Noise-induced transitions in a non-smooth SIS epidemic model with media alert

Anji Yang; Baojun Song; Sanling Yuan; Anji Yang; Baojun Song; Sanling Yuan

doi:10.3934/mbe.2021040

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 745-763. doi: 10.3934/mbe.2021040

Previous Article Next Article

Research article Special Issues

Noise-induced transitions in a non-smooth SIS epidemic model with media alert

1.
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
2.
Department of Applied Mathematics and Statistics, Montclair State University, Montclair, NJ 07043, USA

Received: 03 October 2020 Accepted: 09 December 2020 Published: 18 December 2020

We investigate a non-smooth stochastic epidemic model with consideration of the alerts from media and social network. Environmental uncertainty and political bias are the stochastic drivers in our mathematical model. We aim at the interfere measures assuming that a disease has already invaded into a population. Fundamental findings include that the media alert and social network alert are able to mitigate an infection. It is also shown that interfere measures and environmental noise can drive the stochastic trajectories frequently to switch between lower and higher level of infections. By constructing the confidence ellipse for each endemic equilibrium, we can estimate the tipping value of the noise intensity that causes the state switching.
- SIS model,
- media alert,
- noise-induced state switching,
- stochastic sensitivity,
- confidence domains
Citation: Anji Yang, Baojun Song, Sanling Yuan. Noise-induced transitions in a non-smooth SIS epidemic model with media alert[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 745-763. doi: 10.3934/mbe.2021040

Related Papers:

Abstract

We investigate a non-smooth stochastic epidemic model with consideration of the alerts from media and social network. Environmental uncertainty and political bias are the stochastic drivers in our mathematical model. We aim at the interfere measures assuming that a disease has already invaded into a population. Fundamental findings include that the media alert and social network alert are able to mitigate an infection. It is also shown that interfere measures and environmental noise can drive the stochastic trajectories frequently to switch between lower and higher level of infections. By constructing the confidence ellipse for each endemic equilibrium, we can estimate the tipping value of the noise intensity that causes the state switching.

