2015; 77 |
| References_xml | – volume: 509 start-page: 921 year: 2018 end-page: 936 ident: b50 article-title: A stochastic differential equation SIS epidemic model incorporating ornstein–uhlenbeck process publication-title: Physica A – volume: 405 year: 2021 ident: b15 article-title: Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay publication-title: Appl. Math. Comput. – volume: 23 start-page: 3483 year: 2018 end-page: 3501 ident: b6 article-title: A stochastic SIRI epidemic model with relapse and media coverage publication-title: Discrete Contin. Dyn. Syst. Ser. B. – volume: 404 year: 2021 ident: b9 article-title: The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India publication-title: Appl. Math. Comput. – volume: 305 start-page: 221 year: 2017 end-page: 240 ident: b4 article-title: A stochastic SIRS epidemic model with nonlinear incidence rate publication-title: Appl. Math. Comput. – volume: 65 start-page: 717 year: 2020 end-page: 718 ident: b21 article-title: Social inequalities and collateral damages of the COVID-19 pandemic: when basic needs challenge mental health care publication-title: Int. J. Publ. Health – volume: 28 start-page: 335 year: 1976 end-page: 356 ident: b17 article-title: Qualitative analyses of communicable disease models publication-title: Math. Biosci. – year: 1997 ident: b35 article-title: Stochastic Differential Equations and Applications – volume: 11 start-page: 138A year: 2004 end-page: 146A ident: b1 article-title: Modelling the genital herpes epidemic publication-title: Herpes – volume: 3 start-page: 217 year: 1980 end-page: 228 ident: b31 article-title: A strong law of large numbers for local martingales publication-title: Stochastics – volume: 329 start-page: 210 year: 2018 end-page: 226 ident: b2 article-title: Environmental variability in a stochastic epidemic model publication-title: Appl. Math. Comput. – volume: 330 start-page: 93 year: 2018 end-page: 102 ident: b66 article-title: Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching publication-title: Appl. Math. Comput. – volume: 69 start-page: 1871 year: 2007 end-page: 1886 ident: b25 article-title: Global properties of infectious disease models with nonlinear incidence publication-title: Bull. Math. Biol. – volume: 53 start-page: 187 year: 2016 end-page: 202 ident: b12 article-title: Conditions for permanence and ergodicity of certain stochastic predator–prey models publication-title: J. Appl. Pro. – reference: K. Qi, D. Jiang, T. Hayat, A. Alsaedi, Virus dynamics behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses, Math. Comput. Simulation – volume: 97 start-page: 95 year: 2002 end-page: 110 ident: b36 article-title: Environmental brownian noise suppresses explosions in population dynamics publication-title: Stochastic Process. Appl. – volume: 133 year: 2020 ident: b5 article-title: Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel publication-title: Chaos Solitons Fractals – volume: 6 start-page: 495 year: 2005 end-page: 507 ident: b27 article-title: Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate publication-title: Nonlinear Anal. RWA – volume: 364 year: 2020 ident: b32 article-title: Analysis of a stochastic hybrid population model with Allee effect publication-title: Appl. Math. Comput. – volume: 115 start-page: 700 year: 1927 end-page: 721 ident: b23 article-title: A contribution to the mathematical theory of epidemics publication-title: Proc R Soc Lond A. – year: 2020 ident: b41 article-title: Coronavirus disease (COVID-19) pandemic – volume: 359 start-page: 512 year: 2019 end-page: 524 ident: b65 article-title: Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties publication-title: Appl. Math. Comput. – volume: 73 start-page: 1280 year: 2013 end-page: 1302 ident: b48 article-title: Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses publication-title: SIAM J. Appl. Math. – volume: 339 start-page: 701 year: 2018 end-page: 726 ident: b37 article-title: Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay publication-title: Appl. Math. Comput. – volume: 483 start-page: 94 year: 2017 end-page: 108 ident: b56 article-title: Dynamical behavior of a stochastic SVIR epidemic model with vaccination publication-title: Physica A – volume: 259 start-page: 7463 year: 2015 end-page: 7502 ident: b3 article-title: A stochastic SIRS epidemic model with infectious force under intervention strategies publication-title: J. Differ. Equ. – year: 2019 ident: b51 article-title: Stationary distribution of stochastic NP ecological model under regime switching publication-title: Physica A – volume: 2014 year: 2014 ident: b61 article-title: An SIRS epidemic model incorporating media coverage with time delay publication-title: Comput. Math. Meth. Med. – volume: 77 start-page: 1285 year: 2015 end-page: 1326 ident: b62 article-title: Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment publication-title: Bull. Math. Biol. – volume: 