{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:56:02Z","timestamp":1760784962192,"version":"3.40.3"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,2,15]],"date-time":"2021-02-15T00:00:00Z","timestamp":1613347200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,2,15]],"date-time":"2021-02-15T00:00:00Z","timestamp":1613347200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871201","11961023"],"award-info":[{"award-number":["11871201","11961023"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["2019CFB241"],"award-info":[{"award-number":["2019CFB241"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s12190-021-01504-1","type":"journal-article","created":{"date-parts":[[2021,2,18]],"date-time":"2021-02-18T19:09:25Z","timestamp":1613675365000},"page":"785-805","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A stochastic epidemic model with infectivity in incubation period and homestead\u2013isolation on the susceptible"],"prefix":"10.1007","volume":"67","author":[{"given":"Dongchen","family":"Shangguan","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3383-5621","authenticated-orcid":false,"given":"Zhijun","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Lianwen","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Ronghua","family":"Tan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,2,15]]},"reference":[{"key":"1504_CR1","first-page":"700","volume":"115","author":"WO Kermack","year":"1927","unstructured":"Kermack, W.O., Mckendrick, A.G.: Combined effects of prevention and quarantine on a breakout in SIR model. Proc. R. Soc. Edin. A 115, 700\u2013721 (1927)","journal-title":"Proc. R. Soc. Edin. A"},{"key":"1504_CR2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198545996.001.0001","volume-title":"Infectious Diseases of Humans: Dynamics and Control","author":"RM Anderson","year":"1991","unstructured":"Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, New York (1991)"},{"key":"1504_CR3","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1007\/s002850050051","volume":"35","author":"K Cooke","year":"1996","unstructured":"Cooke, K., Van Den Driessche, P.: Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 35, 240\u2013260 (1996)","journal-title":"J. Math. Biol."},{"key":"1504_CR4","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0022-0396(02)00089-X","volume":"188","author":"SG Ruan","year":"2003","unstructured":"Ruan, S.G., Wang, W.D.: Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differ. Equ. 188, 135\u2013163 (2003)","journal-title":"J. Differ. Equ."},{"key":"1504_CR5","doi-asserted-by":"crossref","first-page":"267","DOI":"10.3934\/mbe.2006.3.267","volume":"3","author":"WD Wang","year":"2006","unstructured":"Wang, W.D.: Epidemic models with nonlinear infection forces. Math. Biosci. Eng. 3, 267\u2013279 (2006)","journal-title":"Math. Biosci. Eng."},{"key":"1504_CR6","doi-asserted-by":"crossref","first-page":"7463","DOI":"10.1016\/j.jde.2015.08.024","volume":"259","author":"YL Cai","year":"2015","unstructured":"Cai, Y.L., Kang, Y., Banerjee, M., Wang, W.M.: A stochastic SIRS epidemic model with infectious force under intervention strategies. J. Differ. Equ. 259, 7463\u20137502 (2015)","journal-title":"J. Differ. Equ."},{"key":"1504_CR7","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1016\/j.jmaa.2016.07.027","volume":"444","author":"JL Wang","year":"2016","unstructured":"Wang, J.L., Yang, J., Kuniya, T.: Dynamics of a PDE viral infection model incorporating cell-to-cell transmission. J. Math. Anal. Appl. 444, 1542\u20131564 (2016)","journal-title":"J. Math. Anal. Appl."