References

[1]	M. S. Rahman, M. L. Rahman, Media and education play a tremendous role in mounting aids awareness among married couples in bangladesh, AIDS Res. Ther., 4 (2007), 1–7. doi: 10.1186/1742-6405-4-1
[2]	J. Cui, X. Tao, H. Zhu, An sis infection model incorporating media coverage, Rocky Mt. J. Math., 38 (2008), 1323–1334.
[3]	J. Cui, Y. Sun, H. Zhu, The impact of media on the control of infectious diseases, J. Dyn. Differ. Equ., 20 (2008), 31–53. doi: 10.1007/s10884-007-9075-0
[4]	L. Wang, D. Zhou, Z. Liu, D. Xu, X. Zhang, Media alert in an sis epidemic model with logistic growth, J. Biol. Dynam., 11 (2017), 120–137. doi: 10.1080/17513758.2016.1181212
[5]	R. Liu, J. Wu, H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153–164. doi: 10.1080/17486700701425870
[6]	J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith, C. T. Bauch, The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11 (2011), 1–16. doi: 10.1186/1471-2458-11-1
[7]	C. Sun, W. Yang, J. Arino, K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci., 230 (2011), 87–95. doi: 10.1016/j.mbs.2011.01.005
[8]	A. K. Misra, A. Sharma, J. B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model., 53 (2011), 1221–1228. doi: 10.1016/j.mcm.2010.12.005
[9]	A. Wang, Y. Xiao, A Filippov system describing media effects on the spread of infectious diseases, Nonlinear Anal. Hybr. Syst., 11 (2014), 84–97. doi: 10.1016/j.nahs.2013.06.005
[10]	Y. Xiao, X. Xu, S. Tang, Sliding mode control of outbreaks of emerging infectious diseases, Bull. Math. Biol., 74 (2012), 2403–2422. doi: 10.1007/s11538-012-9758-5
[11]	R. Gallotti, F. Valle, N. Castaldo, Assessing the risks of "infodemics" in response to COVID-19 epidemics, Nat. Hum. Behav., (2020).
[12]	Y. Zhao, L. Zhang, S. Yuan, The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model, Phys. A, 512 (2018), 248–260. doi: 10.1016/j.physa.2018.08.113
[13]	A. C. Lowen, J. Steel, Roles of humidity and temperature in shaping in uenza seasonality, J. Virol., 88 (2014), 7692–7695. doi: 10.1128/JVI.03544-13
[14]	I. Bashkirtseva, L. Ryashko, Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with allee effect, Chaos, 21 (2011), 047514.
[15]	I. Bashkirtseva, L. Ryashko, Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system, Front. Life Sci., 5 (2011), 141–148. doi: 10.1080/21553769.2012.702666
[16]	I. Bashkirtseva, L. Ryashko, Stochastic bifurcations and noise-induced chaos in a dynamic prey–predator plankton system, Int. J. Bifurcat. Chaos, 24 (2014), 1450109.
[17]	X. Yu, S. Yuan, Asymptotic properties of a stochastic chemostat model with two distributed delays and nonlinear perturbation, Discrete Cont. Dyn. B, 25 (2020), 2373–2390.
[18]	S. Zhao, S. Yuan, H. Wang, Threshold behavior in a stochastic algal growth model with stoichiometric constraints and seasonal variation, J. Differ. Equations, 268 (2020), 5113–5139. doi: 10.1016/j.jde.2019.11.004
[19]	X. Yu, S. Yuan, T. Zhang, Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling, Nonlinear Anal.-Hybri., 34 (2019), 209–225. doi: 10.1016/j.nahs.2019.06.005
[20]	C. Xu, S. Yuan, T. Zhang, Average break-even concentration in a simple chemostat model with telegraph noise, Nonlinear Anal.-Hybri. 29 (2018), 373–382.
[21]	C. Xu, S. Yuan, Competition in the chemostat: A stochastic multi-species model and its asymptotic behavior, Math. Biosci., 280 (2016), 1–9. doi: 10.1016/j.mbs.2016.07.008
[22]	C. Xu, S. Yuan, T. Zhang, Competitive exclusion in a general multi-species chemostat model with stochastic perturbations, Bull. Math. Biol., DOI: 10.1007/s11538-020-00843-7.
[23]	Y. Zhao, S. Yuan, J. Ma, Survival and stationary distribution analysis of a stochastic competitive model of three species in a polluted environment, Bull. Math. Biol., 77 (2015), 1285–1326. doi: 10.1007/s11538-015-0086-4
[24]	D. Wu, H. Wang, S. Yuan, Stochastic sensitivity analysis of noise-induced transitions in a predator-prey model with environmental toxins, Math. Biosci. Eng., 16 (2019), 2141–2153. doi: 10.3934/mbe.2019104
[25]	C. Xu, S. Yuan, T. Zhang, Stochastic sensitivity analysis for a competitive turbidostat model with inhibitory nutrients, Int. J. Bifurcat. Chaos, 26 (2016), 707–723.
[26]	L. Gammaitoni, P. Jung, F. Marchesoni, Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223.
[27]	W. Horsthemke, Noise induced transitions, Non-Equi. Dyna. Chem. Sys., (1984), 150–160.
[28]	K. Matsumoto, I. Tsuda, Noise-induced order, J. Stat. Phys., 31 (1983), 87–106.
[29]	J. Gao, S. Hwang, J. Liu, When can noise induce chaos? Phys. Rev. Lett., 82 (1999), 1132–1135.
[30]	M. A. Zaks, X. Sailer, L. S. Geier, A. Neiman, Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems, Chaos, 15 (2005), 026117.
[31]	S. Kim, S. H. Park, C. S. Ryu, Colored-noise-induced multistability in nonequilibrium phase transitions, Phys. Rev. E, 58 (1998), 7994-7997.
[32]	S. L. Souza, A. M. Batista, I. L. Caldas, R. L. Viana, T. Kapitaniak, Noise-induced basin hopping in a vibro-impact system, Chaos Soliton. Fract., 32 (2007), 758–767. doi: 10.1016/j.chaos.2005.11.056
[33]	M. I. Dykman, R. Mannella, P. V. E. McClintock, N. Stocks, Fluctuation-induced transitions between periodic attractors: Observation of supernarrow spectral peaks near a kinetic phase transition, Phys. Rev. Lett., 65 (1990), 48–51. doi: 10.1103/PhysRevLett.65.48
[34]	S. Yuan, D. Wu, G. Lan, H. Wang, Noise-induced transitions in a nonsmooth producer-grazer model with stoichiometric constraints, Bull. Math. Biol., 82 (2020), 55.
[35]	S. Kraut, U. Feudel, Multistability, noise, and attractor hopping: The crucial role of chaotic saddles, Phys. Rev. E, 66 (2002), 015207.
[36]	I. Bashkirtseva, L. Ryashko, I.Tsvetkov, Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems, Dyna. Cont. Dis. Imp. Syst., 17 (2010), 501–515.
[37]	I. Bashkirtseva, T. Ryazanova, L. Ryashko, Confidence domains in the analysis of noiseinduced transition to chaos for Goodwin model of business cycles, Int. J. Bifurc. Chaos, 24 (2014), 1440020.

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)