14 start-page: 2353 year: 2009 end-page: 2365 ident: b28 article-title: The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage publication-title: Commun. Nonlinear Sci. Numer. Simul. – volume: 143 year: 2021 ident: b63 article-title: Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vacinnation publication-title: Chaos Solitons Fractals – volume: 34 start-page: 90 year: 2014 end-page: 93 ident: b60 article-title: The threshold of a stochastic SIRS epidemic model with saturated incidence publication-title: Appl. Math. Lett. – volume: 433 start-page: 121 year: 2016 end-page: 148 ident: b57 article-title: Asymptotic behavior of a three species eco-epidemiological model perturbed by white noise publication-title: J. Math. Anal. Appl. – volume: 120 start-page: 188 year: 2019 end-page: 199 ident: b22 article-title: Stability and bifurcation analysis of an epidemic model with the effect of media publication-title: Chaos Solitons Fractals – volume: 2009 year: 2009 ident: b53 article-title: Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate publication-title: Discrete Dyn. Nat. Soc. – volume: 266 start-page: 3973 year: 2019 end-page: 4017 ident: b29 article-title: Threshold dynamics and ergodicity of an SIRS epidemic model with semi-Markov switching publication-title: J. Differ. Equ. – volume: 140 year: 2020 ident: b52 article-title: A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China publication-title: Chaos Solitons Fractals – volume: 17 year: 2020 ident: b20 article-title: Evolutionary dynamics drives role specialization in a community of players publication-title: J. R. Soc. Interface – year: 1983 ident: b13 article-title: Handbook of stochastic methods for physics publication-title: Chemistry and the Natural Sciences – volume: 236 start-page: 1 year: 2014 end-page: 9 ident: b30 article-title: Long-time behavior of a stochastic SIR model publication-title: Appl. Math. Comput. – volume: 160 start-page: 81 year: 2019 end-page: 99 ident: b11 article-title: Conditions for permanence and ergodicity of certain SIR epidemic models publication-title: Acta Appl. Math. – volume: 188 start-page: 135 year: 2003 end-page: 163 ident: b46 article-title: Dynamical behavior of an epidemic model with a nonlinear incidence rate publication-title: J. Differ. Equ. – volume: 25 start-page: 518 year: 1993 end-page: 548 ident: b38 article-title: Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes publication-title: Adv. Appl. Pro. – start-page: 116 year: 2009 end-page: 119 ident: b42 article-title: An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage publication-title: Second International Conference on Information and Computing Science – year: 2011 ident: b24 article-title: Stochastic Stability of Differential Equations – volume: 230 start-page: 87 year: 2011 end-page: 95 ident: b49 article-title: Effect of media-induced social distancing on disease transmission in a two patch setting publication-title: Math. Biosci. – year: 2015 ident: b34 article-title: Qualitative and Stability Methods for Ordinary Differential Equations – volume: 85 start-page: 378 year: 2020 end-page: 404 ident: b43 article-title: The impact of virus carrier screening and actively seeking treatment on dynamical behavior of a stochastic HIV/AIDS infection model publication-title: Appl. Math. Model. – volume: 421 start-page: 1651 year: 2015 end-page: 1672 ident: b47 article-title: Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity publication-title: J. Math. Anal. Appl. – year: 2011 ident: b40 article-title: The top 10 causes of death – volume: 137 year: 2020 ident: b64 article-title: Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate publication-title: Chaos Solitons Fractals – volume: 43 start-page: 525 year: 2001 end-page: 546 ident: b18 article-title: An algorithmic introduction to numerical simulation of stochastic differential equations publication-title: SIAM Rev. – reference: . – volume: 532 year: 2019 ident: b16 article-title: A stochastic SIS model driven by random diffusion of air pollutants publication-title: Physica A – volume: 269 start-page: 117 year: 2020 end-page: 148 ident: b7 article-title: Global threshold dynamics of an infection age-structured SIR epidemic model with diffusion under the Dirichlet boundary condition publication-title: J. Differ. Equ. – volume: 390 year: 2021 ident: b8 article-title: Effects of global warming on pattern dynamics of vegetation: Wuwei in China as a case publication-title: Appl. Math. Comput. – volume: 514 start-page: 671 year: 2018 end-page: 685 ident: b54 article-title: Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate publication-title: Physica A – volume: 22 start-page: 267 year: 2020 end-page: 278 ident: b55 article-title: Periodic solutions of a stochastic food-limited muatualism model publication-title: Methodol. Comput. Appl. Probab. – volume: 77 start-page: 258 year: 2019 end-page: 270 ident: b58 