},{"key":"1504_CR8","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.nonrwa.2016.04.009","volume":"32","author":"LW Wang","year":"2016","unstructured":"Wang, L.W., Liu, Z.J., Zhang, X.A.: Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination. Nonlinear Anal. Real World Appl. 32, 136\u2013158 (2016)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"1504_CR9","first-page":"3749","volume":"22","author":"SP Li","year":"2017","unstructured":"Li, S.P., Jin, Z.: Impacts of cluster on network topology structure and epidemic spreading. Discrete Contin. Dyn. Syst. Ser. B 22, 3749\u20133770 (2017)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"1504_CR10","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.nonrwa.2017.02.009","volume":"37","author":"ZJ Liu","year":"2017","unstructured":"Liu, Z.J., Hu, J., Wang, L.W.: Modelling and analysis of global resurgence of mumps: a multi-group epidemic model with asymptomatic infection, general vaccinated and exposed distributions. Nonlinear Anal. Real World Appl. 37, 137\u2013161 (2017)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"1504_CR11","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.3934\/mbe.2018065","volume":"15","author":"JQ Li","year":"2018","unstructured":"Li, J.Q., Wang, X.Q., Lin, X.L.: Impact of behavioral change on the epidemic characteristics of an epidemic model without vital dynamics. Math. Biosci. Eng. 15, 1425\u20131434 (2018)","journal-title":"Math. Biosci. Eng."},{"key":"1504_CR12","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.chaos.2017.12.027","volume":"111","author":"CY Xu","year":"2018","unstructured":"Xu, C.Y., Li, X.Y.: The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination. Chaos Solitons Fractals 111, 227\u2013234 (2018)","journal-title":"Chaos Solitons Fractals"},{"key":"1504_CR13","doi-asserted-by":"crossref","first-page":"2218","DOI":"10.1137\/18M1231493","volume":"79","author":"ZZ Liu","year":"2019","unstructured":"Liu, Z.Z., Shen, Z.W., Wang, H., Jin, Z.: Analysis of a local diffusive SIR model with seasonality and nonlocal incidence of infection. SIAM J. Appl. Math. 79, 2218\u20132241 (2019)","journal-title":"SIAM J. Appl. Math."},{"key":"1504_CR14","doi-asserted-by":"crossref","first-page":"11385","DOI":"10.1016\/j.jfranklin.2019.03.043","volume":"356","author":"XJ Mu","year":"2019","unstructured":"Mu, X.J., Zhang, Q.M., Rong, L.B.: Optimal vaccination strategy for an SIRS model with imprecise parameters and L\u00e9vy noise. J. Frankl. Inst. 356, 11385\u201311413 (2019)","journal-title":"J. Frankl. Inst."},{"key":"1504_CR15","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.apm.2020.01.035","volume":"82","author":"LL Liu","year":"2020","unstructured":"Liu, L.L., Xu, R., Jin, Z.: Global dynamics of a spatial heterogeneous viral infection model with intracellular delay and nonlocal diffusion. Appl. Math. Model. 82, 150\u2013167 (2020)","journal-title":"Appl. Math. Model."},{"key":"1504_CR16","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1137\/10081856X","volume":"71","author":"A Gray","year":"2011","unstructured":"Gray, A., Greenhalgh, D., Hu, L., Mao, X., Pan, J.: A stochastic differnetial equation SIS epidemic model. SIAM J. Appl. Math. 71, 876\u2013902 (2011)","journal-title":"SIAM J. Appl. Math."},{"key":"1504_CR17","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.physa.2017.02.028","volume":"476","author":"Q Liu","year":"2017","unstructured":"Liu, Q., Jiang, D.Q., Shi, N.Z., Hayat, T., Ahmad, B.: Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence. Phys. A 476, 58\u201369 (2017)","journal-title":"Phys. A"},{"key":"1504_CR18","first-page":"6367","volume":"24","author":"T Feng","year":"2019","unstructured":"Feng, T., Qiu, Z.P., Meng, X.Z.: Dynamics of a stochastic hepatitis C virus system with host immunity. Discrete Contin. Dyn. Syst. Ser. B 24, 6367\u20136385 (2019)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"1504_CR19","doi-asserted-by":"crossref","unstructured":"Wei, F.Y., Chen, L.H.: Extinction and stationary