Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2021

15.02.2021 | Original Research

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

verfasst von: Dongchen Shangguan, Zhijun Liu, Lianwen Wang, Ronghua Tan

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A stochastic epidemic model with infectivity rate in incubation period and homestead–isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.
Vorheriger Artikel Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator
Nächster Artikel Constacyclic codes of length over mixed alphabets

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Kermack, W.O., Mckendrick, A.G.: Combined effects of prevention and quarantine on a breakout in SIR model. Proc. R. Soc. Edin. A 115, 700–721 (1927)MATH
2.
Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, New York (1991)
3.
Cooke, K., Van Den Driessche, P.: Analysis of an SEIRS epidemic model with two delays. J. Math. Biol. 35, 240–260 (1996)MathSciNetMATH
4.
Ruan, S.G., Wang, W.D.: Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differ. Equ. 188, 135–163 (2003)MathSciNetMATH
5.
Wang, W.D.: Epidemic models with nonlinear infection forces. Math. Biosci. Eng. 3, 267–279 (2006)MathSciNetMATH
6.
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, 7463–7502 (2015)MathSciNetMATH
7.
Wang, J.L., Yang, J., Kuniya, T.: Dynamics of a PDE viral infection model incorporating cell-to-cell transmission. J. Math. Anal. Appl. 444, 1542–1564 (2016)MathSciNetMATH
8.
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, 136–158 (2016)MathSciNetMATH
9.
Li, S.P., Jin, Z.: Impacts of cluster on network topology structure and epidemic spreading. Discrete Contin. Dyn. Syst. Ser. B 22, 3749–3770 (2017)MathSciNetMATH
10.
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, 137–161 (2017)MathSciNetMATH
11.
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, 1425–1434 (2018)MathSciNetMATH
12.
Xu, C.Y., Li, X.Y.: The threshold of a stochastic delayed SIRS epidemic model with temporary immunity and vaccination. Chaos Solitons Fractals 111, 227–234 (2018)MathSciNetMATH
13.
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, 2218–2241 (2019)MathSciNetMATH
14.
Mu, X.J., Zhang, Q.M., Rong, L.B.: Optimal vaccination strategy for an SIRS model with imprecise parameters and Lévy noise. J. Frankl. Inst. 356, 11385–11413 (2019)MATH
15.
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, 150–167 (2020)MathSciNetMATH
16.
Gray, A., Greenhalgh, D., Hu, L., Mao, X., Pan, J.: A stochastic differnetial equation SIS epidemic model. SIAM J. Appl. Math. 71, 876–902 (2011)MathSciNetMATH
17.
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, 58–69 (2017)MathSciNet
18.
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, 6367–6385 (2019)MathSciNetMATH
19.
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)
20.
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 Lévy noise. Phys. A 537, 122749, 17pp (2020)
21.
Liu, X.N., Wang, Y., Zhao, X.Q.: Dynamics of a climate-based periodic Chikungunya model with incubation period. Appl. Math. Model. 80, 151–168 (2020)MathSciNetMATH
22.
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, 500–510 (2008)MathSciNetMATH
23.
Yang, Q.S., Mao, X.R.: Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations. Nonlinear Anal. Real World Appl. 14, 1434–1456 (2013)MathSciNetMATH
24.
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, 3444–3453 (2014)MathSciNetMATH
25.
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, 870–882 (2016)MathSciNetMATH
26.
Tian, B.C., Yuan, R.: Traveling waves for a diffusive SEIR epidemic model with non-local reaction. Appl. Math. Model. 50, 432–449 (2017)MathSciNetMATH
27.
Han, S.Y., Lei, C.X.: Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence. Appl. Math. Lett. 98, 114–120 (2019)MathSciNetMATH
28.
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, 956–965 (2012)MathSciNetMATH
29.
Lv, G.C., Lu, Z.Y.: Global asymptotic stability for the SEIRS models with varying total population size. Math. Biosci. 296, 17–25 (2018)MathSciNetMATH
30.
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, 1019–1031 (2018)MathSciNet
31.
32.
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, 107–114 (2020)