article-title: Early warning and basin stability in a stochastic vegetation-water dynamical system publication-title: Commun. Nonlinear Sci. Numer. Simul. – year: 2000 ident: b39 article-title: Stochastic Differential Equations: An Introduction with Applications – volume: 394 year: 2021 ident: b59 article-title: A stochastic chemostat model with mean-reverting Ornstein–Uhlenbeck process and Monod-Haldane response function publication-title: Appl. Math. Comput. – year: 2020 ident: b14 article-title: Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth publication-title: Chaos Solitons Fractals – year: 2003 ident: b26 article-title: Statistical Inference for Ergodic Diffusion Processes – volume: 8 start-page: 153 year: 2007 end-page: 164 ident: b33 article-title: Media/psychological impact on multiple outbreaks of emerging infectious diseases publication-title: Comput. Math. Methods Med. – volume: 377 year: 2020 ident: b45 article-title: Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence publication-title: Appl. Math. Comput. – volume: 30 start-page: 93 year: 2018 end-page: 106 ident: b10 article-title: Asymptotic properties of a stochastic SIR epidemic model with Beddington–DeAngelis incidence rate publication-title: J. Dyn. Diff. Equ. – volume: 38 start-page: 5067 year: 2014 end-page: 5079 ident: b19 article-title: Threshold behaviour of a stochastic SIR model publication-title: Appl. Math. Model. – year: 1997 ident: 10.1016/j.matcom.2022.01.014_b35 – volume: 377 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b45 article-title: Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence publication-title: Appl. Math. Comput. – volume: 17 issue: 168 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b20 article-title: Evolutionary dynamics drives role specialization in a community of players publication-title: J. R. Soc. Interface doi: 10.1098/rsif.2020.0174 – volume: 483 start-page: 94 year: 2017 ident: 10.1016/j.matcom.2022.01.014_b56 article-title: Dynamical behavior of a stochastic SVIR epidemic model with vaccination publication-title: Physica A doi: 10.1016/j.physa.2017.04.173 – year: 2011 ident: 10.1016/j.matcom.2022.01.014_b40 – year: 2020 ident: 10.1016/j.matcom.2022.01.014_b41 – volume: 329 start-page: 210 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b2 article-title: Environmental variability in a stochastic epidemic model publication-title: Appl. Math. Comput. – volume: 69 start-page: 1871 year: 2007 ident: 10.1016/j.matcom.2022.01.014_b25 article-title: Global properties of infectious disease models with nonlinear incidence publication-title: Bull. Math. Biol. doi: 10.1007/s11538-007-9196-y – volume: 38 start-page: 5067 year: 2014 ident: 10.1016/j.matcom.2022.01.014_b19 article-title: Threshold behaviour of a stochastic SIR model publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2014.03.037 – volume: 188 start-page: 135 year: 2003 ident: 10.1016/j.matcom.2022.01.014_b46 article-title: Dynamical behavior of an epidemic model with a nonlinear incidence rate publication-title: J. Differ. Equ. doi: 10.1016/S0022-0396(02)00089-X – volume: 137 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b64 article-title: Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2020.109865 – volume: 11 start-page: 138A year: 2004 ident: 10.1016/j.matcom.2022.01.014_b1 article-title: Modelling the genital herpes epidemic publication-title: Herpes – volume: 43 start-page: 525 year: 2001 ident: 10.1016/j.matcom.2022.01.014_b18 article-title: An algorithmic introduction to numerical simulation of stochastic differential equations publication-title: SIAM Rev. doi: 10.1137/S0036144500378302 – volume: 230 start-page: 87 year: 2011 ident: 10.1016/j.matcom.2022.01.014_b49 article-title: Effect of media-induced social distancing on disease transmission in a two patch setting publication-title: Math. Biosci. doi: 10.1016/j.mbs.2011.01.005 – volume: 359 start-page: 512 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b65 article-title: Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties publication-title: Appl. Math. Comput. – volume: 28 start-page: 335 year: 1976 ident: 10.1016/j.matcom.2022.01.014_b17 article-title: Qualitative analyses of communicable disease models publication-title: Math. Biosci. doi: 10.1016/0025-5564(76)90132-2 – year: 2020 ident: 10.1016/j.matcom.2022.01.014_b14 article-title: Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth publication-title: Chaos Solitons Fractals – volume: 143 year: 2021 ident: 10.1016/j.matcom.2022.01.014_b63 article-title: Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vacinnation publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2020.110601 – volume: 390 year: 2021 ident: 10.1016/j.matcom.2022.01.014_b8 article-title: Effects of global warming on pattern dynamics of vegetation: Wuwei in China as a case publication-title: Appl. Math. Comput. – volume: 30 start-page: 