distribution of an epidemic model with partial vaccination and nonlinear incidence rate. Phys. A 545, 122852, 10pp (2020)","DOI":"10.1016\/j.physa.2019.122852"},{"key":"1504_CR20","doi-asserted-by":"crossref","unstructured":"Cao, Z.W., Shi, Y., Wen, X.D., Liu, L.Y., Hu, J.W.: Analysis of a hybrid switching SVIR epidemic model with vaccination and L\u00e9vy noise. Phys. A 537, 122749, 17pp (2020)","DOI":"10.1016\/j.physa.2019.122749"},{"key":"1504_CR21","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.apm.2019.11.038","volume":"80","author":"XN Liu","year":"2020","unstructured":"Liu, X.N., Wang, Y., Zhao, X.Q.: Dynamics of a climate-based periodic Chikungunya model with incubation period. Appl. Math. Model. 80, 151\u2013168 (2020)","journal-title":"Appl. Math. Model."},{"key":"1504_CR22","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1016\/j.matcom.2008.02.007","volume":"79","author":"Z Zhao","year":"2008","unstructured":"Zhao, Z., Chen, L.S., Song, X.Y.: Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate. Math. Comput. Simul. 79, 500\u2013510 (2008)","journal-title":"Math. Comput. Simul."},{"key":"1504_CR23","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1016\/j.nonrwa.2012.10.007","volume":"14","author":"QS Yang","year":"2013","unstructured":"Yang, Q.S., Mao, X.R.: Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal. Real World Appl. 14, 1434\u20131456 (2013)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"1504_CR24","doi-asserted-by":"crossref","first-page":"3444","DOI":"10.1016\/j.cnsns.2014.02.025","volume":"19","author":"M Liu","year":"2014","unstructured":"Liu, M., Bai, C.Z., Wang, K.: Asymptotic stability of a two-group stochastic SEIR model with infinite delays. Commun. Nonlinear Sci. Numer. Simul. 19, 3444\u20133453 (2014)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"1504_CR25","doi-asserted-by":"crossref","first-page":"870","DOI":"10.1016\/j.physa.2016.06.095","volume":"462","author":"Q Liu","year":"2016","unstructured":"Liu, Q., Jiang, D.Q., Shi, N.Z., Hayat, T., Ahmad, A.: Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence. Phys. A 462, 870\u2013882 (2016)","journal-title":"Phys. A"},{"key":"1504_CR26","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.apm.2017.05.040","volume":"50","author":"BC Tian","year":"2017","unstructured":"Tian, B.C., Yuan, R.: Traveling waves for a diffusive SEIR epidemic model with non-local reaction. Appl. Math. Model. 50, 432\u2013449 (2017)","journal-title":"Appl. Math. Model."},{"key":"1504_CR27","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.aml.2019.05.045","volume":"98","author":"SY Han","year":"2019","unstructured":"Han, S.Y., Lei, C.X.: Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence. Appl. Math. Lett. 98, 114\u2013120 (2019)","journal-title":"Appl. Math. Lett."},{"key":"1504_CR28","first-page":"956","volume":"386","author":"A Abta","year":"2012","unstructured":"Abta, A., Kaddar, A., Alaoui, H.T.: Global stability for delay SIR and SEIR epidemic models with saturated incidence rates. Electron. J. Differ. Equ. 386, 956\u2013965 (2012)","journal-title":"Electron. J. Differ. Equ."},{"key":"1504_CR29","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.mbs.2017.11.010","volume":"296","author":"GC Lv","year":"2018","unstructured":"Lv, G.C., Lu, Z.Y.: Global asymptotic stability for the SEIRS models with varying total population size. Math. Biosci. 296, 17\u201325 (2018)","journal-title":"Math. Biosci."