33.
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, 1973–1987 (2020)
34.
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, 434–436 (2020)
35.
Maier, B.F., Brockmann, D.: Effective containment explains subexponential growth in recent confirmed COVID-19 cases in china. Science 368, 742–746 (2020)MathSciNet
36.
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, 1–4 (2020)
37.
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, 1239–1242 (2020)
38.
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)
39.
Arnold, L., Horsthemke, W., Stucki, J.W.: The influence of external real and white noise on the Lotka–Volterra model. Biom. J. 21, 451–471 (1979)MathSciNetMATH
40.
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, 118–131 (2014)MathSciNetMATH
41.
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)
42.
Lewontin, R.C., Cohen, D.: On population growth in a randomly varying environment. Proc. Nat. Acad. Sci. 62, 1056–1060 (1969)MathSciNet
43.
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, 179–193 (2018)MathSciNetMATH
44.
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, 347–369 (2019)MathSciNetMATH
45.
Zhang, X.H., Wang, K.: Stochastic SEIR model with jumps. Appl. Math. Comput. 239, 133–143 (2014)MathSciNetMATH
46.
47.
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)
48.
Xu, R., Guo, R.: Pontryagin’s maximum principle for optimal control of stochastic SEIR models. Complexity 2020, 1–5 (2020)MATH
49.
Allen, L.J.S., Burgin, A.M.: Comparison of deterministic and stochastic SIS and SIR models in discrete time. Math. Biosci. 163, 1–33 (2000)MathSciNetMATH
50.
Artalejo, J.R., Economou, A., Lopez-Herrero, M.J.: The stochastic SEIR model before extinction: computational approaches. Appl. Math. Comput. 265, 1026–1043 (2015)MathSciNetMATH
51.
52.
Mao, X.R., Marion, G., Renshaw, E.: Environmental Brownian noise suppresses explosions in population dynamics. Stoch. Process. Appl. 97, 95–110 (2002)MathSciNetMATH
53.
Dalal, N., Greenhalgh, D., Mao, X.R.: A stochastic model of AIDS and condom use. J. Math. Anal. Appl. 325, 36–53 (2007)MathSciNetMATH
54.
Zhao, Y.N., Jiang, D.Q.: The threshold of a stochastic SIRS epidemic model with saturated incidence. Appl. Math. Lett. 34, 90–93 (2014)MathSciNetMATH
55.
Cai, S., Cai, Y., Mao, X.: A stochastic differential equation SIS epidemic model with two correlated Brownian motions. Nonlinear Dyn. 97, 2175–2187 (2019)MATH
56.
Mummert, A., Otunuga, O.M.: Parameter identification for a stochastic SEIRS epidemic model: case study influenza. J. Math. Biol. 79, 705–729 (2019)MathSciNetMATH
57.
Beretta, E., Kolmanovskii, V., Shaikhet, L.: Stability of epidemic model with time delays influenced by stochastic perturbations. Math. Comput. Simul. 45, 269–277 (1998)MathSciNetMATH
58.
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)
59.
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, 221–232 (2011)MathSciNetMATH
60.
Mao, X.R.: Stochastic Differential Equations and Applications, vol. 47. Horwood Publishing, Chichester (2007)MATH
61.
Hasminskii, R.Z.: Stochastic Stability of Differential Equations. Sijthoff Noordhoff, Alphen aan den Rijn, The Netherlands (1980)
62.
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, 310–325 (2018)MathSciNetMATH
Metadaten
Titel
A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible
verfasst von
Dongchen Shangguan
Zhijun Liu
Lianwen Wang
Ronghua Tan
Publikationsdatum
15.02.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-021-01504-1

Weitere Artikel der Ausgabe 1-2/2021

Journal of Applied Mathematics and Computing 1-2/2021 Zur Ausgabe

Original Research

Some results for initial value problem of nonlinear fractional equation in Sobolev space

Original Research

On the watching number of graphs using discharging procedure

Original Research

Decision-making analysis based on q-rung picture fuzzy graph structures

Correction

Correction to: A new full-Newton step interior-point method for P*(κ)-LCP based on a positive-asymptotic kernel function

Original Research

Constacyclic codes of length over mixed alphabets

Original Research

Extremal phenylene chains with respect to detour indices