93 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b10 article-title: Asymptotic properties of a stochastic SIR epidemic model with Beddington–DeAngelis incidence rate publication-title: J. Dyn. Diff. Equ. doi: 10.1007/s10884-016-9532-8 – volume: 532 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b16 article-title: A stochastic SIS model driven by random diffusion of air pollutants publication-title: Physica A doi: 10.1016/j.physa.2019.121759 – volume: 259 start-page: 7463 year: 2015 ident: 10.1016/j.matcom.2022.01.014_b3 article-title: A stochastic SIRS epidemic model with infectious force under intervention strategies publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2015.08.024 – volume: 133 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b5 article-title: Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2020.109643 – volume: 22 start-page: 267 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b55 article-title: Periodic solutions of a stochastic food-limited muatualism model publication-title: Methodol. Comput. Appl. Probab. doi: 10.1007/s11009-019-09697-6 – volume: 266 start-page: 3973 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b29 article-title: Threshold dynamics and ergodicity of an SIRS epidemic model with semi-Markov switching publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2018.09.026 – volume: 140 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b52 article-title: A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China publication-title: Chaos Solitons Fractals – volume: 405 year: 2021 ident: 10.1016/j.matcom.2022.01.014_b15 article-title: Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay publication-title: Appl. Math. Comput. – volume: 364 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b32 article-title: Analysis of a stochastic hybrid population model with Allee effect publication-title: Appl. Math. Comput. – volume: 339 start-page: 701 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b37 article-title: Global analysis and numerical simulations of a novel stochastic eco-epidemiological model with time delay publication-title: Appl. Math. Comput. – volume: 2014 year: 2014 ident: 10.1016/j.matcom.2022.01.014_b61 article-title: An SIRS epidemic model incorporating media coverage with time delay publication-title: Comput. Math. Meth. Med. doi: 10.1155/2014/680743 – year: 2000 ident: 10.1016/j.matcom.2022.01.014_b39 – start-page: 116 year: 2009 ident: 10.1016/j.matcom.2022.01.014_b42 article-title: An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage – volume: 509 start-page: 921 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b50 article-title: A stochastic differential equation SIS epidemic model incorporating ornstein–uhlenbeck process publication-title: Physica A doi: 10.1016/j.physa.2018.06.099 – volume: 65 start-page: 717 issue: 6 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b21 article-title: Social inequalities and collateral damages of the COVID-19 pandemic: when basic needs challenge mental health care publication-title: Int. J. Publ. Health doi: 10.1007/s00038-020-01426-y – volume: 73 start-page: 1280 issue: 3 year: 2013 ident: 10.1016/j.matcom.2022.01.014_b48 article-title: Global stability of a nonlinear viral infection model with infinitely distributed intracellular delays and CTL immune responses publication-title: SIAM J. Appl. Math. doi: 10.1137/120896463 – volume: 514 start-page: 671 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b54 article-title: Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate publication-title: Physica A doi: 10.1016/j.physa.2018.09.124 – volume: 23 start-page: 3483 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b6 article-title: A stochastic SIRI epidemic model with relapse and media coverage publication-title: Discrete Contin. Dyn. Syst. Ser. B. doi: 10.3934/dcdsb.2018250 – year: 1983 ident: 10.1016/j.matcom.2022.01.014_b13 article-title: Handbook of stochastic methods for physics – year: 2015 ident: 10.1016/j.matcom.2022.01.014_b34 – volume: 8 start-page: 153 issue: 3 year: 2007 ident: 10.1016/j.matcom.2022.01.014_b33 article-title: Media/psychological impact on multiple outbreaks of emerging infectious diseases publication-title: Comput. Math. Methods Med. doi: 10.1080/17486700701425870 – year: 2011 ident: 10.1016/j.matcom.2022.01.014_b24 – volume: 421 start-page: 1651 issue: 2 year: 2015 ident: 10.1016/j.matcom.2022.01.014_b47 article-title: Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2014.08.019 – volume: 330 start-page: 93 year: 2018 ident: 10.1016/j.matcom.2022.01.014_b66 article-title: Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching publication-title: Appl. Math. Comput. – volume: 236 start-page: 1 year: 2014 ident: 10.1016/j.matcom.2022.01.014_b30 article-title: Long-time behavior of a stochastic SIR model publication-title: Appl. Math. Comput. – ident: 