},{"key":"1504_CR30","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/j.physa.2018.08.006","volume":"512","author":"DL Zhao","year":"2018","unstructured":"Zhao, D.L., Sun, J.B., Tan, Y.J., Wu, J.H., Dou, Y.J.: An extended SEIR model considering homepage effect for the information propagation of online social networks. Phys. A 512, 1019\u20131031 (2018)","journal-title":"Phys. A"},{"key":"1504_CR31","unstructured":"National Health Commission of the People\u2019s Republic of China. (2020). http:\/\/www.nhc.gov.cn\/. Accessed 26 Jan 2020"},{"key":"1504_CR32","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.jinf.2020.04.024","volume":"81","author":"VCC Cheng","year":"2020","unstructured":"Cheng, V.C.C., Wong, S.C., Chuang, V.W.M., So, S.Y.C., Chen, J.H.K., Sridhar, S., To, K.K.W., Chan, J.F.W., Hung, I.F.N., Ho, P.L., Yuen, K.Y.: The role of community-wide wearing of face mask for control of coronavirus disease 2019 (COVID-19) epidemic due to SARS-CoV-2. J. Infect. 81, 107\u2013114 (2020)","journal-title":"J. Infect."},{"key":"1504_CR33","doi-asserted-by":"crossref","first-page":"1973","DOI":"10.1016\/S0140-6736(20)31142-9","volume":"395","author":"DK Chu","year":"2020","unstructured":"Chu, D.K., Akl, E.A., Duda, S., et al.: Physical distancing, face masks, and eye protection to prevent person-to-person transmission of sars-cov-2 and covid-19: a systematic review and meta-analysis. Lancet 395, 1973\u20131987 (2020)","journal-title":"Lancet"},{"key":"1504_CR34","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/S2213-2600(20)30134-X","volume":"8","author":"S Feng","year":"2020","unstructured":"Feng, S., Shen, C., Xia, N., Song, W., Fan, M., CowlingCowling, B.J.: Rational use of face masks in the COVID-19 pandemic. Lancet Respir. Med. 8, 434\u2013436 (2020)","journal-title":"Lancet Respir. Med."},{"key":"1504_CR35","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1126\/science.abb4557","volume":"368","author":"BF Maier","year":"2020","unstructured":"Maier, B.F., Brockmann, D.: Effective containment explains subexponential growth in recent confirmed COVID-19 cases in china. Science 368, 742\u2013746 (2020)","journal-title":"Science"},{"key":"1504_CR36","first-page":"1","volume":"27","author":"A Wilder-Smith","year":"2020","unstructured":"Wilder-Smith, A., Freedman, D.O.: Isolation, quarantine, social distancing and community containment: pivotal role for old-style public health measures in the novel coronavirus (2019-nCoV) outbreak. J. Travel Med. 27, 1\u20134 (2020)","journal-title":"J. Travel Med."},{"key":"1504_CR37","doi-asserted-by":"crossref","first-page":"1239","DOI":"10.1001\/jama.2020.2648","volume":"323","author":"Z Wu","year":"2020","unstructured":"Wu, Z., McGoogan, J.M.: Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: summary of a report of 72314 cases from the Chinese Center for Disease Control and Prevention. JAMA 323, 1239\u20131242 (2020)","journal-title":"JAMA"},{"key":"1504_CR38","doi-asserted-by":"crossref","unstructured":"Jiao, J.J., Liu, Z.Z., Cai, S.H.: Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible. Appl. Math. Lett. 107, 106442, 7pp (2020)","DOI":"10.1016\/j.aml.2020.106442"},{"key":"1504_CR39","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1002\/bimj.4710210507","volume":"21","author":"L Arnold","year":"1979","unstructured":"Arnold, L., Horsthemke, W., Stucki, J.W.: The influence of external real and white noise on the Lotka\u2013Volterra model. Biom. J. 21, 451\u2013471 (1979)","journal-title":"Biom. J."},{"key":"1504_CR40","first-page":"118","volume":"244","author":"YL Zhou","year":"2014","unstructured":"Zhou, Y.L., Zhang, W.G., Yuan, S.L.: Survival and stationary distribution of a SIR epidemic model with stochastic perturbations. Appl. Math. Comput. 244, 118\u2013131 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1504_CR41","doi-asserted-by":"crossref","unstructured":"Zhang, X.B., Wang, X.D., Huo, H. F.: Extinction and stationary distribution of a stochastic SIRS epidemic model with standard incidence rate and partial immunity. Phys. A 531, 121548, 14pp (2019)","DOI":"10.1016\/j.physa.2019.121548"},{"key":"1504_CR42","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1073\/pnas.62.4.1056","volume":"62","author":"RC Lewontin","year":"1969","unstructured":"Lewontin, R.C., Cohen, D.: On population growth in a randomly varying environment. Proc. Nat. Acad. Sci. 62, 1056\u20131060 (1969)","journal-title":"Proc. Nat. Acad. Sci."},{"key":"1504_CR43","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1080\/00036811.2016.1257123","volume":"97","author":"XH Zhang","year":"2018","unstructured":"Zhang, X.H., Jiang, D.Q., Hayat, T., Alsaedi, A.: Periodic solution and stationary distribution of stochastic S-DI-A epidemic models. Appl. Anal. 97, 179\u2013193 (2018)","journal-title":"Appl. Anal."},{"key":"1504_CR44","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1007\/s12346-018-0289-9","volume":"18","author":"HK Qi","year":"2019","unstructured":"Qi, H.K., Leng, X.N., Meng, X.Z., Zhang, T.H.: Periodic solution and ergodic stationary distribution of SEIS dynamical systems with active and latent patients. Qual. Theory Dyn. Syst. 18, 347\u2013369 (2019)","journal-title":"Qual. Theory Dyn. Syst."},{"key":"1504_CR45","first-page":"133","volume":"239","author":"XH Zhang","year":"2014","unstructured":"Zhang, X.H., Wang, K.: Stochastic SEIR model with jumps. Appl. Math. Comput. 239, 133\u2013143 (2014)","journal-title":"Appl. Math. Comput."},{"key":"1504_CR46","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.110361","author":"B Boukanjime","year":"2020","unstructured":"Boukanjime, B., Caraballo, T., El Fatini, M., El Khalifi, M.: Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching. Chaos Solitons Fractals (2020). https:\/\/doi.org\/10.1016\/j.chaos.2020.110361","journal-title":"Chaos Solitons Fractals"},{"key":"1504_CR47","doi-asserted-by":"crossref","unstructured":"Li, F., Zhang, S.Q., Meng, X.Z.: Dynamics analysis and numerical simulations of a delayed stochastic epidemic model subject to a general response function. Comput. Appl. Math. 38, 95, 30pp (2019)","DOI":"10.1007\/s40314-019-0857-x"},{"key":"1504_CR48","first-page":"1","volume":"2020","author":"R Xu","year":"2020","unstructured":"Xu, R., Guo, R.: Pontryagin\u2019s maximum principle for optimal control of stochastic SEIR models. Complexity 2020, 1\u20135 (2020)","journal-title":"Complexity"},{"key":"1504_CR49","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0025-5564(99)00047-4","volume":"163","author":"LJS Allen","year":"2000","unstructured":"Allen, L.J.S., Burgin, A.M.: Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math. Biosci. 163, 1\u201333 (2000)","journal-title":"Math. Biosci."},{"key":"1504_CR50","first-page":"1026","volume":"265","author":"JR Artalejo","year":"2015","unstructured":"Artalejo, J.R., Economou, A., Lopez-Herrero, M.J.: The stochastic SEIR model before extinction: computational approaches. Appl. Math. Comput. 265, 1026\u20131043 (2015)","journal-title":"Appl. Math. Comput."},{"key":"1504_CR51","doi-asserted-by":"publisher","DOI":"10.1101\/2020.04.13.20063768","author":"R Engbert","year":"2021","unstructured":"Engbert, R., Rabe, M.M., Kliegl, R., Reich, S.: Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics. Bull. Math. Biol. (2021). https:\/\/doi.org\/10.1101\/2020.04.13.20063768","journal-title":"Bull. Math. Biol."},{"key":"1504_CR52","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0304-4149(01)00126-0","volume":"97","author":"XR Mao","year":"2002","unstructured":"Mao, X.R., Marion, G., Renshaw, E.: Environmental Brownian noise suppresses explosions in population dynamics. Stoch. Process. Appl. 97, 95\u2013110 (2002)","journal-title":"Stoch. Process. Appl."