10.1016/j.matcom.2022.01.014_b44 doi: 10.1016/j.matcom.2021.05.009 – volume: 404 year: 2021 ident: 10.1016/j.matcom.2022.01.014_b9 article-title: The effectiveness of contact tracing in mitigating COVID-19 outbreak: A model-based analysis in the context of India publication-title: Appl. Math. Comput. – volume: 6 start-page: 495 year: 2005 ident: 10.1016/j.matcom.2022.01.014_b27 article-title: Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate publication-title: Nonlinear Anal. RWA doi: 10.1016/j.nonrwa.2004.10.001 – volume: 269 start-page: 117 issue: 8 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b7 article-title: Global threshold dynamics of an infection age-structured SIR epidemic model with diffusion under the Dirichlet boundary condition publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2020.04.046 – volume: 160 start-page: 81 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b11 article-title: Conditions for permanence and ergodicity of certain SIR epidemic models publication-title: Acta Appl. Math. doi: 10.1007/s10440-018-0196-8 – volume: 305 start-page: 221 year: 2017 ident: 10.1016/j.matcom.2022.01.014_b4 article-title: A stochastic SIRS epidemic model with nonlinear incidence rate publication-title: Appl. Math. Comput. – volume: 53 start-page: 187 year: 2016 ident: 10.1016/j.matcom.2022.01.014_b12 article-title: Conditions for permanence and ergodicity of certain stochastic predator–prey models publication-title: J. Appl. Pro. doi: 10.1017/jpr.2015.18 – volume: 14 start-page: 2353 year: 2009 ident: 10.1016/j.matcom.2022.01.014_b28 article-title: The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2008.06.024 – volume: 394 year: 2021 ident: 10.1016/j.matcom.2022.01.014_b59 article-title: A stochastic chemostat model with mean-reverting Ornstein–Uhlenbeck process and Monod-Haldane response function publication-title: Appl. Math. Comput. – volume: 433 start-page: 121 year: 2016 ident: 10.1016/j.matcom.2022.01.014_b57 article-title: Asymptotic behavior of a three species eco-epidemiological model perturbed by white noise publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2015.07.025 – year: 2003 ident: 10.1016/j.matcom.2022.01.014_b26 – volume: 3 start-page: 217 year: 1980 ident: 10.1016/j.matcom.2022.01.014_b31 article-title: A strong law of large numbers for local martingales publication-title: Stochastics doi: 10.1080/17442508008833146 – volume: 115 start-page: 700 year: 1927 ident: 10.1016/j.matcom.2022.01.014_b23 article-title: A contribution to the mathematical theory of epidemics publication-title: Proc R Soc Lond A. doi: 10.1098/rspa.1927.0118 – volume: 97 start-page: 95 issue: 1 year: 2002 ident: 10.1016/j.matcom.2022.01.014_b36 article-title: Environmental brownian noise suppresses explosions in population dynamics publication-title: Stochastic Process. Appl. doi: 10.1016/S0304-4149(01)00126-0 – volume: 25 start-page: 518 year: 1993 ident: 10.1016/j.matcom.2022.01.014_b38 article-title: Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes publication-title: Adv. Appl. Pro. doi: 10.2307/1427522 – year: 2019 ident: 10.1016/j.matcom.2022.01.014_b51 article-title: Stationary distribution of stochastic NP ecological model under regime switching publication-title: Physica A – volume: 2009 year: 2009 ident: 10.1016/j.matcom.2022.01.014_b53 article-title: Global dynamics of an epidemic model with a ratio-dependent nonlinear incidence rate publication-title: Discrete Dyn. Nat. Soc. doi: 10.1155/2009/609306 – volume: 85 start-page: 378 year: 2020 ident: 10.1016/j.matcom.2022.01.014_b43 article-title: The impact of virus carrier screening and actively seeking treatment on dynamical behavior of a stochastic HIV/AIDS infection model publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2020.03.027 – volume: 77 start-page: 258 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b58 article-title: Early warning and basin stability in a stochastic vegetation-water dynamical system publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2019.05.001 – volume: 120 start-page: 188 year: 2019 ident: 10.1016/j.matcom.2022.01.014_b22 article-title: Stability and bifurcation analysis of an epidemic model with the effect of media publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2019.01.025 – volume: 34 start-page: 90 year: 2014 ident: 10.1016/j.matcom.2022.01.014_b60 article-title: The threshold of a stochastic SIRS epidemic model with saturated incidence publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2013.11.002 – volume: 77 start-page: 1285 issue: 7 year: 2015 ident: 10.1016/j.matcom.2022.01.014_b62 article-title: Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment publication-title: Bull. Math. Biol. doi: 10.1007/s11538-015-0086-4 |
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| Title | Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process |
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