},{"key":"1504_CR53","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jmaa.2006.01.055","volume":"325","author":"N Dalal","year":"2007","unstructured":"Dalal, N., Greenhalgh, D., Mao, X.R.: A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325, 36\u201353 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1504_CR54","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.aml.2013.11.002","volume":"34","author":"YN Zhao","year":"2014","unstructured":"Zhao, Y.N., Jiang, D.Q.: The threshold of a stochastic SIRS epidemic model with saturated incidence. Appl. Math. Lett. 34, 90\u201393 (2014)","journal-title":"Appl. Math. Lett."},{"key":"1504_CR55","doi-asserted-by":"crossref","first-page":"2175","DOI":"10.1007\/s11071-019-05114-2","volume":"97","author":"S Cai","year":"2019","unstructured":"Cai, S., Cai, Y., Mao, X.: A stochastic differential equation SIS epidemic model with two correlated Brownian motions. Nonlinear Dyn. 97, 2175\u20132187 (2019)","journal-title":"Nonlinear Dyn."},{"key":"1504_CR56","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1007\/s00285-019-01374-z","volume":"79","author":"A Mummert","year":"2019","unstructured":"Mummert, A., Otunuga, O.M.: Parameter identification for a stochastic SEIRS epidemic model: case study influenza. J. Math. Biol. 79, 705\u2013729 (2019)","journal-title":"J. Math. Biol."},{"key":"1504_CR57","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/S0378-4754(97)00106-7","volume":"45","author":"E Beretta","year":"1998","unstructured":"Beretta, E., Kolmanovskii, V., Shaikhet, L.: Stability of epidemic model with time delays influenced by stochastic perturbations. Math. Comput. Simul. 45, 269\u2013277 (1998)","journal-title":"Math. Comput. Simul."},{"key":"1504_CR58","doi-asserted-by":"crossref","unstructured":"Hussain, G., Khan, A., Zahri, M., Zaman, G.: Stochastic permanence of an epidemic model with a saturated incidence rate. Chaos Solitons Fractals 139, 110005, 7pp (2020)","DOI":"10.1016\/j.chaos.2020.110005"},{"key":"1504_CR59","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.mcm.2011.02.004","volume":"54","author":"DQ Jiang","year":"2011","unstructured":"Jiang, D.Q., Yu, J.J., Ji, C.Y., Shi, N.Z.: Asymptotic behavior of global positive solution to a stochastic SIR model. Math. Comput. Modell. 54, 221\u2013232 (2011)","journal-title":"Math. Comput. Modell."},{"key":"1504_CR60","volume-title":"Stochastic Differential Equations and Applications","author":"XR Mao","year":"2007","unstructured":"Mao, X.R.: Stochastic Differential Equations and Applications, vol. 47. Horwood Publishing, Chichester (2007)"},{"key":"1504_CR61","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-9121-7","volume-title":"Stochastic Stability of Differential Equations","author":"RZ Hasminskii","year":"1980","unstructured":"Hasminskii, R.Z.: Stochastic Stability of Differential Equations. Sijthoff Noordhoff, Alphen aan den Rijn, The Netherlands (1980)"},{"key":"1504_CR62","first-page":"310","volume":"316","author":"Q Liu","year":"2018","unstructured":"Liu, Q., Jiang, D.Q., Shi, N.Z.: Threshold behavior in a stochastic SIQR epidemic model with stansard incidence and regime switching. Appl. Math. Comput. 316, 310\u2013325 (2018)","journal-title":"Appl. Math. Comput."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01504-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-021-01504-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-021-01504-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T22:39:37Z","timestamp":1744151977000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-021-01504-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,15]]},"references-count":62,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1504"],"URL":"https:\/\/doi.org\/10.1007\/s12190-021-01504-1","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"type":"print","value":"1598-5865"},{"type":"electronic","value":"1865-2085"}],"subject":[],"published":{"date-parts":[[2021,2,15]]},"assertion":[{"value":"8 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}